Managerial Economics

(Econ231)
Contents
• Production
• Production function
• Short run production function
• Total, Average and Marginal Product
• Law of diminishing returns
• Three stages of production in the short run
• Long run production function-
• Isoquants
• Returns to scale
• Types of Production function

2
Production

3
 PRODUCTION

• Production involves transformation of

inputs such as capital, equipment, labor,
and land into output - goods and services

• In this production process, the manager is

concerned with efficiency in the use of the
inputs
- technical vs. economical efficiency

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 Two Concepts of Efficiency
• Economic efficiency:
– occurs when the cost of producing a given
output is as low as possible

• Technological efficiency:
– occurs when it is not possible to increase
output without increasing inputs
– firm produces a given level of output by using
the least amount inputs.
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You will see that basic production theory is simply an
application of constrained optimization:

the firm attempts either to minimize the

cost of producing a given level of output
or
to maximize the output attainable with a
given level of cost.

Both optimization problems lead to same

rule for the allocation of inputs and
choice of technology

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Production Function

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 Production Function
• A production function is purely technical relation
which connects factor inputs & outputs.
• It describes the transformation of factor inputs into
outputs at any particular time period.
Q = f( L, K, R, Ld, T, t)
Where:
Q = output R= Raw Material
L= Labour Ld = Land
K= Capital T = Technology
t = time

For our current analysis, let’s reduce the inputs to two, capital (K)
and labor (L):
Q = f(L, K)
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 The Production Function
• A production function can be
represented by a table, equation, or graph.
• Example 1:
– Farmer Jack grows wheat.
– He has 5 acres of land.
– He can hire as many workers as he wants.
 EXAMPLE 1: Farmer Jack’s Production Function

L Q 3,000
(no. of (bushels
workers) of wheat) 2,500

Quantity of output
0 0 2,000

1 1000 1,500

2 1800 1,000

3 2400 500

4 2800 0
0 1 2 3 4 5
5 3000
No. of workers
 Technology of Production
•Production technology-
The methods and processes used to produce goods
and services.
•Types of Technology:
Labor-Intensive: Production relies more on human
labor.
Capital-Intensive: Production relies more on
machinery and equipment.
 Production Table
Units of K
Employed Output Quantity (Q)
8 37 60 83 96 107 117 127 128
7 42 64 78 90 101 110 119 120
6 37 52 64 73 82 90 97 104
5 31 47 58 67 75 82 89 95
4 24 39 52 60 67 73 79 85
3 17 29 41 52 58 64 69 73
2 8 18 29 39 47 52 56 52
1 4 8 14 20 27 24 21 17
1 2 3 4 5 6 7 8
Units of L Employed

Same Q can be produced with different combinations of inputs, e.g.

inputs are substitutable in some degree
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Difference between Short run and
Long run Production Function

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 Short-Run and Long-Run
Production
• In the short run some inputs are fixed
and some variable
– e.g. the firm may be able to vary the
amount of labor, but cannot change the
amount of capital
– in the short run we can talk about factor
productivity / law of variable proportion/law
of diminishing returns

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 Short-Run and Long-Run
Production
• In the long run all inputs become
variable
– e.g. the long run is the period in which a
firm can adjust all inputs to changed
conditions
– in the long run we can talk about returns
to scale

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Short-Run Changes in Production
Factor Productivity
Units of K
Employed Output Quantity (Q)
8 37 60 83 96 107 117 127 128
7 42 64 78 90 101 110 119 120
6 37 52 64 73 82 90 97 104
5 31 47 58 67 75 82 89 95
4 24 39 52 60 67 73 79 85
3 17 29 41 52 58 64 69 73
2 8 18 29 39 47 52 56 52
1 4 8 14 20 27 24 21 17
1 2 3 4 5 6 7 8
Units of L Employed

How much does the quantity of Q change,

when the quantity of L is increased? 16
 Long-Run Changes in
Production
Returns to Scale
Units of K
Employed Output Quantity (Q)
8 37 60 83 96 107 117 127 128
7 42 64 78 90 101 110 119 120
6 37 52 64 73 82 90 97 104
5 31 47 58 67 75 82 89 95
4 24 39 52 60 67 73 79 85
3 17 29 41 52 58 64 69 73
2 8 18 29 39 47 52 56 52
1 4 8 14 20 27 24 21 17
1 2 3 4 5 6 7 8
Units of L Employed

How much does the quantity of Q change, when

the quantity of both L and K is increased?
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Question
What is the key difference between the short run and the
long run in economics?
a) In the short run, all inputs are variable, while in the long
run, at least one input is fixed.
b) In the short run, firms cannot change the quantity of any
input, but in the long run, all inputs are fixed.
c) In the short run, at least one input is fixed, while in the
long run, all inputs can be changed.
d) In the short run, firms face no production constraints,
but in the long run, they do.

