Homework 5
1)
a) the IS curve: ln Yt= ln Y(t+1) – (1/Ɵ)rt
so the slope is: drt/dyt (is) = -Ɵ/Yt. That means that an increase in Ɵ will result in a steeper curve.
LM curve: Mt/Pt = Yt^(Ɵ/v) (1+rt / rt)^(1/v)
Ln(Mt/Pt) = (Ɵ/v) ln Yt +(1/v)ln(1+rt) – (1/v)ln rt.
0 = (Ɵ/v)(1/Yt)dYt + (1/v)(1/(1+rt)) drt – (1/v)(1/rt)drt.
The slope is: drt/dyt (LM) = (Ɵrt(1+rt))/Yt. That means that an increase in Ɵ will result in a steeper curve.
b) the curve IS is not affected by the value of V. while curve LM shifts upwards, since a decrease in v will result in an increase for the demand for real money.
c) IS is not affected byΓ(.)
optimal money holdings: BΓ’(Mt/Pt) = (it/(1+it)) U’(Ct)
B(Mt/Pt)^(-v) = (it/1+it) Yt^-Ɵ
Mt/Pt= B^(1/v) Yt^(Ɵ/v) (1+rt/rt)^(1/v)
So this means that the LM curve will shift downwards.
2)
a) AC= (PC/)+(αYP/2)i
AC/ = -(PC/^2) + (αYP/2)I = 0
C/^2 = αYi/2
So *=(2C/αYi)^(1/2)
b) average real money holdings:M/P= αY/2
M/P = (αY/2) (2C/αYi)^(1/2)
M/P= (αCY/2i)^(1/2)
Ln(m/p) = (1/2)(lnα+lnY+lnC-ln2-lni)
(1/(M/P))((M/P)/i) = -(1/2)(1/i)
Elasticity of real money with respect to i: ((M/P)/)(i/(M/P)) = -1/2
The elasticity with respect to Y : ((M/P)/Y)(Y/(M/P)) = ½
Average real money holdings increase in Y, and decrease in i.
4)
a)when p is at a level that generates maximum output, LS meets LD.
b) when p is above the level that generates maximum output, will cause unemployment.
7)
a)
b)i)
ii)
iii)
13)
a) the asset has an expected rate of return r. capital gain/loss plus dividends per unit time = rvp. There is no dividends per unit time while searching for the palm tree, and there is b probability per unit time of capital gain of (vc-vp)-c. the difference in the price of the asset is(vc-vp) and –c is what the asset pays, so at the end we have rvp=b(vc-vp-c)
b) there is probability aL that a person will find another person with a coconut and trade with that person and gain u̅. the difference in the price of the asset is (vp-vc). So we end up with
rvp=al(vp-vc+u̅).
c) vp=(rvc/aL)+vc-u̅.
r((rvc/aL )+vc-u̅)= b(vc-(rvc/aL)-vc+u̅-c)
vc(r(r+aL+b))/aL = u̅(r+b)-bc
the value of being in state C: vc= (aL(u̅(r+b)-bc)) / r(r+aL+b)
the value of being in state p: vp= ((u̅(r+b)-bc)/(r+aL+b)) + (aL(u̅(r+b)-bc)/r(r+aL+b)) - u̅
so finally
vc-vp = (bc+u̅aL)/(r+aL+b).
e) vc-vp ≥c
vc-vp = (bc+u̅a(b/a))/(r+a(b/a)+b) = (bc+bu̅)/(r+2b)
(bc+bu̅)/(r+2b) ≥ c
That means that
Bc+bu̅≥c and c(r+2b-b) ≤ bu̅
So finally we have
c≤ bu̅ / (r+b).
f) it is a steady-state equilibrium for no one who finds a tree to climb it for any value of c>0.
Yes there are values of c which there is more than one steady-state equilibrium for 0<c< bu̅/(r+b)
Yes, L = b/a has a higher welfare than L=0. When L=0 people don’t gain any utility since they don’t climb a tree and don’t have a chance to trade with other people and gain a coconut.
0 1 2 3 4 5 -3 -2.2000000000000002 -1.8 -1.8 -2.2000000000000002 -3
0 1 2 3 4 5 7 6.5 5.5 3.5 1
0 1 2 3 4 -2 -2.5 -3.5 -5.5 -8
LD.
Advanced macroeconomics, 4th edition. Romer.
Chapter12.
12.1. The stability of fiscal policy. (Blinder and Solow, 1973.) By definition, the budget deficit equals the rate of change of the amount of debt outstanding: δ(t) ≡ D ̇(t). Define d(t) to be the ratio of debt to output: d(t) = D(t)/Y(t). Assume that Y(t) grows at a constant rate g > 0.
(a) Suppose that the deficit-to-output ratio is constant: δ(t)/Y(t) = a, where a > 0.
̇
(i) Find an expression for d(t) in terms of a, g, and d(t). ̇
(ii) Sketch d(t) as a function of d(t). Is this system stable?
(b) Suppose that the ratio of the primary deficit to output is constant and equal to a > 0. Thus the total deficit at t, δ(t), is given by δ(t) = aY(t) + r(t)D(t), where r(t) is the interest rate at t. Assume that r is an increasing function of the debt-to-output ratio: r(t) = r(d(t)), where r′(•) > 0, r′′(•) > 0, limd→−∞ r(d) < g, limd→∞ r(d) > g.
̇
(i) Find an expression for d(t) in terms of a, g, and d(t). ̇
(ii) Sketch d(t) as a function of d(t). In the case where a is sufficiently small that d ̇ is negative for some values of d, what are the stability properties of the system? What about the case where a is sufficiently large that d ̇ is positive for all values of d ?
12.2. Precautionary saving, non-lump-sum taxation, and Ricardian equivalence.
(Leland, 1968, and Barsky, Mankiw, and Zeldes, 1986.) Consider an individual who lives for two periods. The individual has no initial wealth and earns labor incomes of amounts Y1 and Y2 in the two periods. Y1 is known, but Y2 is random; assume for simplicity that E[Y2] = Y1. The government taxes income at rate τ1 in period 1 and τ2 in period 2. The individual can borrow and lend at a fixed interest rate, which for simplicity is assumed to be zero. Thus second-period consumption is C2 = (1 − τ1)Y1 − C1 + (1 − τ2)Y2. The individualchoosesC1 tomaximizeexpectedlifetimeutility,U(C1)+E[U(C2)].
(a) Find the first-order condition for C1.
(b) Show that E[C2] = C1 if Y2 is not random or if utility is quadratic.
(c) Show that if U ′′′(•) > 0 and Y2 is random, E[C2] > C1.
(d) Suppose that the government marginally lowers τ1 and raises τ2 by the same amount, so that its expected total revenue, τ1Y1 + τ2E[Y2], is un- changed. Implicitly differentiate the first-order condition in part (a) to find an expression for how C1 responds to this change.
(e) Show that C1 is unaffected by this change if Y2 is not random or if utility is quadratic.
(f) Show that C1 increases in response to this change if U ′′′(•) > 0 and Y2 is random.
12.3
Consider the Barro tax-smoothing model. Suppose that output, Y, and the real interest rate, r, are constant, and that the level of government debt out- standing at time 0 is zero. Suppose that there will be a temporary war from time 0 to time τ. Thus G(t) equals GH for 0 ≤ t ≤ τ, and equals GL there- after,whereGH >GL.Whatarethepathsoftaxes,T(t),andgovernmentdebt outstanding, D(t)?
12.4
Consider the Barro tax-smoothing model. Supp.
Problem Set 4Due Tuesday, April 12ECON 434 Internati.docxsleeperharwell
Problem Set 4
Due: Tuesday, April 12
ECON 434: International Finance and Macroeconomics
Penn State: Spring, 2016
1. Government Budget Constraints. This problem looks at the feasibility constraints facing the
government and the sustainability of current-account balances. This will generalize some of the results
we obtained in class.
