1. This question is on the application of the Binomial option

1. This question is on the application of the Binomial option
pricing model.
PKZ stock is currently trading at 100. Over three-months it will
either
go up by 6% or down by 5%. Interest rates are zero.
a. [25 marks] Using a two period binomial model to construct a
delta-
hedged portfolio, price a six month European call option on
PKZ
stock with a strike price of £105.
b. [3 Marks] Using your answer from the first part, together
with the
put-call parity, price a put option on the same stock with same
strike and expiry.
COMP0041 SEE NEXT PAGE
2
2. This question is on the Binomial method in the limit δt → 0.
[40 Marks] The binomial model for pricing options leads to the
for-
mula
V (S,t) = e−rδt [qV (US,t + δt) + (1 − q) V (DS,t + δt)]

where
U = eσ
√
δt, D = e−σ
√
δt, q =
erδt −D
U −D
.
V (S,t) is the option value, t is the time, S is the spot price, σ is
volatil-
ity and r is the risk-free rate.
By carefully expanding U,D,q as Taylor series in δt or
√
δt (as appro-
priate) and then expanding V (US,t + δt) and V (DS,t + δt) as
Taylor
series in both their arguments, deduce that to O (δt) ,
∂V
∂t
+
1
2
σ2S2

∂2V
∂S2
+ rS
∂V
∂S
− rV = 0.
3
3. This question is on probability and Monte Carlo
a. Consider theprobabilitydensity function p (x) fora
randomvariable
X given by
p (x) =
{
µ exp (−µx) x ≥ 0
0 x < 0
where µ (> 0) is a constant.
i. [15 Marks] Show that for this probability density function
E
[
eθX
]

=
(
1 −
θ
µ
)−1
Hint: You may assume µ > θ in obtaining this result.
ii. [20 Marks] By expanding
(
1 −
θ
µ
)−1
as a Taylor series, show
that
E [xn] =
n!
µn
, n = 0, 1, 2, ....
iii. [15 Marks] Hence calculate the skew and kurtosis for X.
COMP0041 CONTINUED ON NEXT PAGE

4
b. [32 Marks] An Exchange Option gives the holder the right to
exchange one asset for another. The discounted payoff for this
contract V is
V = e−rT max (S1 (T) −S2 (T) , 0) .
The option price is then given by θ = E [V ] where
Si (t) = Si (0) e
(r−12σ
2
i )t+σiφi
√
t
for i = 1, 2, and φi ∼ N (0, 1) with correlation coeffi cient ρ.
Youmayassumethatauniformrandomnumbergenerator isavail -
able. Use a Cholesky factorisation method to show(
φ1
φ2
)
=
(
1 0
ρ
√

1 −ρ2
)(
x1
x2
)
,
where
(
x1
x2
)
is a vector of independent N (0, 1) variables and
has the same distribution as
(
φ1
φ2
)
.
Give a Monte Carlo simulation algorithm that makes use of anti -
thetic variates for the estimation of θ.
5
4. This question is on finite differences

a. [30 Marks] Consider a forward difference operator, ∆, such
that
∆V (S) = V (S + h) −V (S) , (4.1)
where h is an infinitessimal. By introducing the operators
D ≡
∂
∂S
; D2 ≡
∂2
∂S2
show that
∆ ≡ ehD −1 (4.2)
where 1 is the identity operator. Hint: start by doing a Taylor
expansion on V (S + h) .
By rearranging (4.2) show that
D =
1
h
(
∆ −
∆2
2

+
∆3
3
−
∆4
4
+ O
(
∆5
))
.
Hence obtain the second order approximation for
∂V
∂S
.
b. [20 Marks] The Speed of an option V (S,t) is the sensitivity
of its
gamma Γ, to changes in the underlying stock price S and written
Speed =
∂Γ
∂S
=
∂3V
∂S3

Given that
Γ ∼
V mn−1 − 2V mn + V mn+1
δS2
where theoption V (S,t) = V (nδS,mδt) canbeexpressed infinite
difference form as V mn , derive the speed in the form
1
δS3
[
a1V
m
n+2 + a2V
m
n+1 + a3V
m
n + a4V
m
n−1
]
,
where theconstants ai (i = 1, 2, 3, 4) shouldbegiven. Hint: Con-
sider 3 Taylor series expansions
COMP0041 END OF PAPER

6
MCGILL UNIVERSITY
Department of Economics
ECON 219-001
CURRENT ECONOMIC PROBLEMS: TOPICS
Professor Georgi Boichev
Winter 2021
Problem Set 1
Instructions: Please do NOT hand in. These questions are
intended for practice only.
Question 1
A small community has 10 individuals. Two of them earn $ 50
each, another three - $ 20 each and the remaining five - $ 8
each.
a) Construct the cumulative income distribution, where the unit
of analysis is a quintile, i.e., a fifth of the population.
Total income
Cumulative population share
Cumulative income share
20 %
40 %
60 %
80 %
100 %

b) Graph the Lorenz curve corresponding to the income
distribution in part a).
c) Calculate the Gini coefficient corresponding to the income
distribution in part a).
Question 2
Describe the time trend for the Gini coefficient reduction in the
right panel of Table 7 found on p. 88 of the textbook.
a) Briefly describe and interpret the initial condition.
The initial condition measures a 0.08 reduction in the Gini
coefficient in 1980 that is contributed to the role of government
in the economy captured by the difference between market-
income and after-tax income.
b) Briefly describe and interpret the general relationship in the
time trend.
The time trend is sloping upwards since the Gini coefficient has
increased from 0.08 to 0.14. This means that the policies of the
government are contributing to a larger reduction in inequality
relative to the absence of government intervention.
c) Briefly describe and interpret the type(s) of variability in the
time trend.
There two types of variability exhibited by the time trend: a
structural break in the early 1990s and cyclical variability

associated with recessions.
There is a structural break in the early 1990s since the slope of
the time trend abruptly changes. The structural break in the
early 1990s suggest that the role of government in reducing
income inequality increased since the early 1990s and then
declined afterwards.
There is a larger reduction in the Gini coefficient during
recessions, which suggests that the government plays a more
interventionist role in redistributing when the population is
facing hardships (e.g., loss of employment).
d) Briefly explain whether Table 1 on p. 82 and Figure 2 on p.
111 respectively of the textbook provide conflicting evidence
about changes in income inequality since the early 1980s.
Source: IRPP (2016)
Source: IRPP (2016)
Table 1 provides mixed evidence about changes in after-tax
income inequality, which has been decreasing during the period
2000 – 2011 but not during the other subperiods. A decrease in
after-tax income inequality occurs if the income of the lower
quantiles rises faster than the income of upper quantiles.
In contrast, market income inequality has increased as only
those in the highest income brackets (top decile) have been
benefiting from economic growth.
e) Briefly explain how your findings from parts a) – c) help
reconcile any discrepancies in part d).
The findings are consistent with one another as they examine
two different types of income inequality (with or without the
role of government). In addition, we must account for the
increased role of government in redistributing income during
the examined period.
Note: Table 1 on p. 82 and Figure 7 on p. 88 are found in

"Trends in Income Inequality in Canada and Elsewhere" by
Andrew Heisz. Figure 2 on p. 111 is found in "Who Are
Canada’s Top 1 Percent?" by Thomas Lemieux and W. Craig
Riddell.
Question 3
According to Statistics Canada (2019), the relative GDP per
capita of Quebec is in 1950 and that of Ontario in the same
year is, where the benchmark group is Canada. In addition, the
average growth rate of Quebec is 2.1 % and that of Ontario is
1.9 %.
a) Briefly explain why the regional inequality between Ontario
and Quebec will disappear at some point in the future under the
assumption that the average growth rates remain unchanged.
Ontario has a higher initial income per capita than Quebec but
is growing at a lower rate than Quebec. This implies that
Quebec’s and Ontario’s income per capita will be equalized at
some point in time.
b) Calculate how long it will take for the regional income
inequality between Ontario and Quebec to be eliminated.
The equations governing income over time for Ontario and
Quebec are given by:
What we know is that at some point in the future .
This implies that:
Now we have a single equation with one unknown .

Note: The answer is subject to rounding error in the magnitude
of several years.
c) In 2010, Quebec’s relative GDP per capita has decreased to
85.6. Briefly explain whether such fact is compatible with
Quebec’s positive average growth rate of 2.1 %.
The relative GDP per capita is measured relative to Canada’s
GDP per capita, which assumes a value of 100 in every year.
If the (positive) growth rate of Quebec is lower relative to
Canada’s, the relative GDP per capita of Quebec decreases in
relation to Canada but it increases in absolute terms.
Question 4
Consider a closed economy, in which the production function is
. Total national investment, is therefore determined by, . In
addition, suppose that and . Suppose that two provinces –
British Columbia (BC) and Manitoba (MB) – share all of the
above characteristics but their differ with respect to their
productivity: the productivity in BC is and that in MB, . In
addition, suppose that and .
a) Convert the aggregate production function into the per
worker production function. Do NOT skip steps.
Divide both sides of by : .
Collect exponents on the right-hand side: . This expression is
also equal to .
Then use the relationship and to find .
b) Solve for the steady state capital per worker for each of the
two equilibria in BC and in MB.
BC:

Substitute the parameter values and the production function into
the equation.
There are two steady states: and : and
MB:
Substitute the parameter values and the production function into
the equation.

There are two steady states: and : .
c) Solve for the steady state output per worker and consumption
for each of the two equilibria in each province.
British Columbia:
The production function implies that:
The consumption quantities are:
Manitoba:
d) In a single graph, illustrate the steady-state equilibria found

in parts b) and c). Draw all relevant curves and carefully label
your graph.
The construction of the graph is demonstrated in three layers.
First, determining the state through the savings and capital
requirement functions for each province. Then, constructing the
productions for each province. Third, inserting the initial
conditions into the graphs and describing the pattern of regional
inequality in the short-run and the long-run.
e) Briefly describe the changes to regional income inequality in
the short-run (transitional dynamics to a steady state) and in the
long-run (differences between steady states).
The regional income inequality first decreases and during some
point in the transition to each province’s own steady state
becomes completely eliminated. Then, regional income
inequality increases during the transition to each province’s
steady state. This is because the output (income) per worker of
British Columbia declines and that of Manitoba increases.
Once each province reaches its steady state, the regional income
inequality, persists.
f) Briefly explain whether the facts provided in this question
conform with the empirical evidence provided in the lecture
notes for the two provinces with respect to the initial conditions
and the regional inequality in the short-run and in the long-run.