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Short run Production Function
Total, Average and Marginal Product
Law of diminishing returns
Three stages of production in the short run

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Relationship Between Total, Average, and
Marginal Product: Short-Run Analysis

• Total Product (TP) = total quantity of output

• Average Product (AP) = total product per total

input

• Marginal Product (MP) = change in quantity

when one additional unit of input used

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 The Marginal Product of Labor
• The marginal product of labor is the increase in
output obtained by adding 1 unit of labor but
holding constant the inputs of all other factors

Marginal Product of L:
MPL= Q/L (holding K constant)
= Q/L

Average Product of L:
APL= Q/L (holding K constant)
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 Total & Marginal Product
L Q
(no. of (bushels APL
MPL
workers) of wheat)

0 0
∆L = 1 ∆Q = 1000 1000
1 1000
∆L = 1 ∆Q = 800 800 900
2 1800
∆L = 1 ∆Q = 600 600
800
3 2400
∆L = 1 ∆Q = 400 400 700
4 2800
∆L = 1 ∆Q = 200 200 600
5 3000
 MPL = Slope of Production Function

L Q MPL
3,000 equals the
(no. of (bushels MPL slope of the
workers) of wheat) 2,500

Quantity of output
production function.
0 0 2,000
Notice that
1000
1 1000 MPL diminishes
1,500
800 as L increases.
2 1800 1,000
600 This explains why
3 2400 500 production
the
400 function gets flatter
4 2800 0
200 as L0 increases.
1 2 3 4 5
5 3000
No. of workers
 Law of Diminishing Returns
(Diminishing Marginal Product)
• The law of diminishing returns states that when more and
more units of a variable input are applied to a given quantity
of fixed inputs, the total output may initially increase at an
increasing rate and then at a constant rate but it will
eventually increases at diminishing rates.
• Assumptions. The law of diminishing returns is based on the
following assumptions:
(i) the state of technology is given
(ii) labour is homogenous and (iii) input prices are given.

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 Short-Run Analysis of Total,
Average, and Marginal Product

• If MP > AP then AP
is rising
• If MP < AP then AP
is falling
• MP = AP when AP
is maximized
• TP maximized
when MP = 0

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 Three Stages of Production in
Short Run
AP,MP
Stage I Stage II Stage III

APX

MPX X
•TPL Increases at •TPL Increases at
increasing rate. Diminshing rate. • TPL begins to
decline
•MP Increases at •MPL Begins to decline.
•MP becomes
decreasing rate. •TP reaches maximum negative
level at the end of
•AP is increasing and stage II, MP = 0. •AP continues to
reaches its maximum at decline
the end of stage I •APL declines 26
Three Stages of Production
Stages
Labor Total Average Marginal of
Unit Product Product Product Production
(X) (Q or TP) (AP) (MP)
1 24 24 24
2 72 36 48 I
3 138 46 66 Increasing
4 216 54 78 Returns
5 300 60 84
6 384 64 84
7 462 66 78
8 528 66 66 II
9 576 64 48 Diminishing
10 600 60 24 Returns

11 594 54 -6 III
12 552 46 -42 Negative Returns

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Question
When the marginal product of labor is
greater than the average product of labor,
what happens to the average product?
a) It decreases
b) It remains constant
c) It increases
d) It becomes zero

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Question
Diminishing returns to labor occur in the
short run because:
a) Total product starts to increase as more
labor is added.
b) Each additional unit of labor adds less to
total output than the previous unit.
c) The firm has unlimited resources.
d) Marginal product of labor is constant
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Question
In which stage of production does total
product increase at a decreasing rate, and
marginal product is positive but falling?
a) Stage I
b) Stage II
c) Stage III
d) Stage IV

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Question
At what point does a firm typically avoid operating
in the short run because adding more of the
variable input decreases total output?
a) When marginal product is positive
b) When marginal product is zero
c) In Stage II
d) In Stage III

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Long run Production Function

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Production in the Long-Run
– All inputs are now considered to be variable
(both L and K in our case)
– How to determine the optimal combination of
inputs?

To illustrate this case we will use production

isoquants.
An isoquant is a locus of all technically efficient
methods or all possible combinations of inputs for
producing a given level of output.

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 Production Table
Units of KK
Units of
Employed
Employed Output Quantity (Q) Isoquant
8 37 60 83 96 107 117 127 128
7 42 64 78 90 101 110 119 120
6 37 52 64 73 82 90 97 104
5 31 47 58 67 75 82 89 95
4 24 39 52 60 67 73 79 85
3 17 29 41 52 58 64 69 73
2 8 18 29 39 47 52 56 52
1 4 8 14 20 27 24 21 17
1 2 3 4 5 6 7 8
Units of
of KL Employed

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 Isoquant
Isoquant. A curve representing different combinations of two inputs that
produce the same level of output

Graph of Isoquant

Y
7

0
1 2 3 4 5 6 7 X

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 Properties of Isoquants
• Isoquants have a negative slope.

• Isoquants are convex to the origin.

• Isoquants cannot intersect or be tangent to each other.