__ Consider an economy that lasts for N periods. In period t, the government purchases Gt dollars
worth of goods, and it collects Tt dollars worth of taxes. The government can also purchase B
g
t bonds
in period t; if it holds B
g
t bonds in period t, then it receives (1 + r)B
g
t bonds in period t + 1. (For
simplicity, assume that the interest rate r is constant.) If B
g
t < 0, then it means the government is in
debt.
(a) What is the government's period-t budget constraint? (Your answer should contain Gt, Tt, B
g
t ,
and r.)
(b) How do you compute the primary �scal de�cit in period t? How do you compute the secondary
�scal de�cit in period t?
(c) Combine the period budget constraints for t = 1, . . . ,N to show that:
B
g
0 +
N∑
t=1
Tt
(1 + r)
t
=
N∑
t=1
Gt
(1 + r)
t
+
B
g
N
(1 + r)
N
. (1)
(d) Suppose that N is a �xed, �nite number. What condition does B
g
N have to satisfy, and why?
(e) Individuals who pay taxes have �nite lives, but institutions, such as governments, can live a long
time, possibly forever. This leads to the possibility that a government could, in principle, keep
rolling over its debt, even as generations of citizens come and go.1 Mathematically, we model this
by letting N →∞. What condition does B
g
N
(1+r)N
have to satisfy as N →∞? Explain your answer
in words.
(f) Suppose that the government starts out in debt, with B
g
0 < 0. Is it possible for the government
to run primary de�cits forever? Why or why not?
(g) Now, suppose that the government starts out with positive assets B
g
0 > 0. We'll look at the case of
an in�nitely-lived government (N = ∞), and we'll assess whether it's possible for the government
to make purchases while never taxing its citizens (i.e., Tt = 0, for t = 1,2, . . .).
__ Consider the following plan. Before making purchases in period t, the government has
(1 + r)B
g
t−1 dollars at its disposal from the interest it earned on its previous period's assets.
The government decides to take a fraction δ of this money to spend on period-t government
purchases Gt; the remaining fraction 1−δ is used to buy more bonds.
i. Provide an expression for B
g
t in terms of B
g
t−1, and provide an expression for Gt in terms of
B
g
t−1. (Both expressions will depend on δ and r.)
ii. Provide an expression for B
g
t in terms of B
g
0 and t, and provide an expression for Gt in terms
of B
g
0 and t. (Both expressions will depend on δ and r.)
1For an example, see �The Case of the Undying Debt� by François Velde: https://www.chicagofed.org/publications/working-
papers/2009/wp-12.
1
iii. In each period t, does the government run a primary surplus or de�cit.
1. This question is on the application of the Binomial optionAbbyWhyte974
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.
COMP0041 SEE NEXT PAGE
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.
COMP0041 SEE NEXT PAGE
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
...
1. This question is on the application of the Binomial optionSantosConleyha
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.
COMP0041 SEE NEXT PAGE
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.
COMP0041 SEE NEXT PAGE
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
...
Econ 3022 MacroeconomicsSpring 2020Final Exam - Due A.docxtidwellveronique
Econ 3022: Macroeconomics
Spring 2020
Final Exam - Due April 24th 11:59pm
1 Multiple Choice Questions (5 points each)
Question 1 What is Ricardian Equivalence?
(a) The economic hypothesis that agents’ decisions are una↵ected by the timing of taxation
and government spending
(b) The economic hypothesis that agents’ decisions are a↵ected by the timing of taxation
and government spending
(c) The economic hypothesis that taxation must be equal every period.
(d) The economic hypothesis that it is impossible to individually identify taxation today
and taxation tomorrow.
Question 2 Consider the consumer problem from the microeconomic foundations we dis-
cussed in class. Suppose the wage decreases. What do we expect to happen to house-
hold labor supply?
(a) Unclear
(b) Increase
(c) Decrease
(d) Stay constant
1
Question 3 Consider the consumer problem from the real intertemporal model. Which of
the following conditions must be satisfied at the solution?
(a) MRSl,c = w
(b) MRSc0,l0 =
1
w0
(c) MRSl,l0 =
w(1+r)
w0
(d) All of the above
Question 4 If total factor productivity tomorrow, z0, increases. What should happen to
investment?
(a) Unclear
(b) Increase
(c) Decrease
(d) Stay constant
Question 5 Consider the standard Solow model from class where the production function
is zF (K, N) = zK↵N1�↵. What is the golden rule savings rate?
(a) sgr = 1 � ↵
(b) sgr = ↵
(c) The savings rate that leads to a steady state with the highest level of income per capita
(d) The savings rate that leads to a steady state with the lowest level of income per capita
2
2 Economic Growth (20 points)
Consider the Solow Growth Model seen in class where the production function is Cobb-
Douglas and given by:
Y = zK↵ (N)
1�↵
where 0 < ↵ < 1 and z is a constant. Let s be the savings rate of this economy, so that
aggregate savings is just a constant fraction of aggregate output: S = sY . Let n be the rate
of population growth, so N
0
N
= 1 + n. Finally, let d be the depreciation rate, and assume the
law of motion for aggregate capital is given by:
K
0 = (1 � d) K + I
(a) (5 pts) Find an expression for the steady state level of capital per capita (k⇤) that only
depends on parameters of the model. Clearly show your work.
(b) (5 pts) Discuss how per capita variables (consumption and income) as well as aggregate
variables (consumption, capital stock, output, and savings) behave in steady state.
Now, suppose that we have a linear production function given by
Y = zK
where z is a constant. Let s be the savings rate of this economy, so that aggregate savings
is just a constant fraction of aggregate output: S = sY . Let n be the rate of population
growth, so N
0
N
= 1 + n. Finally, let d be the depreciation rate, and assume the law of motion
for aggregate capital is given by:
K
0 = (1 � d) K + I
(c) (5 pts) Find an expression for the level of per capita capital stock today as a function
of per capita capital stock tomorrow. Clea.
CVA In Presence Of Wrong Way Risk and Early Exercise - Chiara Annicchiarico, ...Michele Beretta
We will show how to calibrate the main parameter of the model and how we have used it in order to evaluate the CVA and the CVAW of a one derivative portfolio with the possibility of early exercise.
Advanced macroeconomics, 4th edition. Romer.
Chapter12.
12.1. The stability of fiscal policy. (Blinder and Solow, 1973.) By definition, the budget deficit equals the rate of change of the amount of debt outstanding: δ(t) ≡ D ̇(t). Define d(t) to be the ratio of debt to output: d(t) = D(t)/Y(t). Assume that Y(t) grows at a constant rate g > 0.
(a) Suppose that the deficit-to-output ratio is constant: δ(t)/Y(t) = a, where a > 0.
̇
(i) Find an expression for d(t) in terms of a, g, and d(t). ̇
(ii) Sketch d(t) as a function of d(t). Is this system stable?
(b) Suppose that the ratio of the primary deficit to output is constant and equal to a > 0. Thus the total deficit at t, δ(t), is given by δ(t) = aY(t) + r(t)D(t), where r(t) is the interest rate at t. Assume that r is an increasing function of the debt-to-output ratio: r(t) = r(d(t)), where r′(•) > 0, r′′(•) > 0, limd→−∞ r(d) < g, limd→∞ r(d) > g.
̇
(i) Find an expression for d(t) in terms of a, g, and d(t). ̇
(ii) Sketch d(t) as a function of d(t). In the case where a is sufficiently small that d ̇ is negative for some values of d, what are the stability properties of the system? What about the case where a is sufficiently large that d ̇ is positive for all values of d ?