The initial conditions are incorrect. The graph by Olfert (2016)
indicates that BC’s income per capita exceeds MB’s, while in
the question this information is being reversed. See Figure 1 in
the lecture notes on the Measurement of Economic Inequality.
Source: Olfert (2016)
Barring the initial conditions in 1980, the pattern of regional
inequality between the two provinces is correct with respect to
the fact that regional inequality first decreased and then it
increased.
The growing gap between the two provinces is consistent with
the argument of convergence to different steady states.
The sigma convergence analysis also supports the argument that
the two provinces are in a transition to a steady state as opposed
to in a steady state.
g) Briefly explain how the model in this question should be
modified to conform with the empirical evidence provided in
the lecture notes.
The following information in the question must be modified:
The initial conditions must be reversed, i.e., the output per
worker in BC exceeds that in Manitoba in 1980.
Then, the model will be able to fully explain the pattern of
regional income inequality between the two provinces since
1980.
2

MCGILL UNIVERSITY
ECON 219-001
Winter 2021
Problem Set 2
Question 1
Consider a closed economy, in which the per worker production
function is . Suppose that there are transaction costs taking the
form of legal fees. The parameter measures the per worker
transaction costs of converting savings into investment. In
addition, suppose that two First Nations Reserves (FNRs) share
the following parameters: and . One of the FNR them is in the
low-income steady state equilibrium and the other FNR is in the
high-income steady state equilibrium.
a) Briefly explain why the terms income and output could be
used interchangeably based on the information provided in the
question.
In a closed economy, the output produced in an economy equals
income. Each FNR is assumed to have an economy operating in
isolation from the rest of the world under the closed economy
assumption.
b) Solve for the steady state capital per worker for each of the
two equilibria.
Substitute the production function into the equilibrium
condition and then the parameter values . You may find the

roots in the following manner: . By multiplying by 10 both sides
and collecting terms, we determine that . This yields the values
of the two steady states: and .
c) Solve for the steady state output per worker for each of the
two equilibria.
Use the production function to find: and
d) Suppose that the federal government makes it a criminal
offense for FNRs to hire lawyers to pursue land claims (based
on actual legislation introduced in 1927). As a result, the
transaction costs increase to
i. Briefly describe the transitional dynamics for each of the two
FNRs.
The investment curve shifts down, which means that:
· at now . Consequently, capital per worker for the FNR with
is decreasing until it converges to the new .
is perpetually declining.
ii. Briefly describe the impact on income per capita in the short-
run and in the long-run for each of the two FNRs.
Due to the positive relationship between capital per worker and
output per worker, the answers from the previous part imply
that:
· at now . Consequently, income per worker for the FNR with
is decreasing until it converges to the new .
is perpetually declining.
iii. Briefly describe the impact on the short-run and the long-
run income disparities across the two FNRs.
The impact on income inequality in the short-run is ambiguous
as income per capita for both FNRs is declining.

Income inequality in the long-run is increasing since the income
per capita for the relatively more prosperous FNR stabilizes at
the steady state , while the income per capita for the relatively
less prosperous FNR keeps on declining.
e) In a single graph, illustrate the steady-state equilibria and
transitional dynamic corresponding to and .
Question 2
Consider a closed economy where the production function is
given by for each of the following two cities, Toronto (T) and
Oshawa (O), which differ with respect to their productivity:
and . Both cities share the following parameters and . Suppose
that is the size of the population/workforce and also that . In
addition, you have access to the following actual data reported
in Table 1.
Table 1
Year
GDP per capita (Toronto)
GDP per capita (Oshawa)
2001
41,397
37,551
2005
46,001
32,507
2009
48,532
28,918
Source: Statistics Canada (2014)
a) Transform the production function into per worker terms to .
Divide both sides of by : and simplify to and further to and
finally convert into per capita: .

Substitute into to obtain: .
b) Derive and then solve for the predicted long-run growth rate
of capital per worker and of output per worker.
The long-term growth rate of capital is solved for in a similar
manner:
Toronto:
Oshawa:
c) In a single graph in space, illustrate the predicted long-run
growth performance of the Toronto and Oshawa.
d) Briefly describe the transitional dynamics and their impact
on the short-run and the long-run income inequality between
Toronto and Oshawa.

Toronto’s capital per worker is perpetually increasing, w hile
Oshawa’s capital per worker is decreasing towards the steady
state at .
As a result, both the short-run and the long-run the income
inequality is increasing. However, once Oshawa converges to
the steady state, the income inequality between Toronto and
Oshawa will be decreasing at a slower rate as Oshawa’s income
per capita is no longer declining.
e) Briefly explain whether the actual growth performance of
Toronto and Oshawa from 2001 – 2009 is qualitatively
consistent with the predictions of the model.
The predictions of the model are qualitatively consistent with
the actual data as Toronto has a sustained positive growth rate,
while Oshawa has a sustained negative one.
The increasing income inequality between the two cities is
consistent with the concept of divergence in the Solow model
with a linear production function.
Question 3
For Figure 3 below, answer the following questions.
a) Briefly describe and interpret the initial condition for the
group of occupational task requirements (manual vs. non-
manual).
The initial conditions indicates the composition of skill type of
the 1970 -1974 immigration cohorts.
b) Briefly describe and interpret the general relationship in the
time trends for each of the two groups of occupational task
requirements.
The general trend is:
· downward for non-routine cognitive and analytical skills,
· upward for manual routine and non-routine skills.
This implies that for people with the same educational

attainment, e.g., competition of university, a smaller share of
university graduates worked jobs that required non-routine
cognitive and analytical skills and a larger share worked jobs
that required manual routine and non-routine skills.
c) Briefly describe and interpret the type(s) of variability in the
time trends for each of the two groups of occupational task
requirements.
There is a structural break in the 1990s that increased the share
of university graduates working non-routine cognitive,
analytical and interactive skills at the expense of the manual
routine and non-routine skills.
d) Briefly explain why Figure 3 conveys a different picture than
the corresponding figure about the occupational task
requirements provided in the lecture notes.
Both Figure 2 and 3 investigate the type of jobs that immigrants
over time. Figure 2 explores this relationship by abstracting
away from the completed schooling of the immigrants, Figure 3
takes this information into account.
e) Briefly explain what Figure 3 implies about:
i. the nature of the type of occupations immigrants take on in
the context of increased skilled immigration,
Figure 3 indicates that for immigrants for the same level of
education, a smaller share of the more recent cohorts of
immigrants were working jobs with analytical and cognitive
skills.
In contrast, Figure 2 indicates that a larger share of the more
recent cohorts of immigrants were working jobs with analytical
and cognitive skills.
ii. the consequences of the changing occupational distribution
over time on raising the standard of living.
Figure 3 suggests that the additional training of immigrants
after the reform is only partially utilized as a smaller share of

the immigrants with completed higher education work jobs with
analytical and cognitive tasks. This suggests that the human
capital stock is not being fully utilized with an adverse impact
on output and, in turn, income per capita.
Source: IRPP (2016)
2
MCGILL UNIVERSITY
ECON 219-001
Winter 2021
Midterm Exam I
Submission Deadline: Friday, February 19, 17:00
INSTRUCTIONS
You have 48 hours in a 48-hour window, from Wednesday,
February 17, 17:00 to Friday, February 19, 17:00 to complete
the exam.
This is a take-home exam, i.e., you may access any class
resources posted on myCourses throughout the semester as well
as any of the required readings.
The exam must be completed individually. Any communication
with third parties, e.g., private tutors or classmates, is a form of
academic dishonesty.
Answer ALL questions.
This exam contains four (4) pages.
SUBMISSION INSTRUCTIONS:
Submit your scanned handwritten responses for Question 1 and
your typed responses for Question 2 in a single PDF file in

myCourses. You may write your responses in a software such as
Microsoft Word but you should save your file in a PDF format.
Late submissions will NOT be accepted.
Submissions in files other than a single PDF file will be
disqualified and receive a score of 0 pts.
Please submit your answers in sequential order, i.e., starti ng
with Question 1 a) and finishing off with Question 2 h).
FOR EXAMINERS USE ONLY
Question
Student Score
Number of Points
1
36
2
24
Total points
60
Question 1 (34 pts.)
Consider a closed economy, in which the aggregate production
function is . Suppose that . There are also transaction costs
taking the form of legal fees captured by the parameter , which
measures the per worker transaction costs of converting savings
into investment. In addition, suppose that two First Nations
Reserves (FNRs) have identical population size and share the
following parameters: and . One of the FNRs is in the low -
income steady state equilibrium, , and the other FNR is in the
high-income steady state equilibrium,. All variables and
parameters are defined as in the lecture notes.

