Micro theory of production, the production function, short run and long run,

1. ANALYSIS OF PRODUCTION
LESSON 6:
UNIT 4.2
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2. THEORY OF PRODUCTION
 Micro economics assumes that firms are the
owners, managers and sellers of a
commodity.
 Rational firm – maximise profits, or minimise
loss (costs).
 Instantaneous production (static analysis)
 Ceteris paribus – technology, government
regulations, and demand remain constant.
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3. FACTORS OF PRODUCTION
 Output is produced with the help of inputs.
 Four factors of production (inputs)
o Land, labour, capital and organisation.
 Factors are durable, and available as inputs
in the next time period of production,
 Land is not important in manufacturing, and
Organisation is strictly not a factor of
production.
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4. CAPITAL AND LABOUR
 Capital –
1. Financial capital – funds for investment.
o Possible to change investment from one product to
another.
2. Physical capital - machinery, equipment, tools
buildings, plant, etc.
o Not possible to change after investment in one type
of production has taken place.
 Labour: Workers hire out their labour, for
different time periods: per day, per hour, etc.
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5. PRODUCTION FUNCTION
A production function depicts the technological
relationship between inputs and output.
It shows the maximum output that can be
produced with a given quantity of inputs.
Q = F (K, L)
When K and L increase, Q also increases.
• Short Run: is defined as a period of time when
some factors are fixed (e.g. K),
• Long Run: is the period of time when all
factors can be increased, all factors are
variable.
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6. SHORT RUN PRODUCTION FUNCTION
 The Law of Variable Proportions,
 Assumes one factor (K) is constant, and the
other is variable (L),
 No change in technology, or demand
conditions,
 As L increases, what is the effect on Q?
 Will it also increase proportionately, or not?
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7. THE LAW OF VARIABLE PROPORTIONS
 As the variable input increases, output
initially increases at an increasing rate,
 Then at a decreasing rate,
 Finally when the fixed factor becomes a
bottleneck, Q starts falling.
 The Law of Variable Proportions states that
when one input increases, others remaining
constant, then the returns to the variable
input are not proportionate.
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8. TOTAL, AVERAGE AND MARGINAL PRODUCTS
 This means that Total product does not
increase at a constant rate.
 Total Product (TP) is the total amount of
output produced by the inputs = Q of Kgs or
tonnes,
 Average Product (AP) = TP or TP
L K
 Marginal Product (MP) = ∆TP or ∆TP
∆L ∆K
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9. Capital Labour Total
Product
(TP)
Average
Product of L
(AP = TP/L)
Marginal
Product of L
(MP = ∆TP/∆L)
10 0 0
10 1 30 30 30
10 2 80 40 50
10 3 120 40 40
10 4 150 37.5 30
10 5 170 34 20
10 6 170 28.3 0
10 7 160 22.8 -10
10 8 130 16.25 - 30
K is kept constant, and L increases. Returns to L are not
proportionate.
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10. LAW OF VARIABLE PROPORTIONSQ(Kgs)
L
TP
0
max
L1
AP
MP
1stage
Keeping K
constant and
increasing L,
TP increases
1) at an
increasing
rate, then
2) decreasing
rate, and
3) at a
negative
rate.
Shows the three
stages of
production.
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11. THE THREE STAGES:
Stage I: Increasing Returns: TP increases at an
increasing rate, i.e. MP rises.. When MP,
AP, but < MP.
Stage II: Diminishing Returns: TP increases at a
decreasing rate, i.e. MP falls.. When MP,
AP . MP cuts AP when AP is maximum,
then AP  > MP .
Stage III: Negative returns. TP reaches a maximum,
and starts falling. MP = 0 when TP is
maximum. Then MP < 0, but AP is falling not
negative..
So, when one factor input increases, others
remaining constant, the returns to the
variable factor are not proportionate.
This is called the “Law of Variable
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12.  How much of labour should be employed?
o In the first stage, MP, every extra L adds more to
output, TP is rising.
o In the second stage, MP, but TP is still rising. At the
end of this stage TP is maximum, MP = 0.
o In the third stage, any further increase in L will
decrease TP, and the contribution of the extra L is
negative.
 So1st stage should continue as TP is rising, but
in 3rd stage TP is falling, it is uneconomical.
 Therefore the economical stage of analysis is
the 2nd stage – Stage of Diminishing Returns.
THE ECONOMIC RANGE OF PRODUCTION:
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13. LAW OF DIMINISHING MARGINAL
PRODUCTIVITY:
 Other things remaining constant, if the input of
one factor alone increases, a point will be
reached when the additions to TP made by it
will diminish.
 Therefore the producer has to decide how
much of L input to employ so as to maximise
his output.
 Assuming w = 0, free L, the producer will
employ L up to the point where TP is
maximum.