12.2. Precautionary saving, non-lump-sum taxation, and Ricardian equivalence.
(Leland, 1968, and Barsky, Mankiw, and Zeldes, 1986.) Consider an individual who lives for two periods. The individual has no initial wealth and earns labor incomes of amounts Y1 and Y2 in the two periods. Y1 is known, but Y2 is random; assume for simplicity that E[Y2] = Y1. The government taxes income at rate τ1 in period 1 and τ2 in period 2. The individual can borrow and lend at a fixed interest rate, which for simplicity is assumed to be zero. Thus second-period consumption is C2 = (1 − τ1)Y1 − C1 + (1 − τ2)Y2. The individualchoosesC1 tomaximizeexpectedlifetimeutility,U(C1)+E[U(C2)].
(a) Find the first-order condition for C1.
(b) Show that E[C2] = C1 if Y2 is not random or if utility is quadratic.
(c) Show that if U ′′′(•) > 0 and Y2 is random, E[C2] > C1.
(d) Suppose that the government marginally lowers τ1 and raises τ2 by the same amount, so that its expected total revenue, τ1Y1 + τ2E[Y2], is un- changed. Implicitly differentiate the first-order condition in part (a) to find an expression for how C1 responds to this change.
(e) Show that C1 is unaffected by this change if Y2 is not random or if utility is quadratic.
(f) Show that C1 increases in response to this change if U ′′′(•) > 0 and Y2 is random.
12.3
Consider the Barro tax-smoothing model. Suppose that output, Y, and the real interest rate, r, are constant, and that the level of government debt out- standing at time 0 is zero. Suppose that there will be a temporary war from time 0 to time τ. Thus G(t) equals GH for 0 ≤ t ≤ τ, and equals GL there- after,whereGH >GL.Whatarethepathsoftaxes,T(t),andgovernmentdebt outstanding, D(t)?
12.4
Consider the Barro tax-smoothing model. Supp.
Problem Set 4Due Tuesday, April 12ECON 434 Internati.docxsleeperharwell
Problem Set 4
Due: Tuesday, April 12
ECON 434: International Finance and Macroeconomics
Penn State: Spring, 2016
1. Government Budget Constraints. This problem looks at the feasibility constraints facing the
government and the sustainability of current-account balances. This will generalize some of the results
we obtained in class.
__ Consider an economy that lasts for N periods. In period t, the government purchases Gt dollars
worth of goods, and it collects Tt dollars worth of taxes. The government can also purchase B
g
t bonds
in period t; if it holds B
g
t bonds in period t, then it receives (1 + r)B
g
t bonds in period t + 1. (For
simplicity, assume that the interest rate r is constant.) If B
g
t < 0, then it means the government is in
debt.
(a) What is the government's period-t budget constraint? (Your answer should contain Gt, Tt, B
g
t ,
and r.)
(b) How do you compute the primary �scal de�cit in period t? How do you compute the secondary
�scal de�cit in period t?
(c) Combine the period budget constraints for t = 1, . . . ,N to show that:
B
g
0 +
N∑
t=1
Tt
(1 + r)
t
=
N∑
t=1
Gt
(1 + r)
t
+
B
g
N
(1 + r)
N
. (1)
(d) Suppose that N is a �xed, �nite number. What condition does B
g
N have to satisfy, and why?
(e) Individuals who pay taxes have �nite lives, but institutions, such as governments, can live a long
time, possibly forever. This leads to the possibility that a government could, in principle, keep
rolling over its debt, even as generations of citizens come and go.1 Mathematically, we model this
by letting N →∞. What condition does B
g
N
(1+r)N
have to satisfy as N →∞? Explain your answer
in words.
(f) Suppose that the government starts out in debt, with B
g
0 < 0. Is it possible for the government
to run primary de�cits forever? Why or why not?
(g) Now, suppose that the government starts out with positive assets B
g
0 > 0. We'll look at the case of
an in�nitely-lived government (N = ∞), and we'll assess whether it's possible for the government
to make purchases while never taxing its citizens (i.e., Tt = 0, for t = 1,2, . . .).
__ Consider the following plan. Before making purchases in period t, the government has
(1 + r)B
g
t−1 dollars at its disposal from the interest it earned on its previous period's assets.
The government decides to take a fraction δ of this money to spend on period-t government
purchases Gt; the remaining fraction 1−δ is used to buy more bonds.
i. Provide an expression for B
g
t in terms of B
g
t−1, and provide an expression for Gt in terms of
B
g
t−1. (Both expressions will depend on δ and r.)
ii. Provide an expression for B
g
t in terms of B
g
0 and t, and provide an expression for Gt in terms
of B
g
0 and t. (Both expressions will depend on δ and r.)
1For an example, see �The Case of the Undying Debt� by François Velde: https://www.chicagofed.org/publications/working-
papers/2009/wp-12.
1
iii. In each period t, does the government run a primary surplus or de�cit.
1. This question is on the application of the Binomial optionAbbyWhyte974
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.
COMP0041 SEE NEXT PAGE
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.
COMP0041 SEE NEXT PAGE
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
...
1. This question is on the application of the Binomial optionSantosConleyha
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.
COMP0041 SEE NEXT PAGE
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.
COMP0041 SEE NEXT PAGE
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
...
Econ 3022 MacroeconomicsSpring 2020Final Exam - Due A.docxtidwellveronique
Econ 3022: Macroeconomics
Spring 2020
Final Exam - Due April 24th 11:59pm
1 Multiple Choice Questions (5 points each)
Question 1 What is Ricardian Equivalence?
(a) The economic hypothesis that agents’ decisions are una↵ected by the timing of taxation
and government spending
(b) The economic hypothesis that agents’ decisions are a↵ected by the timing of taxation
and government spending
(c) The economic hypothesis that taxation must be equal every period.
(d) The economic hypothesis that it is impossible to individually identify taxation today
and taxation tomorrow.
Question 2 Consider the consumer problem from the microeconomic foundations we dis-
cussed in class. Suppose the wage decreases. What do we expect to happen to house-
hold labor supply?
(a) Unclear
(b) Increase
(c) Decrease
(d) Stay constant
1
Question 3 Consider the consumer problem from the real intertemporal model. Which of
the following conditions must be satisfied at the solution?
(a) MRSl,c = w
(b) MRSc0,l0 =
1
w0
(c) MRSl,l0 =
w(1+r)
w0
(d) All of the above
Question 4 If total factor productivity tomorrow, z0, increases. What should happen to
investment?
(a) Unclear
(b) Increase
(c) Decrease
(d) Stay constant
Question 5 Consider the standard Solow model from class where the production function
is zF (K, N) = zK↵N1�↵. What is the golden rule savings rate?
(a) sgr = 1 � ↵
(b) sgr = ↵
(c) The savings rate that leads to a steady state with the highest level of income per capita
(d) The savings rate that leads to a steady state with the lowest level of income per capita
2
2 Economic Growth (20 points)
Consider the Solow Growth Model seen in class where the production function is Cobb-
Douglas and given by:
Y = zK↵ (N)
1�↵
where 0 < ↵ < 1 and z is a constant. Let s be the savings rate of this economy, so that
aggregate savings is just a constant fraction of aggregate output: S = sY . Let n be the rate
of population growth, so N
0
N
= 1 + n. Finally, let d be the depreciation rate, and assume the
law of motion for aggregate capital is given by:
K
0 = (1 � d) K + I
(a) (5 pts) Find an expression for the steady state level of capital per capita (k⇤) that only
depends on parameters of the model. Clearly show your work.
(b) (5 pts) Discuss how per capita variables (consumption and income) as well as aggregate
variables (consumption, capital stock, output, and savings) behave in steady state.
Now, suppose that we have a linear production function given by
Y = zK
where z is a constant. Let s be the savings rate of this economy, so that aggregate savings
is just a constant fraction of aggregate output: S = sY . Let n be the rate of population
growth, so N
0
N
= 1 + n. Finally, let d be the depreciation rate, and assume the law of motion
for aggregate capital is given by:
K
0 = (1 � d) K + I
(c) (5 pts) Find an expression for the level of per capita capital stock today as a function
of per capita capital stock tomorrow. Clea.