Suppose that the federal government signs a treaty with each of
the two FNRs that reduce the size of the transaction costs to .
a) (2 pts.) Convert the aggregate production function into the
per worker production function by expressing as a function of .
Divide both sides of by N: and simplify further to and finally
convert into per worker terms: . Using the relationship and the
fact that yields , which is also equivalent to .
b) (4 pts.) Solve for the steady state human capital per wor ker,,
for each of the two equilibria corresponding to .
Substitute the production function into the equilibrium
condition and then insert the parameter values to obtain:
Use the substitution and multiplying both sides by 10 gives:
The roots of the quadratic equation are determined from the
formula:
Which are and .
This implies that 11.67 and
c) (2 pts.) Solve for the steady state output per worker, , for
each of the two equilibria corresponding to .
d) (8 pts.) Briefly describe the transitional dynamics in response
to the reduction in the transaction costs from to

Word limit for the entire part d): 100 words. The word limit
does not apply to mathematical symbols or expressions.
Penalties for non-compliance will be imposed.
i. (2 pts.) Briefly describe the transitional dynamics for each of
the two FNRs.
The investment curve shifts up, which means that:
· at now . Consequently, human capital per worker for the FNR
with is increasing until it converges to the new .
· at now . Consequently, human capital per worker for the FNR
with is increasing until it converges to the new .
ii. (2 pts.) Briefly describe the impact on human capital per
worker in the short-run and in the long-run for each of the two
FNRs.
Human capital per worker in both FNRs is increasing in the
short-run until they converge to the steady state .
long-run remains unchanged at .
iii. (2 pts.) Briefly describe the impact on income per capita in
the short-run and in the long-run for each of the two FNRs.
short-run until they converge to the steady state .
long-run remains unchanged at .
iv. (2 pts.) Briefly describe the impact on the short-run and the
long-run income disparities across the two FNRs.
The income disparities across the two jurisdictions are
decreasing in the short-run and are completely eliminated in the
long-run once the two FNRs are at .
e) (8 pts.)In a single properly labeled graph in () space,
illustrate the steady-state equilibria corresponding to and as
well as transitional dynamics of the two FNRs.

f) (4 pts.) In a single graph, construct the Lorenz curves for the
income inequality corresponding to and to in an imaginary
jurisdiction consisting of only the two FNRs.
Population share
Income share
(b = 30 %)
Income share
(b = 20 %)
50 %
25 %
50 %
100 %
100 %
100 %
Note:
g) (4 pts.) Calculate the Gini coefficient for the income
inequality corresponding to and for that corresponding to in an
imaginary jurisdiction consisting only the two FNRs.
For ,
.
The Gini coefficient.
For , there is perfect income inequality. The Gini coefficient.
h) (4 pts.) The federal government is interested in evaluating

the impact of signing treaties with FNRs. Calculate the range of
values of , for which big push educational policies pursued by
the federal government are no longer necessary for FNRs to
escape the poverty trap.
This is the horizontal distance between whose numerical values
are .
Answer the following set of questions about Figure 1 in the
Appendix found on p. 4 of the exam.
Word limit for the entire question: 400 words. Penalties for
non-compliance will be imposed.
a) (8 pts.) Briefly describe and interpret the actual performance
of Alberta with respect to:
i. (2 pts.) the initial condition.
Alberta’s GDP per capita was approx. 16 % higher than
Canada’s in 1950. (Numbers between 15 and 20 % are accepted
as correct.)
ii. (2 pts.) the general relationship observed in the time trend.
Alberta’s income per capita increased relative to Canada over
the period 1950 – 2005.
iii. (4 pts.) the type(s) of variability observed in the time tre nd.
There was a structural break in 1972 when the trend of
Alberta’s income per capita was closing in to Canada’s was
reversed.
Alberta experienced cyclical fluctuations during the period that
bounced around the trend prior to the structural break and
around the new trend after the structural break.
b) (2 pts.) Briefly explain from the perspective of the Solow
growth model why the shape of the steady state line is a straight

horizontal line prior to 1972.
The horizontal steady state line indicates than Alberta’s steady
state was unchanged between 1950 to 1972.
c) (2 pts.) Briefly interpret the numerical value of the initial
condition of the steady state line.
The Alberta’s steady state income per capita was approximately
10 % higher than Canada’s in 1950.
d) (2 pts.) Briefly describe the phenomenon from the
perspective of the Solow growth model that impacted the steady
state line in 1972/73.
Alberta experienced a change in one or more of the parameters
of the Solow model that resulted in Alberta converging to a new
steady state value.
e) (2 pts.) Briefly explain whether the 1972/73 phenomenon is
also captured by the analysis of sigma-convergence for the
Canadian provinces.
Alberta (and other oil producing provinces) experienced an
abrupt change relative to the non-oil-producing provinces with
respect to their convergence behaviour in 1972/73. This abrupt
change here is reflected in an upward shift of the steady state
line.
f) (4 pts.) Briefly describe and interpret the predicted line from
the perspective of the Solow growth model.
The predicted line indicates that until 1972 Alberta was
converging to the steady state value of approx. 1.10 and
afterwards it was converging to the steady state value of approx.
1.28.
g) (4 pts.) Briefly explain whether:
i. (2 pts.) in the short-run, Alberta’s income per capita is
diverging from that of Canada.

No, Alberta is converging to its own steady state. That is, the
relevant concept is conditional convergence, not divergence.
ii. (2 pts.) in the long-run, Alberta’s income per capita is
diverging from that of Canada.
No, in the long run the approx. 28 % gap in the living standard
between Alberta and Canada is sustained.
h) (2 pts.) Based on the information provided in Figure 1,
briefly explain whether your analysis from parts a) – g)
challenges the view that regional inequality in Canada has
decreased over time.
The analysis challenges the view that regional inequality has
decreased since Alberta has been following the reverse of what
we observe for regional inequality in Canada as a whole.
APPENDIX
Figure 1: Alberta’s relative economic performance
Legend: The horizontal axis measures Year (e.g., 50 represents
the year 1950). The vertical axis measures relative GDP per
capita where Canada serves as the benchmark jurisdiction. Each
of the three curves represent Alberta’s actual, predicted and
steady state performance respectively.
Source: Coulombe (2000)

2
MCGILL UNIVERSITY
ECON 219-001
Winter 2021
Midterm Exam II
Submission Deadline: Friday, March 26, 17:00
INSTRUCTIONS
You have 48 hours in a 48-hour window, from Wednesday,
March 24, 17:00 to Friday, March 26, 17:00 to complete the
exam.
This is a take-home exam, i.e., you may access any class
resources posted on myCourses throughout the semester as well
as any of the required readings.
The exam must be completed individually. Any communication
with third parties, e.g., private tutors or classmates, is a form of
academic dishonesty.
Answer ALL questions.
This exam contains six (6) pages.
SUBMISSION INSTRUCTIONS:
Submit your scanned handwritten responses for Questions 1 and
2 and your typed responses for Question 3 in a single PDF file
in myCourses. You may write your responses in a software such
as Microsoft Word but you should save your file in a PDF
format.
Late submissions will NOT be accepted.
Submissions in files other than a single PDF file will be
disqualified and receive a score of 0 pts.
Please submit your answers in sequential order, i.e., starting

with Question 1 a) and finishing off with Question 3 i).
FOR EXAMINERS USE ONLY
Question
Student Score
Number of Points
1
28
2
14
3
18
Total points
60
Consider the labour markets for skilled labour and unskilled
labour, which are defined as in the lecture notes.
The labour demand curve for skilled workers is given by. The
labour demand curve for unskilled workers is . The labour
supply for each of the two labour markets is given by .
The effort of a firm's skilled workers depends on their wage
according to the following schedule:
Table 1
Wage
20
25

30
35
40
45
Effort
16
24
30
34
36
36
a) (3 pts.) Calculate the equilibrium employment,
unemployment, and wage for unskilled workers.
At and
b) (2 pts.) Calculate the profit-maximizing contract .
The profit-maximizing contract is since it delivers the highest
effort per wage ratio of 1. All other contracts deliver an effort
per wage ratio of less than 1.
c) (3 pts.) Calculate the equilibrium employment,
unemployment, and wage for skilled workers.
At and

d) (8 pts.)In a single properly labeled graph in () space,
illustrate the labour market equilibria for skilled and unskilled
workers.
e) (4 pts.) Calculate the cumulative income distribution for each
labour market by reporting the cumulative shares for the
following percentiles: 50 % and 100 %.
Population share
Income share
(Skilled labour market)
Income share
(Unskilled labour market)
50 %
0 %
50 %
100 %
100 %
100 %
f) (4 pts.) In a single graph, construct the Lorenz curves
representing labour income inequality for each labour market.
Construct the cumulative shares for the following percentiles:
50 % and 100 %.
g) (2 pts.) Briefly explain why the declining share of labour
income in recent decades could entirely be attributed to the
shape of the labour supply curve.

A flatter labour supply curve results in a larger increase in
capitalists’ income and a smaller increase in workers’ income.
As a result, the labour share of income, defined as the share of
labour (or workers’) income over total (capitalists’ and
workers’) income, declines.
h) (2 pts.) Briefly explain why the temporary foreign workers
program run by the federal government influences the shape of
the labour supply curve but the permanent residence program
does not.
The temporary foreign workers program commonly permits a
worker to work only for a specific employer, which reduces
their opportunity cost. This effect is represented by a flatter
shape of the labour supply curve. In contrast, permanent
residents face no such restrictions with respect to being tied to a
specific employer.
Suppose that the wage of skilled labour equals 30 and the wage
of unskilled labour equals 20. The total labour force is 35. In
addition, the number of unskilled workers who are employed is
twice as large as the number of skilled workers who are
employed. The markets for skilled labour and unskilled labour
are defined as in the lecture notes.
a) (2 pts.) Calculate the opportunity cost of skill acquisition as
a function of the probability of finding a job in the skilled
sector.
Opportunity cost of skill acquisition = Net gain from not
acquiring skills – Net gain from skill acquisition
b) (2 pts.) Briefly describe the nature of the trade-off faced by
an unskilled worker.

