Production and Costs
INPUTS
COSTS
OUTPUT
(Physical Product )
Inputs: Factors of Production
Factors of production:
• Land Labor Capital
• Intermediate goods
• (Entrepreneurial Services )
• Production Costs = Costs of Inputs
Production in the Short Run
versus Production in the Long Run
• In the short run at least one of the factors of
production remains unchanged (fixed).
• In the long run all factors of production are
variable.
• In a two-input production process, in the short
run, only one input is variable.
• In a two-input production model, in the short
run, the changes in the output (physical
product) are the result of changes in the
variable input.
Production in the Long Run
• In the long run all inputs used in the
production process by the firm are variable.
• In a two-input production model, in the long
run, both inputs (say, capital and labor) are
variable.
• In the long run the level of the output of a
firm can change as a result of changes in
any or all inputs.
A Short-Run Production (Function)
Analysis
Our model:
A firm using two inputs:
Capital (K); Fixed Input
Labor (L); Variable input
We examine the relationship between the variable
input (labor) and the output.
We examine how changes in labor (the variable input)
affect the out put.
Output Measures
• Total (Physical) Product (output), TPP: The total
amount of output produced by the firm over a
certain period
• Average (Physical) Product (of the variable
input), APP: Total (Physical) Product divided by
the number units of the variable input
• Marginal (Physical) Product (of the variable
input), MPP: The change in total product
resulting from employing one additional unit of
the variable input
Production in the Short Run
Inputs: Capital (K) and Labor (L)
K = 20 (Fixed) Labor: Variable
Total
Marginal
P. Product
Labor (L) P. Product
0
0
1
10
10
2
25
15
3
35
10
4
44
9
5
51
7
6
56
5
7
60
4
8
62
2
9
62
0
Average
P. Product
10.0
12.5
11.7
11.0
10.2
9.3
8.6
7.8
6.9
Total (Physical) Product and
Marginal Physical Product
Marginal Product
T ot al P r oduct
16
14
70
60
12
50
10
40
8
30
6
20
4
10
2
0
0
0
5
10
0
2
4
6
8
10
Average (Physical) Product and
Marginal Physical Product
Average Product
20
14
12
10
8
6
4
2
0
15
10
5
AP
MP
0
0
5
10
1 2 3 4 5 6 7 8 9 10
MPP and APP
Change in TPP
Marginal Physical Product = MPP =
Change in V. Input
Total Physical Product
Average Physical Product = APP =
Total V. Input
The “Law” of Diminishing Return
• Increases in the amount of any one input,
holding the amounts all other inputs constant,
would eventually result in decreasing marginal
product of the variable input.
Explanation: Unless all inputs are perfectly and
infinitely substitutable, as we increase the
amount of one input, while keeping other inputs
constant, at some point the productive
effectiveness of that input starts to decline.
Long-Run Production Function
Capital =>
Labor ||
V
1
2
3
4
5
0
1
2
3
4
3
5
6
6
5
10
18
23
25
26
15
30
40
45
47
18
40
47
52
56
20
46
52
60
65
Choosing the Optimal Mix of Inputs
• One approach to choosing the optimal (least costly)
mix of inputs is to compare the (marginal) cost of
producing one extra unit of out put across different
inputs.
• The firm would likely use the input that increases its
output at the lowest cost by comparing
Input Price
across all available inputs.