CVA In Presence Of Wrong Way Risk and Early Exercise - Chiara Annicchiarico, ...Michele Beretta
We will show how to calibrate the main parameter of the model and how we have used it in order to evaluate the CVA and the CVAW of a one derivative portfolio with the possibility of early exercise.
IIT JAM EN - Economics 2022 Question Paper | Sourav Sir's ClassesSOURAV DAS
IIT JAM Preparation Tips
IIT JAM Economics 2022 Question Paper
Economics Preparation
Sourav Sir's Classes
For any quarries feel free to contact us.
Call - 9836793076
Stochastic Local Volatility Models: Theory and ImplementationVolatility
1) Hedging and volatility
2) Review of volatility models
3) Local volatility models with jumps and stochastic volatility
4) Calibration using Kolmogorov equations
5) PDE based methods in one dimension
5) PDE based methods in two dimensions
7) Illustrations
It is not too late for you to hire our experts to tackle your assignment. All you have to do is send us a simple message saying, “I want to pay someone to do my public economics assignment.” Have your exam done by the best by contacting us at: info@economicshomeworkhelper.com or visiting our website http://bit.ly/3D2e59p
Inventory Model with Different Deterioration Rates under Exponential Demand, ...inventionjournals
An inventory model with different deterioration rates under exponential demand with inflation and permissible delay in payments is developed. Holding cost is taken as linear function of time. Shortages are allowed. Numerical examples are provided to illustrate the model and sensitivity analysis is also carried out for parameters.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Non-tradable Goods, Factor Markets Frictions, and International Capital FlowsGRAPE
International capital flows - data vs. theory
1 Feldstein-Horioka puzzle
• corr (S, I ) > 0 in the data
2 Lucas puzzle
• K has not flown to poor countries, despite
K
Y
poor
<
K
Y
rich
3 Allocation Puzzle
• corr (ΔTFP, Δexternal debt) < 0
4 Quantity Puzzle (not as famous as the other three)
• Neo-classical 1-sector model over-predicts international
capital flows by a factor of 10
• Gourinchas and Jeanne (REStud, 2013); Rothert (EL, 2016)
HLEG thematic workshop on Economic Insecurity, Walter Bossert, presenterStatsCommunications
HLEG thematic workshop on Economic Insecurity, 4 March 2016, New York, United States. More information at: http://oecd/hleg-workshop-on-economic-insecurity-2016
You are a project manager and believe that your initiative would be .docxadampcarr67227
You are a project manager and believe that your initiative would be more successful if you had a change manager on your team.
Describe
an actual project you have been part of (not necessarily the leader).
Develop
an argument to your manager on the importance of change management.
Describe
the role of a change manager and how it will benefit the project.
Write
a 1,050- word paper using a minimum of two peer-reviewed sources.
Format
your paper consistent with APA guidelines.
.
You are a project manager at a food agricultural organization and yo.docxadampcarr67227
You are a project manager at a food agricultural organization and you are assigned to review nutritional policies.
1). Write the nutritional policies
2). Identify five stakeholders and their roles in the implementation of the nutritional programs at the community level.
.
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IIT JAM EN - Economics 2022 Question Paper | Sourav Sir's ClassesSOURAV DAS
IIT JAM Preparation Tips
IIT JAM Economics 2022 Question Paper
Economics Preparation
Sourav Sir's Classes
For any quarries feel free to contact us.
Call - 9836793076
Stochastic Local Volatility Models: Theory and ImplementationVolatility
1) Hedging and volatility
2) Review of volatility models
3) Local volatility models with jumps and stochastic volatility
4) Calibration using Kolmogorov equations
5) PDE based methods in one dimension
5) PDE based methods in two dimensions
7) Illustrations
It is not too late for you to hire our experts to tackle your assignment. All you have to do is send us a simple message saying, “I want to pay someone to do my public economics assignment.” Have your exam done by the best by contacting us at: info@economicshomeworkhelper.com or visiting our website http://bit.ly/3D2e59p
Inventory Model with Different Deterioration Rates under Exponential Demand, ...inventionjournals
An inventory model with different deterioration rates under exponential demand with inflation and permissible delay in payments is developed. Holding cost is taken as linear function of time. Shortages are allowed. Numerical examples are provided to illustrate the model and sensitivity analysis is also carried out for parameters.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Non-tradable Goods, Factor Markets Frictions, and International Capital FlowsGRAPE
International capital flows - data vs. theory
1 Feldstein-Horioka puzzle
• corr (S, I ) > 0 in the data
2 Lucas puzzle
• K has not flown to poor countries, despite
K
Y
poor
<
K
Y
rich
3 Allocation Puzzle
• corr (ΔTFP, Δexternal debt) < 0
4 Quantity Puzzle (not as famous as the other three)
• Neo-classical 1-sector model over-predicts international
capital flows by a factor of 10
• Gourinchas and Jeanne (REStud, 2013); Rothert (EL, 2016)
HLEG thematic workshop on Economic Insecurity, Walter Bossert, presenterStatsCommunications
HLEG thematic workshop on Economic Insecurity, 4 March 2016, New York, United States. More information at: http://oecd/hleg-workshop-on-economic-insecurity-2016
You are a project manager and believe that your initiative would be .docxadampcarr67227
You are a project manager and believe that your initiative would be more successful if you had a change manager on your team.
Describe
an actual project you have been part of (not necessarily the leader).
Develop
an argument to your manager on the importance of change management.
Describe
the role of a change manager and how it will benefit the project.
Write
a 1,050- word paper using a minimum of two peer-reviewed sources.
Format
your paper consistent with APA guidelines.
.
You are a project manager at a food agricultural organization and yo.docxadampcarr67227
You are a project manager at a food agricultural organization and you are assigned to review nutritional policies.
1). Write the nutritional policies
2). Identify five stakeholders and their roles in the implementation of the nutritional programs at the community level.
.
You are a nursing educator and you are given an assignment to teach .docxadampcarr67227
You are a nursing educator and you are given an assignment to teach a RN/LPN NCLEX review course.
Please develop a complete review course power point presentation with detail speaker notes that will be used to teach the review in its entirely. You want student to pass the nclex exam on the first try. please rearrange order and at to it as you deem fit if I left out some thing (please insert pictures and diagram to enhance lecture) Please be very creative and colorful (Presentation to be shown to a large audience. Please be very detail but highlighting the most important detail.
The power points must include elements as follow:
1. nclex question types
2. steps of question analysis
3. critical thinking and rewording
4. how to dissect nclex question
5. what are considered hig level questions
6. deciding what is important
7. looking for patterns and relationships
8. identifying the problem
9. transferring knowledge from one situation to another
10. applying knowledge
11. discriminating between possible choices and/or course of action
12. evaluating according to criteria established
13. eliminating incorrect answer choices
14. strategies for alternate formate question: select all that apply
15. solving alternate formate questions: select all that apply.
16. prioritization
17. delegation
18. safety and infection control
19. maslow's hierarchy of needs
20. how to approach psychosocial condition question
21. how to answer psych questions
22. how to identify psych diagnosis and nursing care of the psychiatric patient
how to answer health promotion and maintenance question
23. tips on how to pass nclex exam
24. hot spot questions and how to solve them
25. fill in blank question and how to solve them and select all that apply
drag and drop question and how to solve them
26. tips on how to analyze a question
27. NURSING LAB VALUES TO KNOW
28. NURSING DRUGS TO KNOW AND LEVELS
INFORMATION ON THE FOLLOWING(with nursing most important intervention and things to watch for/ complication problems up each system)
Care of the pediatric patient
Care of OB (maternity) patient
Care of a pre-op patient
Care of a patient post op
Care of a respiratory patient
Care of a cardiac patient
Care of a gastro/intestinal patient
Care of caner patient
Care of urinary system patient
endoceine system
liver
pancreas
nutritional problem
chronic neurological problems
stroke
intracranial problems
muscle skeletal problems
emergency, terrorism and disaster nursing
fluid and electrolytes
the different in IV solution
Administering Blood
Conscious sedation
Reproductive system
nutrition for a newborn
drug calculation
Immunization when due and side effect
Kidney disorders and care of a renal patient with labs
Diabetes management
spinal cord injury
musculoskeletal problem
alzheimer's disease
ABG interpetation
drug calculation
oxygen supplement and delivery system
integumentary system
bur.