An unskilled worker faces the prospect of a higher wage in the
skilled sector but there is uncertainty in the actual outcome, i.e.,
they receive unemployment with probability and are
unemployed with the remaining probability.
c) (4 pts.) Calculate the number of employed workers in the
skilled sector if unskilled workers are paid just enough to
forego skill acquisition. Show ALL steps.
First, we must determine the probability of finding a job such
that unskilled workers are paid just enough to forego skill
acquisition.
Secondly, we could use that and also that since .
To solve this equation, we must use two facts. First, there is no
unemployment in the unskilled sector, i.e., . In addition, it is
given in the question that . Replacing with gives us a linear
equation with one unknown.
d) (2 pts.) Briefly explain why neither of the two labour markets
is in equilibrium if the probability of finding a job in the skill ed
sector is 80 %.
A probability of finding a job in the skilled sector larger than
2/3 induces unskilled workers to acquire skills.
Consequently, the labour supply in the skilled sector is
increasing, while the labour supply in the unskilled sector is
decreasing. This implies that neither of the labour markets are
in equilibrium (stable outcome).

e) (4 pts.) Briefly discuss the validity of the statement: “New
jobs in the skilled sector increase unemployment in the skilled
sector if the probability of finding a job in the skilled sector is
80 %.”
The statement is correct for the following reasons.
First, for the probability of 80 %, unskilled workers have an
incentive to acquire skills since average income in the skilled
sector exceeds average income in the unskilled sector.
In addition, each new vacancy each new vacancy entices more
than one unskilled worker to acquire skills.
Since only 80 % of those who acquire skills end up finding a
skilled job, unemployment in the skilled sector increases.
Answer the following set of questions about Figure 1 and Figure
2 in the Appendix found on pp. 5 – 6 of the exam.
Word limit for the entire question: 400 words. Penalties for
non-compliance will be imposed.
a) (2 pts.) Briefly explain why Figure 1, panel c) is more
appropriate than Figure 1, panel d) to evaluate the impact of the
childcare policy in Quebec on women’s earnings.
Figure 1, panel c) is more appropriate as it includes information
on both employed and unemployed women. Mothers often face
the choice of working and sending their kid to childcare vs. not
working at all.
b) (2 pts.) Briefly explain why the decomposition of the total
variance into between-variance and within-variance is useful in
determining how the childcare policy in Quebec affected
women’s earnings.
This decomposition is useful to determine whether it is mothers
of different skill levels or of the same skill level are more
affected by the introduction of the childcare policy. For
instance, a reduction of the between variance will be indicative
that less skilled mothers benefited more from the introduction

of the childcare policy.
c) (2 pts.) Briefly explain why the opportunity cost of working
for a mother with no post-secondary education was more likely
to be impacted by the size of the childcare subsidy relative to a
mother with post-secondary education.
A mother without post-secondary education would on average
have lower income. The reduction in the cost of childcare is
more likely to be pivotal in switching her decision to work and
send her kid to childcare.
d) (2 pts.) Briefly describe and interpret the between-group
variance curve (Figure 1, panel c) with respect to the general
relationship observed in the time trend over the examined
period.
The between-group variance curve has decreased from approx.
1.8 to approx. 1 during the examined period meaning that
income inequality between more educated vs. less educated
mothers has decreased.
e) (2 pts.) Briefly explain how the introduction the childcare
policy in Quebec has contributed to your answer in part d).
Some mothers are likely to have started working instead of
taking care of their kids at home.
f) (2 pts.) Briefly explain why we need to group female workers
of the same educational attainment and age group for the
within-group variance to be a meaningful concept.
The within-group variance is a meaningful concept if we could
compare the earnings of people with the same level of schooling
and work experience.
g) (2 pts.) Briefly explain why we may view as problematic a
large within-group variance if measured as noted in part f).
This would suggest that there is a sizable income inequality
among workers with the same level of schooling and work

experience. That is, factors other than one’s skill level
contribute to substantial differences in earnings.
h) (2 pts.) Briefly describe and interpret the within-group
variance curve (Figure 1, panel c) with respect to the general
relationship observed in the time trend over the examined
period.
The within-group variance curve is flat at approx. 7.5 meaning
that within-group inequality among women has remained fairly
constant over the examined period.
i) (4 pts.) Suppose that the only difference between the changes
in the males’ and females’ within-group variance is the impact
of introducing the childcare policy in Quebec. If we use the
within-group variance of the male earnings as the control group
(Figure 2 panel c) and that of the female earnings as the
treatment group (Figure 1 panel c), briefly describe the i mpact
of the childcare policy on the within-group income inequality.
It is important to have a control group because factors other the
introduction of the childcare policy could have impacted both
males and females. Comparing the time trends of the treatment
and the control groups provide us with the opportunity to
disentangle the impact of the childcare policy from those other
factors.
The within-group variance curve is flat for both women
(treatment group) and men (control group). This would imply
that the childcare policy has had virtually no impact on within-
group income inequality among women.

APPENDIX
Figure 1
Source: IRPP (2016)
Figure 2
Source: IRPP (2016)
2
MCGILL UNIVERSITY
ECON 219-001
Winter 2021
Problem Set 5
Question 1

Consider the dual labour market model based on Ghatak and
Jiang (2002). Suppose that . Suppose that 40 % of the
population have asset holdings and the remaining 60 % of the
population . All parameters are defined as in the lecture notes.
a) Calculate the threshold level of assets required for a loan of
size to be approved.
The threshold level of asset is determined from . Substituting
the numerical values yields or equivalently .
b) Briefly explain why we need to calculate the incentive
compatibility constraint (ICC) for an entrepreneur but not for a
worker.
An ICC is determined from the perspective of a lender who is to
approve or reject a loan. An entrepreneur can invest the loan
and earn income that exceeds the cost of the loan. The loan
application of a worker will be automatically rejected.
c) Calculate the threshold wage that leaves a credit-constrained
individual indifferent between becoming a worker and a self-
employed.
The wage that leaves a credit-constrained individual indifferent
between becoming a worker and a self-employed is the solution
of , which is .
d) Calculate the threshold wage that leaves a non-credit-
constrained individual indifferent between becoming a worker
and an entrepreneur.
The wage that leaves a non-credit-constrained individual
indifferent between becoming a worker and an entrepreneur is
the solution of the equation , which is .
e) Briefly describe the implications on technology use if the

entrepreneur’s participation constraint is violated.
No individual would like to become an entrepreneur as they
could earn a higher income by choosing a different occupation.
The entrepreneurial technology requires one entrepreneur and
one worker. In the absence of entrepreneurs, all individuals will
become self-employed.
f) Briefly explain why and and the critical wages for
determining labour demand and labour supply.
These are the wages, for which individuals have an incentive to
switch their occupation. This indirectly affects the size of
labour demand and labour supply.
g) Briefly explain why the asset distribution does not affect
your answer in part f). Hint: Compare your answer to the other
asset distribution (70 % have and 30 % have ) we went over in
the lecture notes.
The asset holdings and the return do not change if one chooses
a different occupation.
h) Briefly explain you must analyze labour demand and labour
supply at, below and above each of the wages and .
These are the only two wages at which quantity the labour
demanded (share of entrepreneurs each of which demanding one
worker) and/or the quantity labour supplied (share of
individuals willing to become workers) change.
i) Determine the labour demand and the labour supply for each
of the relevant wage ranges noted in part h). Justify your answer
with the concept of an opportunity cost as well as the
relationship between and .
1)
If , all non-credit constrained individuals want to become
entrepreneurs () but no one wants to become a worker (). All
credit constrained individuals want to become self-employed. A
wage cannot be sustained as an equilibrium since .

2)
If , all non-credit-constrained workers want to become
entrepreneurs and all credit-constrained workers are indifferent
between becoming self-employed and becoming workers. This
implies that . That is, a wage can be sustained as an equilibrium
since there is a potential intersection between and .
For this to be an equilibrium, each entrepreneur must be
matched with one worker, that is , due the production
requirements of the entrepreneurial technology. In addition, no
individual has an incentive to switch their occupation.
3)
If , all non-credit constrained individuals want to become
entrepreneurs () and all credit constrained individuals want to
become workers (). No one has an incentive to become self-
employed. A wage cannot be sustained as an equilibrium since .
4)
If , all credit-constrained individuals want to become workers
and all non-credit-constrained workers are indifferent between
becoming entrepreneurs and becoming workers. No individual
has an incentive to become self-employed. This implies that
and . That is, a wage cannot be sustained as an equilibrium
since there is no overlap between and .
5)
If , everyone wants to be a worker () but no one wants to be an
entrepreneur () or self-employed. A wage cannot be sustained as
an equilibrium since .
j) Draw a carefully labelled graph depicting the labour demand
and supply curves as well as the labour market equilibrium.
k) Calculate the occupational distribution and the corresponding
income distribution.
The labour market equilibrium results in:
· occupational distribution (shares individuals who become
entrepreneurs, workers and self-employed), i.e., and .2,

· labour market outcomes in the entrepreneurial sector, i.e.,
employment and wage ,
· Income distribution: there is income inequality since ,
l) Verify that the modern technology is superior to the self-
employment technology. Justify your answer.
Any pair of individuals operating the entrepreneurial technology
as entrepreneur and worker generates more income than these
same two individuals becoming self-employed.
m) Briefly explain why is the critical mass of credit
constrained individuals that gives rise to a poverty trap for an
economy.
The fixed proportions labour requirement of the modern
technology ensures that there is a unique equilibrium, where 1/2
become entrepreneurs and 1/2 become workers. Since for this
equilibrium, i.e., an individual is indifferent between becoming
an entrepreneur and a worker, some individuals switch
occupations until there is no exceed demand for workers or
excess supply of workers.
n) Briefly explain why this critical mass depends on the
technological requirement of the entrepreneurial technology.
For the entire population to use the entrepreneurial technology,
each entrepreneur must be matched with one worker. For this to
happen, at least one half of the population must be non-credit
constrained.

2
MCGILL UNIVERSITY
ECON 219-001
Winter 2021
Problem Set 3
Question 1
Consider the labour market for high-skilled labour.
The effort of a firm's workers depends on their real wage
according to the following schedule:
Table 1
Wage
16
17
18
19
20
21
Effort
10
13
18
22
25

26
0.63
0.76
1
1.16
1.25
1.24
The labour demand curve is given by. The labour supply is
given by .
a) Calculate the profit-maximizing contract .
See Table 1. The profit-maximizing contract since it maximizes
the effort per wage ratio.
b) Briefly explain why paying the lowest wage of $ 16 does not
maximize profit.
There are two factors that contribute to profit: higher revenue
resulting from the higher effort exerted by a worker and smaller
cost from paying a lower wage to the worker.
In this instance, the lowest wage reduces the cost but it also
yield the lowest exerted effort. Ultimately, this is the least
preferred outcome by a firm since the effort per wage is the
lowest.
c) Calculate the equilibrium employment.
Insert the values of the profit-maximizing contract in to the
labour demand function:

Solving for yields:
The equilibrium employment is:
d) Calculate the equilibrium unemployment.
The number of workers who would like to be employed at is
determined from the supply curve, .
The equilibrium unemployment is the difference between the
people willing to work, , at the prevailing wage, , and the
employed workers, . That is, .
e) Draw a carefully labeled graph to illustrate the equilibrium
outcome.
f) Calculate the probability of finding a high skilled job at the
efficiency wage.
The probability of finding high skilled job at the efficiency
wage is the ratio between the number of employed workers to
the total number of skilled workers willing to accept
employment at the prevailing wage, .
g) Calculate the wage for unskilled labour at which unskilled
workers will stop acquiring skills, e.g., attending post-
secondary education.
First, write down the equation that determines whether an
unskilled worker has an incentive to acquire skills.

