The Production Process
and Costs
By Asst. Prof. Kessara Thanyalakpark, Ph.D.
1
Production Analysis
Production Function
◦ Q = F(K,L)
◦ The maximum amount of output that can
be produced with K units of capital and L
units of labor.
 Short-Run vs. Long-Run Decisions
 Fixed vs. Variable Inputs

2
Total Product
Production Function
 Example: Q = F(K,L) = K.5 L.5
◦ K is fixed at 16 units.
◦ Short run production function:
Q = (16).5 L.5 = 4 L.5
◦ Production when 100 units of labor are
used?
Q = 4 (100).5 = 4(10) = 40 units

3
Marginal Product of Labor
MPL = DQ/DL
 Measures the output produced by the last
worker.

4
Average Product of Labor
APL = Q/L
 Measures the output of an “average”
worker.

5
Stages of Production
Q
Increasing
Marginal
Returns
Diminishing
Marginal
Returns
Negative
Marginal
Returns
Q=F(K,L)
MP
AP
L
6
The Law of Diminishing Marginal Returns
As the use of an input increases with other
inputs fixed, the resulting additions to
output will eventually decrease.
 This law applies to a given production
technology (assume technology constant)
 Technological Improvement may make it
appear that there is not marginal returns
when in fact there is

7
8
The Effect of Technological
Improvement
8
Choice of Inputs : Production
Isoquants
Most production functions allow some
substitution of inputs
 Suppose Q = K1/2L1/2 ; to produce Q = 100,
there are many combinations of K and L
yield the result
 An isoquant shows all input combinations
that produce the same quantity assuming
efficient production.

9
10
Isoquants
“Substitution”

50
Unit of capital
40

20
T
10
0
15 20
75
40
Unit of labor
Q3 = 300
Q2 = 200
Q1 = 100
Labors must be added
for each unit of K
eliminated, holding
output constant.=
-( K/ L)
as K decreases, L
increases : use more
labor to compensate
for one additional K
10
Slope and MP ( MPL , MPK)






output( Q) = (MPl) x ( L) + (MPk) x ( K)
(Slope) = - ( K/ L)
MPl = output / labor
MPk =
output/ capital
In an isoquant curve, output is constant - hence
Q = (MPl) x ( L) + (MPk) x ( K) = 0
Slope = - ( K/ L) = (MPl) / (MPk)
11
Returns to Scale
Input substitution show what happen when
a firm substitute one input for another
while keeping output constant
 In long run, all input variable, one of the
best ways to change output is to change the
scale of operation (increase all inputs to
production in proportion)

12
Returns to Scale

Increasing Returns to Scale : output more
than doubles when all inputs are doubled

Constant Returns to Scale : output
doubles when all inputs are doubled

Decreasing Returns to Scale : output less
than doubles when all inputs are doubled
13
Constant RTS
14
Increasing RTS
15
Isocost Line
As we see,there are many ways to produce a
given level of output, how does a firm choose
its input mix?
 Depending on the costs of the inputs
 Cost is the sum of the quantities of each
input used in the production process times
their respective prices;
 TC = Wage x Labor + Rent x Capital

16
Capital
K
10
8 A
6
4
2
0 2
Illustration of Isocost curve
B
C
K=a-bL
D
4 6 8 10 12 14 16 18 20
Labor
L

Total cost = wage (labor) + rent (capital)

Given TC is fixed, isocost can be expressed as : K = (TC/ r) - (wage/r)
Labor

Slope of isocost curve = - wage / rent ; slope is used to determine how
much K must be given up if 1 more unit of labor is purchased.

If TC increases - a parallel upward shift in the isocost curve because
prices of inputs are constant
17
Isocost



The combinations of
inputs that cost the
producer the same
amount of money
For given input prices,
isocosts farther from
the origin are
associated with higher
costs.
Changes in input
prices change the
slope of the isocost
line
K
C0
C1
L
K
New Isocost Line for
a decrease in the
wage (price of
labor).
L
18
Cost Minimization
K
Slope of Isocost
=
Slope of Isoquant
Point of Cost
Minimization
Q
L
19
Cost Minimization

Marginal product per dollar spent should be
equal for all inputs:
MPL MPK
=
w
r
20
Optimal Input Mix and Changes in
Input Prices
K
B
A
High wage
Low wage
L
21
Optimal Input Mix