You are a paralegal working at law office of James Adams, Esq. On No.docxadampcarr67227
You are a paralegal working at law office of James Adams, Esq. On November 10, 2010, Adams is assigned by the court to represent John Edwinson, against whom a paternity petition has been filed. There is a hearing scheduled for march 13, 2011. Edwinson is not a cooperative client. He frequent misses appointment at the law firm office. Frustrated, Adams sends Edwinson a short letter on March 1,2011 that says, " Due to your noncooperation, I am withdrawing from the case as your representative effective immediately." Any ethical problem
.
you are a paralegal working at the law office of Smith & Smith. The .docxadampcarr67227
you are a paralegal working at the law office of Smith & Smith. The office represents David Gerry in a divorce action against his wife, Lena Gerry. One of the disputes is how to divide business assets acquired during the marriage. In an effort to pressure Lena to divide the assets in his favor, David tells his attorney to request sole physical and legal custody of their children even though David has no desire to raise the children. He knows, however, that Lena is terrified at the thought of losing sole custody herself. David wants his attorney to engage in extensive discovery (depositions, interrogatories, etc.) On the custody issue for the sole purpose of wearing Lena down in hope that she will reduce her claims on the business assets. Any ethical problems?
.
You are a police officer who has been selected to participate in a p.docxadampcarr67227
You are a police officer who has been selected to participate in a public relations task force to address a growing problem: the negative public perception of the police.
The media has been tough on departments around the city, and the police chief wants to address the issue head on. You just completed the first task force meeting, and the facilitator wants you to present information and recommendations regarding how to change the public’s perception.
Create
an 8- to 10-slide Microsoft® PowerPoint® presentation in which you:
Explain how an inductive fallacy (e.g., generalizations, weak analogy) or a fallacy of language (e.g., confusing explanations) may affect the public perception of the police.
Provide a categorical claim related to the negative public perception of the police.
Create a visual showing a categorical relation that is negative between the police and the public.
Provide recommendations and examples about what the department can do to:
Change the perception
Develop a positive relationship with the public.
Include
comprehensive speaker notes.
Cite
at least 1 reference to support your assignment.
Format
your citations according to APA guidelines
.
You are a newly-minted, tax-paying and law-abiding, permanent res.docxadampcarr67227
"You are a newly-minted, tax-paying and law-abiding, permanent resident of Canada.
In the context of the Canadian multicultural society, you are involved in your community, holding a volunteer office (e.g. VP, Secretary etc.) in your community association.
At the last community meeting several members raised the issue of whether what is going on the Canadian political scene, such as:
the Jody Wilson- Raybould, former federal Justice Minister and Attorney General, story
the Bill Morneau, former federal Minister of Finance, story, and especially
the Julie Payette, former Governor General of Canada, story
are indicative of changes, in the Canadian society, which will impact the country and its communities.
You were asked to write a report, of maxim 8 pages
( .... your community members appreciate effective communication)
, addressing issues such as:
what Julie Payette's case says about employee-employer relations in Canada?
what Bill Morneau's case says about ethics in Canada?
what Jody Wilson-Raybould's case says about globalization, global competition, competitiveness and ethics in Canada?
Your community is generally optimistic about the state of affairs in Canada, and about the future of the country which depends on its functioning democracy.
Are there warning signs and "red flags" to watch for by engaged members of the Canadian society?"
.
You are a new university police chief in a medium-sized city, an.docxadampcarr67227
You are a new university police chief in a medium-sized city, and today is a huge football game. You have received information from a patrol sergeant that one of your male officers is at the football stadium working overtime and wearing an earring and sporting a new, visible and rather risqué tattoo on his lower front arm. The sergeant says that both are highly visible, and that a rudimentary dress code exists in your agency but does not cover earrings. You are aware that the other officers are anxiously watching the situation to see what you do. What are you going to do? Explain yourself.
.
You are a native speaker of French living in a mainly English speaki.docxadampcarr67227
You are a native speaker of French living in a mainly English speaking part of Canada. You would like to send your children to a French school, but none is available. Remembering how the Gaulois culture and language progressively disappeared in what is now France, you would like to alert the French speaking population and its leaders to the importance of having a Francophone system of education
400-500 words
double spaced
tiems new roman
I need by nov 19th at 4pm
.
You are a new high school teacher, and have been captured at the end.docxadampcarr67227
You are a new high school teacher, and have been captured at the end of Open House by a parent who is upset about one of your classroom procedures. You have tried to explain the value of the procedure; however, the parent continues to adamantly disagree and hold you hostage after everyone has left. What do you think would be the best course of action?
.
You are a member of the Human Resource Department of a medium-sized .docxadampcarr67227
You are a member of the Human Resource Department of a medium-sized organization that is implementing a new inter-organizational system that will impact employees, customers, and suppliers. Your manager has requested that you work with the system development team to create a communications plan for the project. He would like to meet with you in two hours to review your thoughts on the KEY OBJECTIVES OF THE COMMUNICATIONS PLAN. What should those objectives be?
.
You are a network analyst on the fly-away team for the FBIs cyberse.docxadampcarr67227
You are a network analyst on the fly-away team for the FBI's cybersecurity sector engagement division. You've been deployed several times to financial institutions to examine their networks after cyberattacks, ranging from intrusions and data exfiltration to distributed denial of services to their network supporting customer transaction websites. A representative from the Financial Services Information Sharing and Analysis Center, FS-ISAC, met with your boss, the chief net defense liaison to the financial services sector, about recent reports of intrusions into the networks of banks and their consortium.
He's provided some of the details of the reports in an email. "Millions of files were compromised, and financial officials want to know who entered the networks and what happened to the information. At the same time, the FS-ISAC has seen extensive distributed denial of service disrupting the bank's networks, impacting the customer websites, and blocking millions of dollars of potential transactions," his email reads.
You realize that the impact from these attacks could cause the downfall of many banks and ultimately create a strain on the US economy. In the email, your chief asks you to travel to one of the banks and using your suite of network monitoring and intrusion detection tools, produce two documents—a report to the FBI and FS-ISAC that contains the information you observed on the network and a joint network defense bulletin to all the banks in the FS-ISAC consortium, recommending prevention methods and remediation against the types of malicious traffic activity that they may face or are facing.
Network traffic analysis and monitoring help to distinguish legitimate traffic from malicious traffic. Network administrators must protect networks from intrusions. This can be done using tools and techniques that use past traffic data to determine what should be allowed and what should be blocked. In the face of constantly evolving threats to networks, network administrators must ensure their intrusion detection and prevention systems are able to analyze, monitor, and even prevent these advanced threats.
In this project, you will research network intrusion and prevention systems and understand their use in a network environment. You will also use monitoring and analysis technologies in the Workspace to compile a Malicious Network Activity Report for financial institutions and a Joint Network Defense Bulletin for a financial services consortium.
The following are the deliverables for this project:
Deliverables
•Malicious Network Activity Report: An eight- to 10-page double-spaced Word document with citations in APA format. The page count does not include figures, diagrams, tables, or citations.
•Joint Network Defense Bulletin: A one- to two-page double-spaced document.