An unskilled worker will not accept employment if the expected
income in the skilled sector equals the income in the unskilled
sector.
The unskilled wage is the solution to this equation:
h) Briefly explain why the unskilled workers will stop being
enticed by the higher wage for skilled workers at the wage in
part g).
As the expected income of a skilled worker equals the income
of an unskilled worker, an unskilled worker has no incentive to
acquire skills.
Question 2
Consider the labour market for unskilled labour, which is
perfectly competitive. Firms use both capital and unskilled
labour to produce output, where the capital stock is 50, i.e., is
fixed in a given period.
The labour demand curve is given by . There are 40 workers
willing to work at any positive wage. During the pandemic, the
borders are shut down and no workers are permitted to enter or
leave the country. In addition, there is no population growth.
a) Calculate the equilibrium employme nt and wage.
First, substitute the capital stock into the labour demand
function:
Then, use the fact that labour supply curve is vertical,
Equilibrium employment is trivially determined but must be
verified that the wage is positive by substituting i nto the labour

demand function.
Since the equilibrium wage is positive, is the equilibrium
employment.
b) Briefly explain why there is no involuntary employment.
All workers who would like to be employed at the prevailing
wage end up employed.
c) Calculate workers’ income, capitalists’ income and total
income.
Workers’ income
Capitalists’ income
Total income = 800 + 1,600 = 2,400
For the remainder of the question, suppose that all profit
(capital income) is re-invested into new capital.
d) Calculate the new labour demand curve.
First, substitute the initial capital stock plus the re-invested
profit (the capitalists’ income) of 1,600 into into the labour
demand function:
e) Calculate the new equilibrium employment and wage.
The equilibrium employment and wage are found in the same
manner is part b).
f) Calculate the workers’ income, capitalists’ income and total

income.
Workers’ income
Capitalists’ income
Total income = 64,800 + 1,600 = 66,400
g) Briefly describe the impact of re-investing profit on total and
average income increase.
Total income increases. Average income also increases since the
number of both capitalists and workers remains unchanged.
h) Briefly explain how the income gains from the re-invested
profit are redistributed between the capitalists and the workers.
The entire income increases are captured by the workers since
area C (capitalists’ income after the profit re-investment) equals
areas A (capitalists’ income before the profit re-investment)
2
MCGILL UNIVERSITY
ECON 219-001
Winter 2021
Problem Set 4
Question 1

Jake has three options upon graduating from a CEGEP:
attending university, working upon completing CEGEP or
receiving government assistance. If he attends university, he
receives a lifetime labour income of $ 3 million. If he starts
working upon completing a CEGEP, he receives a lifetime
labour income of $ 2 million. The lifetime income he would
receive from social assistance is $ 0.5 million. The cost of
university education is $ 0.1 million.
Calculate the opportunity cost of attending university.
Step 1:
To determine the highest-valued alternative to attending
university, we limit the set of options to working and receiving
government assistance.
Opportunity cost of working = Net gain from gov. assistance –
Net gain from working = 0.5 – 2 = -1.5 < 0
This result implies that the highest-valued alternative is
working (upon graduating from CEGEP).
Step 2:
Opportunity cost of attending university = Net gain of working
- Net gain of attending university = 2 – (3 – 0.1) = -0.9 < 0
This result implies that it is on one’s self-interest to go to
university.
Question 2
Answer the following questions regarding to the design of
social assistance program in Québec in 1986.
a) Briefly describe the time trend of social assistance income
(monthly) represented by the black line in Figure 1.
The black line represents that social assistance income is
increasing with age but there is a break in the time trend at age
30 when social assistance income rises by approximately $ 500.
A few notes:
Each blue dot represents the average social assistance income
for a given age, e.g., 27.

The black line is a time-trend where the unit of analysis is age
as opposed to time.
Black line smooths any fluctuations over one’s lifecycle, i.e., it
depicts a general linear relationship.
b) Based on the income characteristics of two age groups, 16-
24-year-olds and 35-44-year-olds, provided in Table 1, briefly
explain whether it is appropriate to use one group as a treatment
group and the other one as a control group.
These two age groups have very difference average labour
income characteristics, which would cast doubt whether it is the
generosity of social assistance income is driving this
relationship.
c) Briefly explain why comparing two age groups in proximity
to the vertical line (age 30) is appropriate for a natural
experiment.
Using the two age groups in proximity to the vertical line (age
30) is appropriate for a natural experiment since the two groups
are likely to have almost identical average characteristics, e.g.
educational attainment, work experience, etc.
Question 3
Answer the following questions regarding labour income
inequality based on Figure 2, panel a) Census 1980 – 2000,
provided in the Appendix.
You may assume that the labour markets for skilled and
unskilled workers function as described in the lecture notes.
You may also use the evidence provided in the lecture notes that
a large increase in skilled workers measured by the post-
secondary graduation rates occurred during the examined period
1980 – 2000.
The variance is a measurement of income inequality that has a
similar interpretation as the Gini coefficient, where a larger

variance represents greater income inequality.
a) Briefly describe the key distinction between the terms: total
variance, within-group variance, and between-group variance.
Total variance (TV) refers to labour income inequality of all
people in the labour force irrespective of skill level.
Within-group variance (WGV) refers to labour income
inequality among workers of the same skill level.
Between-group variance (BGV) refers to labour income
inequality among workers of different skill level.
b) Briefly describe and interpret the decomposition of total
variance into within-group variance and between-group variance
in 1980.
TV was approximately 4.2, WGV = 4 and BGV = 0.2.
Note that in any year.
This implies that approx. 95 % of the labour income inequality
is due to income inequality among male workers of the same
skill level. Only about 5 % of the labour income inequality is
due to income inequality resulting from a pay differential
between skilled and unskilled male workers.
c) Briefly describe how the decomposition of the total variance
into within-group variance and between-group variance has
changed from 1980 to 2000.
Absolute:
The total variance increased from 4.2 to 6.2 as both its
components increased. WGV increased from 4 to 5.8 and BGV
from 0.2 to 0.4. This means that both types of labour income
inequality increased, thereby contributing to an overall increase
in labour income inequality.
Relative:
This implies that during the examined period the share of
income inequality among male workers of the same skill level
has declined to 93.5 % and that corresponding share of the
income inequality resulting from a pay differential between

skilled and unskilled male workers has increased from 5 to 6.5
%.
d) Briefly explain if the increase in skilled labour during the
period 1980 – 2000 has been effective in reducing income
inequality between skilled and unskilled workers.
The larger variance in 2000 relative 1980 implies that the
income inequality between skilled and unskilled workers has in
fact increased both in absolute terms (0.2 to 0.4) and in relative
terms (5 % to 6.5 %).
e) Briefly explain if the increase in skilled labour during the
period 1980 – 2000 has been effective in reducing income
inequality among skilled workers.
The larger variance in 2000 relative 1980 implies that the
income inequality among workers of the same skill level has
increased in absolute terms (4 to 5.8) but decline in relative
terms (95 % to 93.5 %).
Appendix
Figure 1
Source: Lemieux and Milligan (2008)
Table 1
Age group: 16 - 24
Age group: 35 - 44
Average Labour Income (1986)
17,800
51,200

Figure 2
Source: IRPP (2016)
2
Occupational and Income Inequality in Labour Markets
Part I
1. Second part of the course.
a) Revisiting the key objectives
The main objectives of this class:
· Documenting the increasing economic inequality in recent
decades,
· Dissecting the key sources of economic inequality,
· Explaining these phenomena through economic models.
b) Reviewing what we have already done
We have explained the following phenomena:
· Regional income inequality across provinces has decreased,
· Income disparities across FNRs have widened due to the
partial implementation of modern treaties,
· Income disparities between large CMRs and small cities/towns
have increased.
c) Roadmap

In the second part of the course, we will attempt to explain two
phenomena:
· the shrinking middle class,
· the disappearance of good jobs.
To this end, will focus on the functional distribution of income
inequality by:
· distinguishing between capital vs. labour income,
· explaining individuals’ self-selection into different
occupations and the presence of involuntary unemployment.
We will also explore the role of redistributive government
policies in offsetting the impact of increasing market income
inequality.
2. Introduction.
a) Overview
In this lecture, we will explore how the functional distribution
of income has contributed to increased income inequality in
recent decades.
Figure 1
Source: IRPP (2016)
In the first part of this lecture, we will build a labour market
model, in which we distinguish between capitalists (firm
owners) and workers.
The objective of our model is to explain three key facts:
· Declining labour share of income (Figure 1),
· Increasing within-provincial income inequality (Figure 2),
· Rising standard of living.
Figure 2
Source: IRPP (2016)
3. Labour market.
a) Voluntary transactions and markets
A voluntary exchange is a transaction where two people trade

goods or services freely in the sense that there is no coercive or
restrictive force involved in the transaction. Both parties want
to make the exchange of items, and both parties will benefit
from the trade.
In a labour market, a worker offers labour services, for which
they are paid a wage. A capitalist receives revenue from the sale
of goods and services produced using labour services and incurs
a cost by paying a wage to a worker.
· Worker’s decision-making
Workers have a reservation wage, above which they are willing
to accept an offer of employment and below it they decline it.
A reservation wage could be the wage at one’s current job or
the social assistance payments one receives.
Accept employment if and reject if .
· Firm’s decision making
A firm owned by a capitalist hires a worker if the revenue it
generates from employing the worker exceeds the wage the firm
pays to the worker. The profit is automatically generated as
income to the
Example:
Consider a simple example, in which each firm hires one
worker.
Table 1
Firm
Revenue from hiring worker
Reservation Wage
Potential gains from employment
Transaction
(Employment)
1
30
12
18
Yes
2

25
16
9
Yes
3
20
20
0
Yes
4
15
24
-9
No
b) Labour demand and labour supply
It is often convenient to graphically represent the willingness of
firms and workers to engage in employment.
Labour supply curve – a curve that represents the reservation
wage for each additional worker.
Labour demand curve – a curve that represents the revenue from
employing a worker.
The labour supply curve and the labour demand curve could also
be expressed as equations. This type of representation will also
provide us with the opportunity to calculate the income
distribution between capitalists (firm owners) and workers.
Labour demand curve:
intercept
slope coefficient
For the numerical example at hand, and .
Labour supply curve:
intercept

slope coefficient
For the numerical example at hand, and .
c) Labour market equilibrium
The labour market equilibrium occurs at the intersection point
of the labour demand curve and the labour market curve.
An equilibrium labour – the number of employed workers.
An equilibrium wage – the prevailing wage
Figure 3
In general, we must solve a system of two equations with two
unknowns.
In equilibrium (actual outcome), workers are employed at .
d) Income inequality
· Workers’ income
The income earned by (all) workers is given by:
Note: The per worker income is
· Capitalists’ income
The income earned by (all) capitalists is given by the profit
(revenue minus cost). The revenue to the firm is represented by
the demand curve and the cost by . In a graph, this area is
captured by the triangle A.