MPP
Capital
Labor
10
15
20
25
30
35
40
50
7.36
5.62
4.64
4
3.54
3.19
2.925
2.52
Isoquant and Isocost
Q = f ( K, L)
Cost = rK + w L
where r = price of capital
w = wage
Isoquant
K
Slope = MPL/MPK = MRTS
Q4
Q3
Q2
Q1
0
L
Isocost
K
Cost = r.K +w. L
Cost/r
Slope = w/r
L
0
Cost/w
Isocost
K
Cost = r.K +w. L
Cost/r
Slope = w/r
Q2
Q1
L
0
Cost/w
Input Optimizing Rule
MPL
MPK
MPM
--------- = --------- = ---------
w
or,
r
PM
MPL
w
MPL
w
------ = -------- , ---------- = --------MPM
r
MPM
PM
X path
K
Cost/r
Q2
Q1
L
0
Cost/w
$TC
LTC
Q
o
$
LTC
LAC = LTC/Q
LMC
LMC = dLTC/dQ
LAC
LMC
LAC= LMC
MC
Q
$
LMC
LAC
Q
o
Q1
Q*
Inputs: Capital (K) andLabor (L)
CapPrice =
K=
20 Lab: Variable
Wage =
Total T.Fixed T. Var Total Average Average Average
Labor (L) Product Cost Cost Cost F.Cost V.Cost T.cost
0
0
40
0
40
1
10
40
6
46 4.00 0.60 4.60
2
25
40
12
52 1.60 0.48 2.08
3
35
40
18
58 1.14 0.51 1.66
4
44
40
24
64 0.91 0.55 1.45
5
51
40
30
70 0.78 0.59 1.37
6
56
40
36
76 0.71 0.64 1.36
7
60
40
42
82 0.67 0.70 1.37
8
62
40
48
88 0.65 0.77 1.42
9
62
40
54
94 0.65 0.87 1.52
2
6
Marginal
Cost
0.60
0.40
0.60
0.67
0.86
1.20
1.50
3.00
Plotting the Cost Measures
5
10 0
4. 5
90
4
80
3. 5
70
3
TC
60
MC
2. 5
50
2
40
TVC
TFC
30
1 .5
AT C
20
1
AVC
0. 5
10
0
0
0
20
40
60
80
0
20
40
60
80
Plotting the Cost Measures
5
$
$
4 .5
MC
4
ATC
3 .5
MC
3
2 .5
AVC
2
1 .5
AT C
1
AVC
0 .5
A FC
AFC
0
0
20
40
60
Q
80
o
Q
Long-Run Average Total Cost (LATC)
K = 10 Wage=
L TPP TC
0
20
1
12 25
2
25 30
3
37 35
4
47 40
5
55 45
6
61 50
7
65 55
8
68 60
9
69 65
10 69 70
5 K=
ATC L
0
2.08 1
1.20 2
0.95 3
0.85 4
0.82 5
0.82 6
0.85 7
0.88 8
0.94 9
1.01 10
20
TPP TC
40
20 45
45 50
70 55
90 60
108 65
127 70
141 75
149 80
155 85
157 90
ATC
2.25
1.11
0.79
0.67
0.60
0.55
0.53
0.54
0.55
0.57
K=
L
0
1
2
3
4
5
6
7
8
9
10
30
TPP TC
60
28 65
60 70
90 75
118 80
143 85
164 90
183 95
195 100
202 105
204 110
ATC
2.32
1.17
0.83
0.68
0.59
0.55
0.52
0.51
0.52
0.54
Long-Run Average Total Cost
ATC
ATC
ATC
2. 5
2.5
2.5
2
2
2
1. 5
1.5
1.5
1
1
1
0. 5
0.5
0.5
0
0
0
0
50
100
K=30
K=20
K=1 0
0
50
100
150
200
0
100
200
300
LATC
K= 10
L= 6
.82
K= 20
L= 7
.53
.51
K= 30
L=8
LATC
Q
o
61
141
195
Long-Run Average Total Cost
$
(SATC)1
(SATC)2
(SATC)3
LATC
0
Q
Return to Scale
$
Constant Return to Scale
LATC
Increasing Return to Scale
0
Decreasing Return to Scale
Q
Return to Scale
• Output elasticity: εQ
% Change in Output
%Change in all inputs
ε >1
Constant Return: ε = 1
Diminishing Return: ε < 1
Cobb-Douglas function: Q = a Kb1Lb2
Increasing Return:
Q
Q
Q
b1+ b2 >1
b1 + b2 = 1
b1 + b2 < 1
Input Optimization Revisited
Marginal revenue product of an input is the value
of the output produced from applying one
additional unit of that input:
MRPL = MPL .Price of output = MPL. MR
MRPK = MPK.Price of output = MPK. MR
Input-optimizing rule: A firm will hire/buy each
input to the point where the marginal revenue
product the input is equal to its price.
MRPL = MPL. MR = w
MRPK = MPK . MR= r
Input optimization and demand for input:
Wage
6.00
4.30
3.10
DL: MRPL=MPL.MR
2.00
o
10
22
45
90
L
Another look at optimization rule:
MPL . MR = MRPL= w
MPL/MPK = MRTS = w/r
MPK . MR = MRPK = r
Alternatively:
MPL. MR = w
MPL MPL
 MR = MC