Step 1: Create a Network Architecture Overview
You travel to the various bank locations and gain access to their networks. However, yo.
You are a member of the senior management staff at XYZ Corporation. .docxadampcarr67227
You are a member of the senior management staff at XYZ Corporation. You have historically been using a functional structure set up with five departments: finance, human resources, marketing, production, and engineering.
Create a drawing of your simplified functional structure, identifying the five departments.
Assume you have decided to move to a project structure. What might be some of the environmental pressures that would contribute to your belief that it is necessary to alter the structure?
With the project structure, you have four projects currently ongoing: stereo equipment, instrumentation and testing equipment, optical scanners, and defense communications.
Draw the new structure that creates these four projects as part of the organizational chart.
Text
Title:
Project Management
ISBN: 9780134730332
Authors: Pinto
Publisher: Pearson
Edition: 5TH 19
.
You are a member of the senior hospital administration. You become a.docxadampcarr67227
You are a member of the senior hospital administration. You become aware of a problem involving a long-time and well-respected employee, as well as the supervisor of said employee.
The employee in question is a social worker; a very competent and very conscientious professional. His wife has recently suffered a stroke with significant residual neurological deficit. This has resulted in the necessity that the social worker take days off to care for her; come in late or leave early to take her to medical, physical, or occupational therapy appointments; etc.
It is thought that, because of these demands on his time—and the taxing emotional overlay of dealing with the critical illness of a loved one, while simultaneously dealing with patients and families in similar situations—that his charting fell behind. In fact, it was discovered that he was writing social work notes 1–2 days after the fact, back-dating the notes, and placing them in the patients chart between notes of the same time frame as the date on the note.
When the social worker’s immediate supervisor became aware of this, she told him that such behavior must stop immediately. Given the circumstances, however, she opted to take no further action, did not document this in his personnel file, nor did she advise her superiors.
Other members of the staff became aware of this, and someone reported it to the CEO via a “Tell Us About Problems” Dropbox.
You have been assigned to address these multiple issues of ethics, standards of conduct, truth, and fairness. Also describe what concepts of change management theory you would apply in this situation.
Describe your answer in detail, citing references in APA format where appropriate. Your Journal entry should be at least 500 words.
.
YOU ARE A MEMBER OF THE SENIOR HOSPITAL ADMINISTRATI.docxadampcarr67227
YOU ARE A MEMBER OF THE SENIOR
HOSPITAL ADMINISTRATION.
YOU BECOME AWARE OF A PROBLEM
INVOLVING A LONG-TIME AND WELL-
RESPECTED EMPLOYEE, AS WELL AS THE
SUPERVISOR OF SAID EMPLOYEE.
THE EMPLOYEE IN QUESTION IS A SOCIAL
WORKER; A VERY COMPETENT AND VERY
CONSCIENTIOUS PROFESSIONAL. HIS WIFE
HAS RECENTLY SUFFERED A STROKE WITH
SIGNIFICANT RESIDUAL NEUROLOGICAL
DEFICIT.
THIS HAS RESULTED IN THE NECESSITY THAT
THE SOCIAL WORKER TAKE DAYS OFF TO CARE
FOR HER; COME IN LATE OR LEAVE EARLY TO
TAKE HER TO MEDICAL, PHYSICAL, OR
OCCUPATIONAL THERAPY APPOINTMENTS; ETC.
THAT HIS
CHARTING
FELL BEHIND.
IT IS THOUGHT THAT, BECAUSE OF THESE DEMANDS ON HIS
TIME—AND THE TAXING EMOTIONAL OVERLAY OF DEALING
WITH THE CRITICAL ILLNESS OF A LOVED ONE, WHILE
SIMULTANEOUSLY DEALING WITH PATIENTS AND FAMILIES
IN SIMILAR SITUATIONS—
WHEN THE SOCIAL WORKER’S IMMEDIATE
SUPERVISOR BECAME AWARE OF THIS, SHE TOLD.
IN FACT, IT WAS DISCOVERED THAT HE
WAS WRITING SOCIAL WORK NOTES 1-2
DAYS AFTER THE FACT, BACK-DATING THE
NOTES, AND PLACING THEM IN THE
PATIENTS CHART BETWEEN NOTES OF THE
SAME TIME FRAME AS THE DATE ON THE
NOTE.
GIVEN THE CIRCUMSTANCES,
HOWEVER, SHE OPTED TO TAKE NO
FURTHER ACTION, DID NOT
DOCUMENT THIS IN HIS PERSONNEL
FILE, NOR DID SHE ADVISE HER
SUPERIORS.
JOURNAL TOPIC
POST YOUR RESPONSE ON
THE UNIT 7 JOURNAL AREA.
Other members of the staff became aware of
this, and someone reported it to the CEO via a
“Tell Us About Problems” drop box.
You have been assigned to address these
multiple issues of ethics, standards of conduct,
truth, and fairness. Also describe what concepts
of change management theory you would apply
in this situation.
Describe your answer in detail, citing references
in APA format where appropriate. Your Journal
entry should be at least 500 words.
Slide Number 1Slide Number 2Slide Number 3Slide Number 4
.
You are a member of the Human Resource Department of a medium-si.docxadampcarr67227
You are a member of the Human Resource Department of a medium-sized organization that is implementing a new inter organizational system that will impact employees, customers, and suppliers. Your manager has requested that you work with the system development team to create a communications plan for the project. He would like to meet with you in two hours to review your thoughts on the KEY OBJECTIVES OF THE COMMUNICATIONS PLAN. What should those objectives be?
.
You are a member of the American Indian tribe. Think about how your .docxadampcarr67227
You are a member of the American Indian tribe. Think about how your life has changed since the English settlers (Plymouth Colonists) have settled on your land. How do you feel with them there? Are you happy? Are they happy? Write a letter to the colonists expressing your feelings. Bring in historical facts to make your letter believeable.
Your letter should include:
Describe your life before the arrival of the English settlers.
What were your first impressions on the settlers?
How has having the settlers live nearby changed your life?
Do you think the English settlers have the right to settle in Plymouth? Why or why not?
What can the settlers learn form you, and what can you learn from the settlers?
How can two cultures live together peacefully? What would you have to do to make this happen?
.
You are a juvenile justice consultant creating a proposal that w.docxadampcarr67227
You are a juvenile justice consultant creating a proposal that will be presented to the state legislature concerning the future of the juvenile justice system.
Create
a 10- to 15-slide Microsoft® PowerPoint® presentation, including speaker notes, detailing your proposal. Address recommendations for all aspects of the system, including:
Community involvement
Law enforcement
Courts and sentencing
Corrections
Include
a justification for the system based on history, trends, causation theories, and potential for reform.
.
You are a journalist and you have been sent off to write a story abo.docxadampcarr67227
You are a journalist and you have been sent off to write a story about a break in at a local school. You write for the local paper entitled The Local Post. This is the information that you have got so far.
Things that were stolen include:
Five laptop computers
Money that was raised for Comic Relief
Two digital cameras
The school is called Rosedale Primary School and the Head teacher's name is Mr John Jones.
People that could be interviewed are:
The Head teacher
Mrs Milton - a parent
Mr Thompson - lives down the road
The police have investigated and viewed the CCTV footage. There are two men seen committing this crime, covered in black clothing. Police are appealing for witnesses to come forward.
.
You are a juvenile court probation officer. You have a choice of.docxadampcarr67227
You are a juvenile court probation officer. You have a choice of programs including; mandatory counseling, family counseling, removal from the home and placing in foster care, diversion, incarceration in a youth home or mandatory participation in a 10 week boot camp. You must make recommendations to the judge for sentencing. You must use all the alternatives for the group and you can’t use more than one alternative twice. Make recommendations for each juvenile and explain your rationale. Note your difficulties and what further information you would have liked. Finally what is the overwhelming need for each person and how are you addressing that in your program.