 Or where MP = 0.
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14. LAW OF DIMINISHING MARGINAL
PRODUCTIVITY: WAGE RATE =0
Q(Kgs)
0
L
MPL
MPL = 0
L1
Till L1, each
additional unit of L
input adds to TP.
At L1, MP =0, i.e. TP
is maximum.
So employment of L
stops at this point,
and TP = ΣMP =
0NL1.
After L1, every
additional or
marginal L reduces
TP.
Not economical to
engage more L after
this point.
L1 is the equilibrium.
N
TP = Surplus
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15. LAW OF DIMINISHING MP: WAGE RATE > 0Q(Kgs)
0
MPL
L
w
w0
L0
TP – Total Wages =
Surplus
Total Wages
As long as addition
to TP > w,
employment can
increase.
At w0, w = MPL,
So employment =
0L0.
After this point w >
MPL
Not economical to
employ more L.
W0 is the point of
equilibrium, where
MPL = wage rate.
MPL = w
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16. ISOQUANT ANALYSIS
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17. LONG RUN ANALYSIS OF PRODUCTION:
 In the long run, all factors are variable.
 Both K and L can increase, leading to increase in
output.
Q = F (K, L)
 Different techniques available for production.
 Each technique has a different combination of K and
L, which produce the same TP.
 These can be shown in the form of Isoquants.
 Isoquants are imaginary lines that connect all
combinations of K and L, that produce the same
level of output.
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18. ISOQUANT PRODUCTION FUNCTION:
 Assumptions: Ceteris paribus
o K and L are substitutes in different techniques of
production.
o Isoquants therefore slope down to the left.
o Isoquants are convex to the origin, showing
diminishing returns to the variable factor,
o Higher IQ show higher level of output, with more
inputs,
o Two IQs cannot intersect.
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19. ISOQUANT PRODUCTION FUNCTION:
K
0 L
IQ1 100 Kgs
a
b
c
IQ2 200 Kgs
a1
b1
c1
IQ3 300 Kgs
On a given IQ,
total Q is
constant.
Produced by
different
combinations of
K and L.
K and L are
substitutes, as
K , L , and
vice versa.
An IQ map
shows different
levels of output
when all inputs
increase.
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20. EQUILIBRIUM OUTPUT AND INPUTS:
K
0 L
IQ1 100 Kgs
IQ2 200 Kgs
Isocost
The Isocost curve shows the different
quantities of inputs that can be purchased at
a given level of Investment.
The slope of the Isocost = w/r, i.e.
Ratio of wage rate to rate of interest.
How much of K and L should be used, which
technique and how much Q will be
produced?
a
b1
c
Techniques a, b1 and
c are all on the
Isocost line
At b1, the rational
firm reaches its
highest output for a
given Investment.
This is the point of
equilibrium
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21. RETURNS TO SCALE:
 When K and L both increase, will Q increase
at the same rate?
 Initially Q increases faster than increase in
inputs, this is called Increasing Returns to
Scale.
 Large scale production – leads to labour
specialisation, optimum ratio of inputs (K/L).
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22. I) INCREASING RETURNS TO SCALE:
K
0 L
IQ1 100 Kgs
IQ2 200 Kgs
IQ3 300 Kgs
IQ4 400 Kgs
The Red line
shows the
Expansion Path
of the Firm.
Increase in Q >
increase in K,
L, and
Isoquants
progressively
get closer
together.
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Expansion path
of the firm
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23. II) CONSTANT RETURNS TO SCALE:
K
0 L
IQ1 100 Kgs
IQ2 200 Kgs
IQ3 300 Kgs
IQ4 400 Kgs
Increase in Q
= increase in
K, L, and
Isoquants
equally spaced
out.
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Expansion path
of the firm
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24. III) DECREASING RETURNS TO SCALE
K
0 L
IQ1 100 Kgs
IQ2 200 Kgs
IQ3 300 Kgs
IQ4 400 Kgs
Increase in Q <
increase in K, L,
and Isoquants
spaced out
further and
further away.
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Expansion path
of the firm
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25. QUESTIONS
1. Short Answers:
a) What are the main factors of production? How do
they differ from other “inputs”?
b) What is a Production Function? Give the formula,
and explain.
c) State and explain the Law of Diminishing
Marginal Productivity.
d) What is meant by the term “Negative Returns”?
Depict it on a diagram and explain.
e) Draw an Isoquant, and show the point of
equilibrium of production.
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26. 2. Essay Questions:
a. Define the Law of Variable Proportions.
Draw and show the different stages of
production.
b. Explain what is meant by “Returns to
Scale”. How does it differ from the Law
of Variable Proportions?
c. Draw and explain the following:
1. Increasing returns to scale,
2. Constant returns to scale,
3. Decreasing returns to scale.
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