Figure 4
4. Policy debates.
a) Overview
A main policy debate in previous decades has been whether re-
invested profit by the capitalists will generate widely shared
gain to the economy.
This policy debate could be broken down into two components:
· Will total income rise?
· How will income gains be distributed between capitalists and
workers?
b) Impact of re-investing profit
Profit could be re-invested as new capital. This is equivalent to
an outward shift of the labour demand curve.
We will show that more re-invested profit always leads to a
higher total income. Its redistributive impact depends on the
shape of the labour supply and the labour demand curves.
We will consider the extreme cases of a horizontal labour
supply curve, which captures two ideas:
· All workers have the same reservation wage,
· There is an abundant labour force.
· Horizontal labour supply curve
Table 3
Firm
Reservation Wage
Potential gains from employment
Transaction
(Employment)
1
30
20
10

Yes
2
25
20
5
Yes
3
20
20
0
Yes
4
15
20
-5
No
5
10
20
-10
No
6
5
20
-15
No
For the numerical example at hand, and . That is, the labour
supply curve is given by and the labour demand curve by .
In equilibrium (actual stable outcome), workers are employed
at .
Figure 5

· Income distribution
The income distribution is identical to the one we have already
found.
Suppose that these 22.5 units of income are re-invested, which
results in the following outward shift in the demand curve.
Table 4
Firm
Reservation Wage
Gains from hiring worker
Transaction
(Employment)
1
40
20
20
Yes
2
35
20
15
Yes
3
30
20

10
Yes
4
25
20
5
Yes
5
20
20
0
Yes
6
15
20
-5
No
The demand curve shifts up due to the re-invested profit to .
The labour supply curve given by remains unchanged.
In equilibrium, workers are employed at .
Figure 6

· Functional income distribution
Table 5 describe the income distribution before and after the re-
investment of profit.
Table 5
Functional income distribution
Income share of capitalists
Income share of workers
Before re-investing profit
After re-investing profit
We were able to simultaneous explain the following key facts:
· Total income increased,
· The labour share of income declined.
If capitalists and workers live in the same province, we are also
to provide a key explanation as to why within-provincial income
inequality increased.
c) Role of immigration policy
· Key immigration policies
Did the shape of the labour supply curve change?
It is plausible that the labour supply curve may have been
steeper in previous decades and have become flatter.
Three potential sources related to immigration policy:
· Increased immigration,
· Change in the type of immigration from permanent residents
(PRs) to temporary foreign workers (TFWs) in the last two
decades.
· A large share of TFWs are tied to a specific employer.
· Economic impact
The increased immigration would result in a rightward shift in

the labour supply curve. That is, for each wage there are more
potential workers willing to accept employment.
A greater reliance on TFWs reduces the reservation wage of
those workers relative to them being admitted as PRs. This
generates a pivot of the labour supply curve, which becomes
flatter.
· Evidence
Figure 7 indicates the admission of both PRs and TFWs
increased in recent decades.
In general, the admission of both PRs and TFWs is closely tied
to economic fluctuations (reduced admissions during recessions
and increased admissions during economic recovery and
booms).
Figure 7
Source: IRPP (2013)
Each of the two curves experience a structural change in
response to a major immigration policy change:
· From 1985 to 1992, the admission of PRs sharply increased.
· From 2005 to 2011, the admission of TFWs sharply increased,
while the admission of PRs remains relatively constant (subject
to cyclical fluctuations).
Figure 8 presents some evidence on the impact of tying TFWs to
a specific employer. We will analyze the impact om earnings of
high-skilled whose wages are unlikely to have been influenced
by part-time employment and/or minimum wage policies.
The time trends reveal that the earnings for high-skilled
individuals with a work permit tied to an employer declined
over the examined period (2001 – 2016).
Figure 8

The time trend exhibits a structural break around 2008, which
highlights that the income of high-skilled workers declined
during the boom times prior to the Great Recession and partially
recovered after that.
This evidence highlights that tying TFWs to a specific employer
reduces their earnings during periods when they should have
been increasing (if following the trend for the general
population).
The increasing number of TFWs and their declining earnings are
also likely to have had a spillover effect on the earnings of
citizens and PRs.
2
Measurement of Economic Inequality
1. Economic inequality.
a) Definition
Economic inequality is the unequal distribution of an economic
variable such as income, wealth, pay or opportunity between
different individuals or groups in society.
b) Types of economic inequality
To determine the type of economic inequality, we need to fix:
· The economic variable of interest, e.g., income.
· The unit of analysis, e.g., province, and the reference group,
e.g. Canada.
· Economic variable

The economic variable of interest gives rise to the nature of
economic inequality:
Table 1
Economic Variable
Type of economic inequality
Income
Income inequality
Wealth
Wealth inequality
Wage
Wage inequality
· Unit of analysis and reference group
· Within-regional (income) inequality - differences in individual
incomes within a region;
· Regional (income) inequality - differences in per capita
income across regions.
2. Measuring regional inequality.
a) Creating an index
Income per capita is a measure of average standard of living in
a country.
Low (high) levels of income per capita are indicative of low
(high) standard of living. GDP per capita is commonly used as a
measure of income per capita, where GDP is an abbreviation for
Gross Domestic Product.
GDP per capita is measured in dollars (or other currency). To
make comparisons across jurisdictions such as provinces, it is
convenient to create an index, where for a benchmark country,

e.g., Canada, a value of 100 is assigned. The GDP per capita of
all each province is viewed as an index relative to Canada. For
instance, a province with an index number of 120 has GDP per
capita that is 1.2 higher than that of Canada.
Figure 1:
b) Snapshots of regional inequality.
· Comparison between the extremes
It is a comparison between the two countries with the highest
and the lowest incomes.
Table 2
Year
1926
1933
2011
Max
120
145
127
Min
48
40
83
Ratio
2.50
3.63
1.53
· Key Insights
Canada’s regional inequality first increased around the 1930s
and then declined. This type of pattern is known as the Kuznets

Inverted U-shaped curve.
Regional inequality has first increased, then declined.
· Limitations
This approach of comparing only the extremes ignores the
dynamics for 80 % of the provinces that lie within the range.
3. Distributional measures.
a) Examination of entire distributions
This approach entails the constructio n of the cumulative income
shares (or the cumulative share of another socioeconomic
variable) against the corresponding cumulative population
shares.
This approach has more desirable properties (compared to the
approach of taking a ratio of the extremes) as it provides a
detailed presentation of any development gap. Furthermore,
these distributions are comparable to one another if represented
by Lorenz curves and Gini coefficients.
b) The Lorenz curve
A Lorenz curve is a graphical representation of income
inequality by plotting what income share is being earned a share
of the population.
Step 1: Order the population by increasing income.
Step 2: Determine what fraction of total income they earn (e.g.,
bottom 1% earns .2% of the total, etc.)
The Lorenz curve connects the points with coordinates:
· on the horizontal axis we put the rank in the population (by
income, e.g., bottom 10%, bottom 20%, etc.)
· on the vertical axis we put the corresponding percentage of
total income this group earns (e.g., bottom 10% earn 2% of total
income, the bottom 90% earn 65% of total income, etc.)
Figure 2
Source: Radice (2009)

c) Properties of the Lorenz curve:
i) starts at (0,0), ends at (100,100);
ii) increasing (adding positive numbers);
iii) convex shape (increases at an increasing rate) because we
ordered them in increasing income;
iv) two extreme scenarios:
· perfect equality: LC is the 45-degree line;
· perfect inequality: inverted L shape (0 at up to 100% and 1 at
100%).
v) if we have two LCs, line A is always above line B, then A
corresponds to lower inequality.
For instance, Figure 3 indicates that income inequality in
Canada increased from 1980 to 2011.
Figure 3
· Limitations of the Lorenz curve
A key limitation of the Lorenz curve is that when two Lorenz
curves cross, it is ambiguous which income distribution is more
unequal.
d) The Gini coefficient.
· Definition
The Gini coefficient (GC) is a single number that aggregates the
information from a Lorenz curve.
· Computation
in Figure 2 is the area above the LC and below the 45-degree
line;
in Figure 2 is the entire area below the 45-line bounded by the
axes.
Figure 4
The domain of GC is , where the extremes are interpreted as
follows:

· => perfect equality
· => perfect inequality
Almost all countries have a GC ∈ [0.1, 0.6].
Rule of thumb classification:
=> close to perfect income inequality
=> low levels of income inequality
] => moderate levels of income inequality
=> high levels of income inequality
=> extremely high levels of inequality
e) Properties of the Gini Coefficient:
· anonymity – names of people don't matter, just incomes;
· population size independence – if clone a person into 2, GC
remains the same;
· unit independence – change the units in which income is
measured does not affect GC);
· the 'transfer principle' – holding all else constant, a transfer of
a small amount of income from a richer person to a poorer
person, GC declines.
4. Decomposition of income inequality in Canada.
a) Historical evolution of income inequality
· Time trends
A time trend is the ordered set of natural numbers, e.g., , that
measures the time span between observations. The slope of a
time-trend line represents the growth of a variable, e.g., Gini
coefficient.
Figure 5
Source: IRPP (2016)