• Upper Isoquants represents higher level of output

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 Types of Isoquant
There exists some degree of substitutability
between inputs.
Different degrees of substitution:
Sugar
Natural
Cane Capital
flavoring
syrup

K4
K1 K2 K3
Q

Sugar All other L1 L2 L3 L4 Labor

ingredients
b) Input – Output/ L- c) Kinked/Acitivity
a) Linear Isoquant Shaped Isoquant
(Perfect substitution) (Perfect Analysis Isoquant –
complementarity) 37
(Limited substitutability)
 Marginal Rate of Technical
Substitution MRTS
• The degree of imperfection in substitutability is
measured with marginal rate of technical
substitution (MRTS- Slope of Isoquant):

MRTS = L/K

(in this MRTS some of L is removed from the

production and substituted by K to maintain the
same level of output)

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Production with Two Variable Inputs
Marginal Rate of Technical Substitution
Capital
5
MRTS = − K
per year
(for a fixed level of Q)
2 L
The slope of 4
each isoquant
gives the 1 A
3
trade-off 1
between two 1 B
inputs while 2 Isoquants are downward
2/3 C Q3 =90 sloping and convex
1
keeping output 1/3 DQ =75
like indifference
curves.
constant. 1 1 2
Q1 =55
1 2 3 4 5
Labor per month
 Isoquant Map
• Isoquant map is a set of
Figure : Isoquant Map
isoquants presented on
Y
a two dimensional plain.
Each isoquant shows

Capital Y
various combinations of IQ3
IQ4

two inputs that can be IQ1

IQ2

used to produce a given O Labour X X

level of output.

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 Laws of Returns to Scale

• It explains the behavior of output in response to a

proportional and simultaneous change in input.
• When a firm increases both the inputs, there are three
technical possibilities –
(i) TP may increase more than proportionately –
Increasing RTS
(ii) TP may increase proportionately – constant RTS
(iii) TP may increase less than proportionately –
diminishing RTS

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 Returns to Scale

Capital Increasing Returns:

(machine The isoquants move
Increasing returns to closer together
scale: output more hours) A
than doubles when all
inputs are doubled

Larger output
associated with lower 4
cost (autos)
30
One firm is more
efficient than many 2 20
(utilities)
10
The isoquants get
closer together 0 5 10 Labor (hours)
 Returns to Scale
Constant returns Capital
to scale: output (machine
doubles when all hours) Constant
inputs are Returns:
doubled A
Isoquants are
6 equally spaced
Size does not 30
affect
productivity 4

May have a 20
large number of
2
producers
10
Isoquants are
equidistant apart 0 5 10 15
Labor (hours)
Decreasing
Returns to Scale
returns to
scale: output
less than
Capital
doubles when
all inputs are (machine A Decreasing Returns:
hours) Isoquants get further
doubled apart

Decreasing
efficiency with
4
large size
30
Reduction of
entrepreneurial 2
20
abilities 10

Isoquants 0 5 10
become farther
Labor (hours)
apart
 Returns to Scale
• One way to measure returns to scale is to
use a coefficient of output elasticity, EQ:

• EQ = Percentage change in Q /Percentage change in all inputs

• If EQ >1, we have increasing returns to scale (IRTS).

• If EQ = 1, we have constant returns to scale (CRTS).
• If EQ < 1, we have decreasing returns to scale (DRTS)

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Question
An isoquant represents combinations of inputs
that:
a) Minimize costs for a given output.
b) Yield the same level of output.
c) Maximize profit for any level of input.
d) Reduce inputs to the lowest possible level.

46
Question
If doubling all inputs results in more than double
the output, this production process exhibits:
a) Constant returns to scale
b) Increasing returns to scale
c) Decreasing returns to scale
d) Negative returns to scale

47
Question
Isoquants that are further from the origin
represent:
a) Higher levels of output
b) Lower levels of output
c) Decreasing returns to scale
d) Constant returns to scale

48
Question
If a firm experiences decreasing returns to scale,
what happens when it increases all inputs by
50%?
a) Output increases by more than 50%
b) Output increases by exactly 50%
c) Output increases by less than 50%
d) Output decreases

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Types of Production Function

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 Production Function
A production function is purely technical relation which connects factor inputs & outputs.
It describes the transformation of factor inputs into outputs at any particular time period.
Cobb–Douglas Production function:
• Cobb douglas production function
X= b0 Lb1 Kb2
X= Output, L = Labour, K = Capital
bo, b1 , b2 , Coefficient , b1 – Labour, b2 - Capital
• In cobb-Douglas function factor intensity is
measured by ratio b1/b2.
• The higher is the ratio (b1/b2), the more labour
intensive is the technique.
• Similarly, the lower the ratio (b1/b2) the more
capital intensive is the technique.
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Cobb–Douglas Production function:
X*= Kv f(x0)
X0 = b0 L b1 K b2
X* = b0 (kL) b1 (kK)b2
= Kb1+b2 (bo L b1 K b2)
=Kv f (X0)
(V=b1 + b2)
 X* = K v f (Xo)
In case when
V=1 we have constant RTS
V>1 we have increasing RTS
V<1 we have decreasing RTS
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