When wage is low ; optimal input mix = A
Once wage is high; optimal input mix = B
Optimal input mix ( input combination yield a
given output at the minimized cost) varies
depending on relative prices
It can be shown that the optimal input mix is at
the point where ;
MPw / Wage = MPr / Rent
where slope of isoquant = slope of isocost
22
Cost Analysis

Types of Costs
◦ Fixed costs (FC)
◦ Variable costs
(VC)
◦ Total costs (TC)
23
Total Cost Curves
It is a relationship between each possible
level of output and its lowest cost possible.
 Basically, total cost is derived from the
isoquant and isocost analysis

24
Short Run Versus Long Run
There are two types of cost ; short run and
long run
 Short run is the operating period during
which at least one input is fixed in supply (
have fixed cost)
 Long run : periods where firm has complete
flexibility - no inputs are fixed ( have only
variable cost)

25
Short run Total and Variable Costs
C(Q): Minimum total cost $
of producing alternative
levels of output:
C(Q) = VC + FC
VC(Q)
C(Q) = VC + FC
VC(Q): Costs that vary
with output
FC: Costs that do not vary
with output
FC
Q
26
Fixed Cost
$
FC: Costs that do
not change as output
changes
C(Q) = VC + FC
VC(Q)
FC
Q
27
Some Definitions
Average Total Cost
ATC = AVC + AFC
$
ATC = C(Q)/Q
Average Variable Cost
AVC = VC(Q)/Q
MC
ATC
AVC
Average Fixed Cost
AFC = FC/Q
Marginal Cost
MC = ∆C/∆Q
AFC
Q
28
Fixed Cost
Q0×(ATC-AVC)
$
= Q0× AFC
= Q0×(FC/ Q0)
MC
ATC
AVC
= FC
ATC
AFC
Fixed Cost
AVC
Q0
Q
29
Variable Cost
$
Q0×AVC
= Q0×[VC(Q0)/ Q0]
= VC(Q0)
MC
ATC
AVC
AVC
Variable Cost
Q0
Q
30
Total Cost
Q0×ATC
$
= Q0×[C(Q0)/ Q0]
= C(Q0)
MC
ATC
AVC
ATC
Total Cost
Q0
Q
31
Relation between Production Theory
and Cost

SMC = TVC/
Q = ( Wage x Labor) / Q
= Wage ( Labor/ Output )
= Wage Payment / MP

In the Short-Run, law of diminishing in MP
apply to MC too. Law of diminishing MP
eventually fall
( capital is fixed)
MC rises
32
Long Run Cost Curve
Long run curves - often referred to as
planning curves
 In the long run, AVC always less than or
equal to the short-run AVC
 It can be thought of as an envelop theorem

33
Long-run average cost
envelope of short-run average cost curves
34
Long-run average and marginal
cost curves
35
Economies of Scale
$
LRAC
Economies
of Scale
Diseconomies
of Scale
Output
36
Economies of Scale
Greater Specialization in the use of capital
and labor
 Learning curve effect
 Volume discounts in purchasing inputs
 Relatively cheaper cost of fund

37
Economies of Scale





Overhead cost ( administrative costs –
management salaries, other indirect
expenditures as heating and lighting
expenses)
Reserves of replacement parts and
maintenance personal
Distribution
Marketing and sales promotions
Research and development
38
Diseconomies of Scales
Transportation cost (one plan
distribute to all outlets)
 Problems of coordination and control
encountered by management

39
Economies of Scope

Costs of producing two or more
products jointly by one firm is less
than cost of producing these products
separately by different plants or firms
[TC(Q1,0) + TC(0,Q2) ] > TC(Q1,Q2)
40
Economics of Diversification

Benefits
◦ Economies of
Scope
◦ Promoting
Complements

Costs
◦ More expensive
to manage
◦ Communication
41
A Faulty Reason to Diversify
Should firm enter into a countercyclical
industry to reduce earning volatility?
 It is true that diversification can reduce
earning volatility.
 But the reduction in volatility need not
increase a firm’s value.

42
The costs of integrating diverse business
within the same firm can be significant.
 Investors (shareholders) can diversify
within their own investment portfolio at low
cost.

43
When does Diversification create
value?
Economies of Scope is envisioned
 Likely to occur in related diversification.
For example, when the businesses serve
common markets or use related
technologies.

44
Profit maximization
A firm should increase output as long as
marginal revenue exceeds marginal cost
 A firm should not increase output if
marginal cost exceeds marginal revenue
 At the profit-maximizing level of output,
MR=MC

45
Optimal output and changes in marginal
cost
46