Sally is 13 and lives in the suburbs of Fort Wayne. She was caught riding in a stolen car with two friends from high school. Sally has no record – her mother tells you that Sally was a model child until last year when her father died. Since then Sally’s grades have dropped and she has become unmanageable.
John is 16 and lives in Indianapolis. He has a long juvenile record dating back to when he was 10. John’s prior offenses include arson, disorderly conduct, larceny and assault (3). John was arrested for stealing lawn ornaments worth $23.00. John is unsupervised (no parental control) and missed his last probation meeting.
Don is 14 and lives in the inner-city of Gary, Indiana. Don has no father and his mother is a crack addict. Don lives by himself for long periods of time. In the past Don was arrested for stealing food from a local bakery. Don admitted to the theft, but noted he hadn’t eaten in two days. Don was removed from home – but was returned to his mother one year later. Don was arrested for possession of crack cocaine – it was believed he was selling.
Darlene is 12 and lives in the suburbs with her mother, step-father and new baby sister. Darlene has been in juvenile court a number of times in the past year for being a runaway. She was petitioned last month by her step-father for being incorrigible. Darlene refused to follow the family rules and is defiant to her step-father. Darlene is very intelligent and is openly disrespectful to her mother and step-father.
Stephen Holmes is 16 and lives in Noblesville. His father is a salesman and his mother is an executive with General Advertising Inc. Stephen has a prior record for larceny. Last month Stephen got into a fight with his brother who is 17. After the fight was over Stephen took his father’s gun and shot his brother in the head instantly killing him.
Papers will be completed in Word Format as an attachment. The papers will be typed in Times New Roman using 12 font. Papers will be double-spaced. The papers will be at least 500 words in length. The papers will be a critical examination of a topic area chosen by the instructor. Students are encouraged to critically examine and question a topic area in detail using their book.
.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Homework 51)a) the IS curve ln Yt= ln Y(t+1) – (1Ɵ)rtso th.docx
1. Homework 5
1)
a) the IS curve: ln Yt= ln Y(t+1) – (1/Ɵ)rt
so the slope is: drt/dyt (is) = -Ɵ/Yt. That means that an increase
in Ɵ will result in a steeper curve.
LM curve: Mt/Pt = Yt^(Ɵ/v) (1+rt / rt)^(1/v)
Ln(Mt/Pt) = (Ɵ/v) ln Yt +(1/v)ln(1+rt) – (1/v)ln rt.
0 = (Ɵ/v)(1/Yt)dYt + (1/v)(1/(1+rt)) drt – (1/v)(1/rt)drt.
The slope is: drt/dyt (LM) = (Ɵrt(1+rt))/Yt. That means that an
increase in Ɵ will result in a steeper curve.
b) the curve IS is not affected by the value of V. while curve
LM shifts upwards, since a decrease in v will result in an
increase for the demand for real money.
c) IS is not affected byΓ(.)
optimal money holdings: BΓ’(Mt/Pt) = (it/(1+it)) U’(Ct)
B(Mt/Pt)^(-v) = (it/1+it) Yt^-Ɵ
Mt/Pt= B^(1/v) Yt^(Ɵ/v) (1+rt/rt)^(1/v)
So this means that the LM curve will shift downwards.
2)
a) AC= (PC/)+(αYP/2)i
AC/ = -(PC/^2) + (αYP/2)I = 0
C/^2 = αYi/2
So *=(2C/αYi)^(1/2)
b) average real money holdings:M/P= αY/2
M/P = (αY/2) (2C/αYi)^(1/2)
M/P= (αCY/2i)^(1/2)
Ln(m/p) = (1/2)(lnα+lnY+lnC-ln2-lni)
(1/(M/P))((M/P)/i) = -(1/2)(1/i)
Elasticity of real money with respect to i: ((M/P)/)(i/(M/P)) = -
1/2
The elasticity with respect to Y : ((M/P)/Y)(Y/(M/P)) = ½
Average real money holdings increase in Y, and decrease in i.
2. 4)
a)when p is at a level that generates maximum output, LS meets
LD.
b) when p is above the level that generates maximum output,
will cause unemployment.
7)
a)
b)i)
ii)
iii)
13)
a) the asset has an expected rate of return r. capital gain/loss
plus dividends per unit time = rvp. There is no dividends per
unit time while searching for the palm tree, and there is b
probability per unit time of capital gain of (vc-vp)-c. the
difference in the price of the asset is(vc-vp) and –c is what the
asset pays, so at the end we have rvp=b(vc-vp-c)
b) there is probability aL that a person will find another person
with a coconut and trade with that person and gain u̅ . the
difference in the price of the asset is (vp-vc). So we end up with
rvp=al(vp-vc+u̅ ).
c) vp=(rvc/aL)+vc-u̅ .
r((rvc/aL )+vc-u̅ )= b(vc-(rvc/aL)-vc+u̅ -c)
vc(r(r+aL+b))/aL = u̅ (r+b)-bc
the value of being in state C: vc= (aL(u̅ (r+b)-bc)) / r(r+aL+b)
3. the value of being in state p: vp= ((u̅ (r+b)-bc)/(r+aL+b)) +
(aL(u̅ (r+b)-bc)/r(r+aL+b)) - u̅
so finally
vc-vp = (bc+u̅ aL)/(r+aL+b).
e) vc-vp ≥c
vc-vp = (bc+u̅ a(b/a))/(r+a(b/a)+b) = (bc+bu̅ )/(r+2b)
(bc+bu̅ )/(r+2b) ≥ c
That means that
Bc+bu̅ ≥c and c(r+2b-b) ≤ bu̅
So finally we have
c≤ bu̅ / (r+b).
f) it is a steady-state equilibrium for no one who finds a tree to
climb it for any value of c>0.
Yes there are values of c which there is more than one steady-
state equilibrium for 0<c< bu̅ /(r+b)
Yes, L = b/a has a higher welfare than L=0. When L=0 people
don’t gain any utility since they don’t climb a tree and don’t
have a chance to trade with other people and gain a coconut.
0 1 2 3 4 5 -3 -2.2000000000000002 -
1.8 -1.8 -2.2000000000000002 -3
0 1 2 3 4 5 7 6.5 5.5 3.5 1
0 1 2 3 4 -2 -2.5 -3.5 -5.5 -8
LD 1 2 3 4 5 6 7 8 9 10 10 9
8 7 6 5 4 3 2 1 LS 1 2 3
4. 4 5 6 7 8 9 10 1 2 3 4 5
6 7 8 9 10
AD 2 3 4 5 4 3 2 1 1 2 3 4
5 6 7 8 9
0 1 2 3 4 5 6 7 8 9 10 9 8
7.5 7 6.7 6.5 6.3 6.1 5.9
0 1 2 3 4 5 -2.6 -2 -1.4 -
1.1000000000000001 -0.95 -0.87 0 1
0 1 2 3 4 7 5 4.3 3.5 2
Advanced macroeconomics, 4th edition. Romer.
Chapter12.
12.1. The stability of fiscal policy. (Blinder and Solow, 1973.)
By definition, the budget deficit equals the rate of change of the
amount of debt outstanding: δ(t) ≡ D ̇(t). Define d(t) to be the
ratio of debt to output: d(t) = D(t)/Y(t). Assume that Y(t) grows
at a constant rate g > 0.
(a) Suppose that the deficit-to-output ratio is constant: δ(t)/Y(t)
= a, where a > 0.
̇
(i) Find an expression for d(t) in terms of a, g, and d(t). ̇
(ii) Sketch d(t) as a function of d(t). Is this system stable?
(b) Suppose that the ratio of the primary deficit to output is
constant and equal to a > 0. Thus the total deficit at t, δ(t), is
given by δ(t) = aY(t) + r(t)D(t), where r(t) is the interest rate at
5. t. Assume that r is an increasing function of the debt-to-output
ratio: r(t) = r(d(t)), where r′(•) > 0, r′′(•) > 0, limd→−∞ r(d) <
g, limd→∞ r(d) > g.