A time trend allows us:
· to detect the general relationship through the slope (positive
vs. negative vs. flat),
· to detect whether the relationship is stable or exhibits
variability,
· to detect the type of variability: a break in the time trend vs.
cyclical variability.
A break in the time trend indicates an abrupt change in the
slope at a certain point in time. However, the slope before and
after the break in the time trend is relatively stable.
Cyclical variability in the Gini coefficient could be occurring
due to fluctuations in the price of oil for a country dependent on
the production of natural resources.
Time trends across countries (or provinces) could be used to
compare countries with respect to:
· initial conditions, e.g., Gini coefficient in 1976. The initial
conditions are captured by the differences in the vertical
intercept at 1976 between two regions.
· relative increase in income inequality over tine. The region
with a higher economic growth rate has a time trend with a
steeper slope.
· Within-regional income inequality
Figure 6 indicates that the Gini coefficient increased in every
province from 1985 to 2011. This implies that within-regional
income inequality increased over the period.
Figure 6
Source: IRPP (2016)
· Distribution of income growth gains
Figure 4 indicates that the gains were enjoyed almost
exclusively by the top 10 % of the population (the upper middle

class and the rich). Those who gain the most are the top 0.01 %
and 0.1 % of the population.
Figure 7
Source: IRPP (2016)
This type of unbalanced growth in income shares could have
important implications on:
· Reducing the size of the middle class;
· Increasing poverty rates even when average income is
growing.
Figure 8 indicates that the unbalanced growth across income
groups led to a rapid increase in the income share of the top 1 %
during the examined period.
Figure 8
Source: IRPP (2016)
· Functional income inequality
Functional aspects of income inequality refer to the source of
income:
· Capital income;
· Labour income.
Who were the gainers?
Figure 9 reveals that the share of labour income declined from
1982 to 2008. This implies that the gains were overwhelmingly
captured by capital income earners.
Figure 9
b) Key insights
Income inequality in Canada increased since 1980.
There were three driving forces behind this increase:
· Within-regional inequality increased in every province, while
regional inequality decreased.

· The gains in income inequality were captured exclusively by
the very top income brackets.
· The share of capital income at the expense of the share of
labour income.
2
Property Rights and Income Disparities across First Nations
Reserves
1. Introduction.
a) Key analytical tools and regional inequality
In the previous two topics, we have developed a key set of
analytical tools:
· measuring economic inequality,
· analyzing time trends,
· building an economic model of economic growth.
We have built these analytical tools to explain key facts about
regional inequality across Canadian provinces with respect to:
· short-run dynamics (convergence to a steady state),
· long-run dynamics (elimination of regional inequality for
unconditional convergence vs. persistent regional inequality for
conditional convergence).
b) Focus of this topic
Figure 1
Source: Aragon (2015)
In this lecture, we will attempt to explain why there is a
growing income disparity between two groups First Nations
reserves that differ with respect to treaties status:
· First Nations reserves with treaties;

· First Nations reserves without treaties.
Figure 2
Figure 2 shows that the two groups of reserves had:
· comparable initial conditions (higher income per capita for
treaty FNRs),
· similar income growth rates until the early 1990s.
Two structural breaks, one in the early 1990s and one in the
early/mid 2000s, led to growing income disparities between the
two groups.
These two structural breaks closely follow two waves of modern
treaties (Comprehensive Land Claim Settlements) between
federal/provincial governments and First Nations bands. Until
then, the only type of treaties in place were historical treaties
signed prior to 1923.
The mechanism through which modern treaties could be
influencing an increase in average income on FNRs is through
improved property rights and more specifically reduced
transaction costs.
According to Aragon (2015), modern treaties clarify property
rights by:
· delimiting the boundaries,
· specifying the property rights to the land and natural
resources.
The improved property rights lower transaction costs (e.g.,
expenses incurred for legal disputes) that have the following
implications:
· $ 1 of savings translate into $ 1 of investment in the absence
of transaction costs,

· $ 1 of savings translate into less than $ 1 of investment in the
presence of transaction costs.
We are going to use this framework of transaction costs and
integrate it into the Solow growth model.
c) Economic significance of raising living standards on FNRs
Why should be concerned about the economic implications?
The average income in approximately 80 % of FNRs is below
the national poverty line (Statistics Canada, 2016).
The poverty rates among the Aboriginal population are
disproportionately higher relative to those of the entire
Canadian population.
To this end, Figure 3 provides a time trend of the poverty rate
for the Aboriginal population living off-reserve. However, the
poverty rate among FNRs on-reserve is substantially larger
relative to those living off-reserve (Statistics Canada, 2019).
Figure 3
Source: FRPP (2016)
The encouraging data from Figure 4 is that more Aboriginal
people get out of poverty than fall into it in the period 2005 –
2010 relative to the period 1993 – 1998.

An interesting question is to what extent is this reduction in
poverty rates among FNP contributable to treaty rights.
Figure 4
Source: IRPP (2016)
2. Solow model with transaction costs.
a) Overview
In this lecture, we will augment the Solow model from the
previous lecture with transaction costs. To capture this idea, we
will modify the assumption, , i.e., $ 1 of savings is translated
into $ 1 of investment into new capital.
The modified assumption is, , where measures the aggregate
transaction costs that could take the form of legal fees to
establish property rights.
The corresponding per worker equation is, where measures the
per worker transaction costs. Graphically, the savings function
shifts downwards, and it no longer passes through origin.
Figure 5
There are two main implications of introducing transactions
costs that affect:
· the equilibrium equation, which now becomes ,
· the two steady states, both of which take on positive values.

The lower steady state is now economically meaningful.
As a result, both the short-run and long-run dynamics of
regional inequality could differ remarkably from the baseline
model introduced in the previous lecture.
b) Steady state equilibria and transitional dynamics
The steady state equilibria occur at the intersection of the
savings curve and the capital requirement curve as shown in the
previous lecture.
Numerical example:
In addition, suppose that and . Solve for the equilibrium state.
Start with the equilibrium condition:
Substitute the production function into it:
Insert the numerical values into it:
Use a variable substitution, , to derive a quadratic equation.
Re-arranging yields:
It is more convenient to work this equation if both sides are
multiplied by 5:

To find the roots of the quadratic equation, you may use the
formula:
They are and .
Substituting back each steady state into yields the steady states
of capital per worker: and .
Figure 6
Quiz: Identify the typo in Figure 6.
The corresponding steady state levels of output per worker and
consumption per worker are determined as follows.
Figure 7
c) Key insights
· Income disparities
The unstable steady state equilibrium occurs for and is now

economically meaningful. The Solow growth model can now
explain why:
· long-run differences between FNRs could persist even if they
share the same parameter values.
This occurs if some FNRs are at the high steady state, , while
the other FNRs are at the low steady state, . Unlike the model
without transaction costs, this income disparity occurs for the
same parameter values.
· long-run income disparities between FNRs could be
perpetually increasing even if they share the same parameter
values.
This occurs for a specific set of initial conditions:
For FNRs with initial conditions, , income per worker grows
until they reach the steady state, .
For FNRs with initial conditions, , income per worker
perpetually declines.
The transitional dynamics associated with these transitional
dynamics could be easily verified for the numerical example at
hand.
For
Let’s verify if indeed
For
Let’s verify if indeed

Due to the positive relationship between and , this implies that
whenever , it is also the case that .
· Poverty trap and big push policy
The transitional dynamics in the preceding section imply that
for any , a FNR finds itself in a poverty trap. In each
subsequent period, both capital per worker and output per
worker decline.
To escape a poverty trap, a FNR requires sufficiently largely
investment such that the capital stock per worker exceeds . This
is necessary to change the nature of the transitional dynamics
for a FNR to escape from the poverty trap.
Changes in the transitional dynamics to the extent that an
economy starts to converge to a different equilibrium is an
example of a big push policy.
In our context, a sufficiently large investment acts as a big push
policy. Due to the small population size of most FNR, even a
single large project is capable of letting a FNR escape the
poverty trap.
3. Empirical evidence.
a) Key facts and model predictions
Figure 1 indicates that there is:
· a growing income disparity between the treaty FNRs and the
non-treaty FNRs,
· Income per capita of both treaty FNRs and non-treaty FNRs
grew over time.

Figure 1
The Solow model with transaction costs could explain each one
of the facts in isolation but not both simultaneously.
b) Challenging the closed economy assumption
The closed economy assumption is not reasonable for most
FNRs for the following two reasons:
· FNRs rely on various forms of government assistance
generated outside of the FNR economy,
· Large-scale investment in the capital stock is generated
outside of the FNR economy and not through savings within the
FNRs.
The implication of modifying could reconcile the model’s
predictions with the key facts.
· Government programs
Government assistance programs primarily increase
consumption and, therefore, do not increase the capital stock.
This implies that income per capita rises but output per capita
does not.
In fact, it is possible FNRs to experience a declining capital per
worker and output per worker, while income per capita is rising
due to government assistance programs.
· Investment projects
A large-scale investment project could contribute to a large

increase in capital per worker in a single period such that a FNR
escapes the poverty trap.
The corresponding large increase in output that occurs in a
single period allows domestic savings to also increase
dramatically. Even if outsiders stop investing into the FNR, the
domestic savings generated in the FNR are sufficient to sustain
and change the nature of the transitional dynamics.
c) Final remarks
By augmenting the Solow model with transaction costs and
modifying the closed economy assumption, we were able to
explain:
· the poverty trap many FNRs face,
· the income disparities between treaty FNRs and non-treaty
FNRs.
2
Economic Growth, Regional Inequality and Fiscal Federalism
1. Economic growth and regional inequality.
a) Objectives
In the previous lecture, we found evidence that regional
inequality has followed an inverted U-shape by first increasing
until the 1930s and then decreasing since then.
In this lecture, we would like to build economic theory that
helps us:
· Identify the economic forces that contribute to a high standard

of living.
· Identify the economic forces that give rise to regional
differences in living standards in the short-run and long-run.
· Describe the role of government policy in contributing to high
standard of living and alleviating regional income inequality.
b) Relationship between economic growth and income
To address the objectives of this lecture, we first need to
explore the dynamic relationship between income (GDP per
capita) and economic growth.
Income grows exponentially over time as the level of income in
each year depends on the income level of the preceding year,
i.e., , where is aggregate income in year and is the economic
growth rate.
To calculate the average growth rate, , over an extended period
of time, we must use the following relationship.
We will use this equation to solve for .
Note: In the absence of population growth, the ratio of
aggregate income, , equals the ratio of per capita income, .
Table 1 demonstrates that a small difference in the average

economic growth rate could contribute to closing in a large gap
between two income capita of two countries.
Table 1
Country
Real GDP per capita 1870
Real GDP per capita 2006
Annual growth rate
1870-2006
Australia
3,273
24,343
1.5 %
Canada
1,695
24,951
2.0 %
For cross-country inequality between Australia and Canada to
decrease, we require that for the initial conditions , . This
framework could be expanded to study the impact of regional
inequality among Canadian provinces.
c) Causes
· Economic forces
In this lecture, we are going to build an economic model using
mathematical tools to address the objectives set in this lecture.
An economic model is a simplified version of reality that allows
us to observe, understand, and make predictions about economic
behaviour. The purpose of a model is to take a complex, real -
world situation and pare it down to the essentials by abstracting
away from non-relevant characteristics.

A useful model is:
· is simple enough to be understood while complex enough to
capture key information,
· able to provide predictions that explain phenomena observed
in the data.
Economic models rely on:
· algebra to provide precise relationships,
· graphs to illustrate the key ideas.
2. Economic Growth Model.
a) Model overview
In this section, we will go over the Solow growth model, which
is used to:
· Identify the economic forces that contribute to economic
growth,
· Explain why regional income disparities across provinces (or
countries) may narrow/widen/persist over time.
b) Setup of the model:
· Per-worker variables (small letters) and aggregate variables
(capital letters).
Output:
Capital:
Consumption:
The aggregate production function is given by

In the aggregate production function: capital, and labour, are
the inputs used to produce output, . Typically, we assume that
more input of each input increase output. In addition, is a
productivity parameter that measures the ability of a province
(or country) to produce more output by using the same number
of inputs.
Per worker production function:
We will primarily work with the per worker production function
as will be interested in comparing per worker/per capita living
standards, i.e., abstracting away from population size.
c) Steady state equilibrium:
Two opposing forces:
· savings: , where s is the savings rate.
We will assume that all savings are invested into new capital.
· capital requirement: , where is the population growth rate
and is the depreciation rate.
The capital requirement indicates how much capital needs to be
replenished to replace the obsolete capital stock (e.g. retired
equipment) and to keep up with an increasing population.
Equilibrium condition:
In equilibrium, the investment in per worker capital stock just
replenishes the obsolete capital stock per worker and accounting
for population growth.
Figure 1

Source: Williamson (2013)
· Endogenous and exogenous variables:
· endogenous variables – variables determined in the model ()
· exogenous variables – variables whose value is taken as given
(); also known as parameters.
· Steady state equilibrium:
In a steady state, a variable maintains the same value over time.
· What makes a steady state an equilibrium?
- initial value of k.
show k remains equal to
If because amount of created capital equals amount of
destroyed capital.
Then, i.e., stays constant.
· What makes a steady state equilibrium stable?
Step 1:
, show converges to
If ,
keeps on increasing until it reaches .

Step 2:
, show converges to
If ,
keeps on decreasing until it reaches .
No matter what the initial value converges to . If this statement
is not true, the equilibrium is unstable.
If an economy is not in a steady state equilibrium, it does not
converge instantaneously to a steady state. This process occurs
over a number of periods as gets closer and closer to the
equilibrium.
d) Model predictions:
· Convergence
· provinces converge to the same (differences in living
standards across provinces should disappear over time if
provinces have the same values for the parameters .
· provinces converge to the same because
· provinces converge to the same because .
Numerical example:
Suppose that the per capita production is given by . In addition,
and .
Solve for the steady state values of , , and .

There are two steady states:
implies that
is equivalent to and to
This implies that .
· Unconditional vs. Conditional convergence.
· Unconditional convergence:
If provinces have identical characteristics, i.e., the same value s

for all the parameters used in the model Provinces converge to
the same steady state, and .
· Conditional convergence:
If provinces could have different characteristics, i.e., they differ
in the values for at least one of the parameters in the model .
· Main implications of convergence:
Each country converges to a different steady state and .
Conditional convergence can potentially explain why provinces
differ in their standard of living (GDP per capita).
Why potentially? Parameter values of must be such that they
predict for each country that is consistent with the data.
For instance, the model may predict that (Alberta) (Ontario),
while in the data we observe (Alberta) (Ontario).
If model makes predictions that are inconsistent with the data,
either the model's assumptions should be modified or the model
should be entirely abandoned.
e) Empirical evidence
· Convergence measurement
A crude way to check for unconditional convergence is to
explore whether we require that for , the relationship between
average growth rates, , is maintained. This relationship must
hold for each pair of provinces.
Figure 2 provides no evidence of unconditional convergence

since indicates that , which is contrary to the model predicts.
Figure 2
We will explore an alternative, more sophisticated method, for
checking for convergence called Sigma ()-convergence.
Sigma ()-convergence occurs when the dispersion of the income
levels across provinces tends to decrease over time. That is, ,
i.e., sigma convergence declines in each subsequent year.
Provinces are in proximity to the steady state as .
Figure 3
· Evidence
Figure 3 reveals that there is evidence of:
· unconditional convergence for all provinces until the 1970s
and,
· unconditional convergence for the non-resourced based
provinces since the 1970s.
For detect unconditional convergence, there must be a steady
downward-sloping time trend over time without sizable
fluctuations.

Figure 4 reveals that the provinces whose economies are
resource-based (Alberta, Saskatchewan, Newfoundland and
Labrador) appear to have different characteristics than the rest
of the provinces with respect to the composition of the
economies.
In addition, the fluctuations Figure 3 since the 1970s
correspond to fluctuations in oil prices and other natural
resources.
Figure 4
f) Economic Policies:
· Increasing living standards:
Government policy could target any of the following
parameters:
· savings rate (e.g., mandatory pension plans CPP/QPP);
· population growth rate (e.g., lower birth rates);
· productivity (e.g., technological improvements as well as
improvements in both public and corporate governance);
· any additional parameters introduced into the model.
· Comment about sources of long-term growth:
· Role of productivity

Raising productivity is the only source to achieving sustained
long-term growth. Why? There are bounds on and, and
respectively.
· Decreasing regional income disparities:
Two policies approaches:
· Equalize parameters of ‘have-not’ provinces to those of
‘have’ provinces.
· Redistribute income from the have provinces to the have-not
provinces.
3. Fiscal federalism and equalization payments.
a) Program details
The equalization payments (EP) program is a redistributive
program run by the Canadian federal government that
redistributes income to ‘have-not’ provinces.
The main rationale for running the EP program is that it could
speed up the convergence to the same steady state in the
presence of unconditional convergence.
In the case of conditional convergence, the main impact of the
policy would be towards bridging the gap in current incomes but
not addressing the underlyi ng problem of regional disparities
due to convergence to different steady states.
A controversial component of this policy has been that there are
no strings attached as to how the redistributed funds are spent
by provincial governments.

b) Economic effects of the EP program
· Increases in investment vs. consumption influences short-term
economic growth.
Whether the equalization payments program has an impact on
economic growth, it is critical whether it is spent on
government consumption or on government investment projects.
· If on government investment, it increases total investment, and
in turn, it increases future output.
· If on government consumption, it increases only current
output at the program has no impact on future output.
In the program as it stands, there are no strings attached to
spend any of the equalizations on investment projects or human
capital initiatives.
The debate whether to allocate more resources to investment
(equivalent to future consumption) or to consumption
(equivalent to current consumption) is not resolved. It is more
of a question how much of it achieves the right balance.
· Empirical evidence
Figure 5
The equalization payments program has contributed to bridging
the regional income disparities at two levels:
· Current income levels,
· Future income levels (in transition to a steady state).
The controversial aspect of the EP program has been the second
aspect.

Figure 4 provides evidence that over time provinces have
become less reliant on EP to finance public services.
2
Labour Outcomes Disparities and Government Programs
1. Redistributive government policies.
a) Overview
In the introductory lecture, we have presented evidence that
government policies have a major offsetting effect against
rising income inequality. Figure 1 captures this offsetting effect
by the difference between the Gini coefficient of market income
and the Gini coefficient after taxes and transfers.
Figure 1
Source: IRPP (2016)

In this lecture, we will explore the role of redistributive
government policies as a mitigating factor against rising market
income inequality. Redistributive policies are ‘tax and transfer’
policies, in which use tax revenue to fund social program (e.g.,
childcare) or to provide income support to individuals (e.g.,
social assistance program, employment insurance).
Redistributive government policies commonly use as tools:
· Taxing income of high-income earners,
· Provide transfers (or income subsidies) to low -income earners.
Note that other types of government policies, such as regulatory
policies, could also have a redistributive impact. However,
regulatory policies they are not redistributive, i.e., tax and
transfer, by design. For instance, the immigration policies we
have touched on are regulatory in nature but could have major
redistributive impact on the capital and labour income shares.
b) Types of redistributive programs
Figure 2
Source: IRPP (2016)
Figure 2 represents five major redistributive programs run by
federal and provincial governments.
In this lecture, we will analyze the impact social
assistance/employment insurance and child benefits programs
on labour outcomes. In a subsequent lecture, we will discuss the
economic impact of government pension plans (CPP/QPP) and
old age security.
The use of policies that encourage (e.g., subsidies, benefits) or
discourage (e.g., taxes) a particular type of behaviour that may
unintentionally impact employment even if their objective is to
redistribute income.
Figure 2 panel b) reveals that the spending on child benefits
programs is relatively stable over time with a structural break in
the earl 2000s when Quebec introduced the government-run
childcare program. In contrast, other provinces continued with
the existing policy of providing child benefits.

1. This question is on the application of the Binomial option

1. This question is on the application of the Binomial option

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