̇
(i) Find an expression for d(t) in terms of a, g, and d(t). ̇
(ii) Sketch d(t) as a function of d(t). In the case where a is
sufficiently small that d ̇ is negative for some values of d, what
are the stability properties of the system? What about the case
where a is sufficiently large that d ̇ is positive for all values of
d ?
12.2. Precautionary saving, non-lump-sum taxation, and
Ricardian equivalence.
(Leland, 1968, and Barsky, Mankiw, and Zeldes, 1986.)
Consider an individual who lives for two periods. The
individual has no initial wealth and earns labor incomes of
amounts Y1 and Y2 in the two periods. Y1 is known, but Y2 is
random; assume for simplicity that E[Y2] = Y1. The
government taxes income at rate τ1 in period 1 and τ2 in period
2. The individual can borrow and lend at a fixed interest rate,
which for simplicity is assumed to be zero. Thus second-period
consumption is C2 = (1 − τ1)Y1 − C1 + (1 − τ2)Y2. The
individualchoosesC1
tomaximizeexpectedlifetimeutility,U(C1)+E[U(C2)].
(a) Find the first-order condition for C1.
(b) Show that E[C2] = C1 if Y2 is not random or if utility is
quadratic.
(c) Show that if U ′′′(•) > 0 and Y2 is random, E[C2] > C1.
(d) Suppose that the government marginally lowers τ1 and
raises τ2 by the same amount, so that its expected total revenue,
τ1Y1 + τ2E[Y2], is un- changed. Implicitly differentiate the
first-order condition in part (a) to find an expression for how
C1 responds to this change.
(e) Show that C1 is unaffected by this change if Y2 is not
random or if utility is quadratic.
(f) Show that C1 increases in response to this change if U ′′′(•)
6. > 0 and Y2 is random.
12.3
Consider the Barro tax-smoothing model. Suppose that output,
Y, and the real interest rate, r, are constant, and that the level of
government debt out- standing at time 0 is zero. Suppose that
there will be a temporary war from time 0 to time τ. Thus G(t)
equals GH for 0 ≤ t ≤ τ, and equals GL there- after,whereGH
>GL.Whatarethepathsoftaxes,T(t),andgovernmentdebt
outstanding, D(t)?
12.4
Consider the Barro tax-smoothing model. Suppose there are two
possible val- ues of G(t)—GH and GL—with GH > GL.
Transitions between the two values follow Poisson processes
(see Section 7.4). Specifically, if G equals GH, the probability
per unit time that purchases fall to GL is a; if G equals GL, the
probability per unit time that purchases rise to GH is b. Suppose
also that output, Y, and the real interest rate, r, are constant and
that distortion costs are quadratic.
(a) Derive expressions for taxes at a given time as a function of
whether G equals G H or G L , the amount of
debt outstanding, and the exogenous parameters.
(Hint: Use dynamic programming, described in Section 10.4, to
find an expression for the expected present value of the revenue
the government must raise as a function of G, the amount of
debt outstanding, and the exogenous parameters.)
(b) Discuss your results. What is the path of taxes during an
interval when G equals GH? Why are taxes not constant during
such an interval? What happens to taxes at a moment when G
falls to GL? What is the path of taxes during an interval when G
equals GL?
(Romer 640)
12.9.
Consider the Tabellini–Alesina model in the case where α can
7. only take on the values 0 and 1. Suppose, however, that there
are 3 periods. The period-1 median voter sets policy in periods
1 and 2, but in period 3 a new median voter sets policy. Assume
that the period-1 median voter’s α is 1, and that the probability
that the period-3 median voter’s α is 1 is π.
(a) Does M1 = M2?
(b ) Suppose that after choosing purchases in period 1, the
period-1 median voter learns that the probability that the
period-3 median voter’s α will be1isnotπ butπ′,whereπ′ <
π.Howdoesthisnewsaffecthisor her choice of purchases in period
2?
12.10. ThePersson-
Svenssonmodel.(PerssonandSvensson,1989.)Suppose there are
two periods. Government policy will be controlled by different
policy- makers in the two periods. The objective function of the
period-t policymaker is U + αt [V(G1) + V (G2)], where U is
citizens’ utility from their private consumption; αt is the weight
that the period-t policymaker puts on public consumption; Gt is
public consumption in period t; and V(•) satis-
fiesV′(•)>0,V′′(•)<0.Privateutility,U,isgivenbyU
=W−C(T1)−C(T2), where W is the endowment; Tt is taxes in
period t; and C(•), the cost of raising revenue, satisfies C′(•) ≥
1, C′′(•) > 0. All government debt must be
paidoffattheendofperiod2.ThisimpliesT2
=G2+D,whereD=G1−T1 is the amount of government debt
issued in period 1 and where the interest rate is assumed to
equal zero.
(a) Find the first-order condition for the period-2 policymaker’s
choice of G2 given D. (Note: Throughout, assume that the
solutions to the policy- makers’ maximization problems are
interior.)
(b) How does a change in D affect G2?
(c) Think of the period-1 policymaker as choosing G1 and D.
Find the first-
order condition for his or her choice of D.
8. (d) Show that if α1 is less than α2, the equilibrium involves
inefficiently low taxation in period 1 relative to tax-smoothing
(that is, that it has T1 < T2). Explain intuitively why this
occurs.
(e) Does the result in part (d) imply that if α1 is less than α2,
the period-1 policymaker necessarily runs a deficit? Explain.
Chapter 6.
6.15. Observational equivalence. (Sargent, 1976.) Suppose that
the money supply isdeterminedbymt =c′zt−1
+et,wherecandzarevectorsandet isani.i.d. disturbance
uncorrelated with zt−1. et is unpredictable and unobservable.
Thus the expected component of m t is c ′ zt −1 , and the
unexpected component is et. In setting the money supply, the
Federal Reserve responds only to vari- ables that matter for real
activity; that is, the variables in z directly affect y .
Now consider the following two models: (i ) Only unexpected
money mat- ters,so yt = a′zt−1+bet+vt;(ii)allmoneymatters,so yt
= α′zt−1+βmt +νt.In each specification, the disturbance is i.i.d.
and uncorrelated with zt −1 and et.
(a) Is it possible to distinguish between these two theories? That
is, given a candidate set of parameter values under, say, model
(i), are there param- eter values under model (ii ) that have the
same predictions? Explain.
(b) Suppose that the Federal Reserve also responds to some
variables that donotdirectlyaffectoutput;thatis,supposemt
=c′zt−1+γ′wt−1+et and that models (i) and (ii) are as before
(with their distubances now uncorrelated with wt −1 as well as
with zt −1 and et). In this case, is it pos- sible to distinguish
between the two theories? Explain.
6.16. Consider an economy consisting of some firms with
flexible prices and some with rigid prices. Let pf denote the
9. price set by a representative flexible-price firm and pr the price
set by a representative rigid-price firm. Flexible-price firms set
their prices after m is known; rigid-price firms set their prices
be- fore m is known. Thus flexible-price firms set pf = pi∗ =
(1 − φ)p + φm, and rigid-price firms set pr = Epi∗ = (1 − φ)Ep
+ φEm, where E denotes the expectation of a variable as of
when the rigid-price firms set their prices.
Assume that fraction q of firms have rigid prices, so that p =
qpr+ (1−q)pf.
(a) (b) (c)
Find pf in terms of pr,m, and the parameters of the model (φ
and q). Find pr in terms of Em and the parameters of the model.
(i ) Do anticipated changes in m (that is, changes that are
expected as of when rigid-price firms set their prices) affect y ?
Why or why not?
(ii ) Do unanticipated changes in m affect y ? Why or why not?
