2. In this chapter,
look for the answers to these questions:
What is a production function? What is marginal
product? How are they related?
What are the various costs, and how are they
related to each other and to output?
How are costs different in the short run vs.
the long run?
What are “economies of scale”?
2
3. THE COSTS OF PRODUCTION 3
Total Revenue, Total Cost, Profit
We assume that the firm’s goal is to maximize
profit.
Profit = Total revenue – Total cost
the amount a
firm receives
from the sale
of its output
the market
value of the
inputs a firm
uses in
production
4. THE COSTS OF PRODUCTION 9
The Production Function
A production function shows the relationship
between the quantity of inputs used to produce a
good and the quantity of output of that good.
It 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.
5. THE COSTS OF PRODUCTION 10
0
500
1,000
1,500
2,000
2,500
3,000
0 1 2 3 4 5
No. of workers
Quantity
of
output
Example 1: Farmer Jack’s Production Function
3000
5
2800
4
2400
3
1800
2
1000
1
0
0
Q
(bushels
of wheat)
L
(no. of
workers)
6. THE COSTS OF PRODUCTION 11
Marginal Product
If Jack hires one more worker, his output rises
by the marginal product of labor.
The marginal product of any input is the
increase in output arising from an additional unit
of that input, holding all other inputs constant.
Notation:
∆ (delta) = “change in…”
Examples:
∆Q = change in output, ∆L = change in labor
Marginal product of labor (MPL) =
∆Q
∆L
7. THE COSTS OF PRODUCTION 12
3000
5
2800
4
2400
3
1800
2
1000
1
0
0
Q
(bushels
of wheat)
L
(no. of
workers)
EXAMPLE 1: Total & Marginal Product
200
400
600
800
1000
MPL
∆Q = 1000
∆L = 1
∆Q = 800
∆L = 1
∆Q = 600
∆L = 1
∆Q = 400
∆L = 1
∆Q = 200
∆L = 1
8. THE COSTS OF PRODUCTION 13
MPL equals the
slope of the
production function.
Notice that
MPL diminishes
as L increases.
This explains why
the production
function gets flatter
as L increases.
0
500
1,000
1,500
2,000
2,500
3,000
0 1 2 3 4 5
No. of workers
Quantity
of
output
EXAMPLE 1: MPL = Slope of Prod Function
3000
5
200
2800
4
400
2400
3
600
1800
2
800
1000
1
1000
0
0
MPL
Q
(bushels
of wheat)
L
(no. of
workers)
9. THE COSTS OF PRODUCTION 16
EXAMPLE 1: Farmer Jack’s Costs
Farmer Jack must pay $1000 per month for the
land, regardless of how much wheat he grows.
The market wage for a farm worker is $2000 per
month.
So Farmer Jack’s costs are related to how much
wheat he produces….
10. THE COSTS OF PRODUCTION 17
EXAMPLE 1: Farmer Jack’s Costs
$11,000
$9,000
$7,000
$5,000
$3,000
$1,000
Total
Cost
3000
5
2800
4
2400
3
1800
2
1000
1
$10,000
$8,000
$6,000
$4,000
$2,000
$0
$1,000
$1,000
$1,000
$1,000
$1,000
$1,000
0
0
Cost of
labor
Cost of
land
Q
(bushels
of wheat)
L
(no. of
workers)
11. THE COSTS OF PRODUCTION 18
EXAMPLE 1: Farmer Jack’s Total Cost Curve
Q
(bushels
of wheat)
Total
Cost
0 $1,000
1000 $3,000
1800 $5,000
2400 $7,000
2800 $9,000
3000 $11,000
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
0 1000 2000 3000
Quantity of wheat
Total
cost
12. THE COSTS OF PRODUCTION 19
Marginal Cost
Marginal Cost (MC)
is the increase in Total Cost from
producing one more unit:
∆TC
∆Q
MC =
13. THE COSTS OF PRODUCTION 20
EXAMPLE 1: Total and Marginal Cost
$10.00
$5.00
$3.33
$2.50
$2.00
Marginal
Cost (MC)
$11,000
$9,000
$7,000
$5,000
$3,000
$1,000
Total
Cost
3000
2800
2400
1800
1000
0
Q
(bushels
of wheat)
∆Q = 1000 ∆TC = $2000
∆Q = 800 ∆TC = $2000
∆Q = 600 ∆TC = $2000
∆Q = 400 ∆TC = $2000
∆Q = 200 ∆TC = $2000
14. THE COSTS OF PRODUCTION 21
MC usually rises
as Q rises,
as in this example.
EXAMPLE 1: The Marginal Cost Curve
$11,000
$9,000
$7,000
$5,000
$3,000
$1,000
TC
$10.00
$5.00
$3.33
$2.50
$2.00
MC
3000
2800
2400
1800
1000
0
Q
(bushels
of wheat)
$0
$2
$4
$6
$8
$10
$12
0 1,000 2,000 3,000
Q
Marginal
Cost
($)
15. THE COSTS OF PRODUCTION 23
Fixed and Variable Costs
Fixed costs (FC) do not vary with the quantity of
output produced.
For Farmer Jack, FC = $1000 for his land
Other examples:
cost of equipment, loan payments, rent
Variable costs (VC) vary with the quantity
produced.
For Farmer Jack, VC = wages he pays workers
Other example: cost of materials
Total cost (TC) = FC + VC
16. THE COSTS OF PRODUCTION 24
EXAMPLE 2
Our second example is more general,
applies to any type of firm
producing any good with any types of inputs.
18. THE COSTS OF PRODUCTION 26
Recall, Marginal Cost (MC)
is the change in total cost from
producing one more unit:
Usually, MC rises as Q rises, due
to diminishing marginal product.
Sometimes (as here), MC falls
before rising.
(In other examples, MC may be
constant.)
EXAMPLE 2: Marginal Cost
620
7
480
6
380
5
310
4
260
3
220
2
170
1
$100
0
MC
TC
Q
140
100
70
50
40
50
$70
∆TC
∆Q
MC =
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Costs
19. THE COSTS OF PRODUCTION 27
EXAMPLE 2: Average Fixed Cost
100
7
100
6
100
5
100
4
100
3
100
2
100
1
14.29
16.67
20
25
33.33
50
$100
n/a
$100
0
AFC
FC
Q Average fixed cost (AFC)
is fixed cost divided by the
quantity of output:
AFC = FC/Q
Notice that AFC falls as Q rises:
The firm is spreading its fixed
costs over a larger and larger
number of units.
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Costs
20. THE COSTS OF PRODUCTION 28
EXAMPLE 2: Average Variable Cost
520
7
380
6
280
5
210
4
160
3
120
2
70
1
74.29
63.33
56.00
52.50
53.33
60
$70
n/a
$0
0
AVC
VC
Q Average variable cost (AVC)
is variable cost divided by the
quantity of output:
AVC = VC/Q
As Q rises, AVC may fall initially.
In most cases, AVC will
eventually rise as output rises.
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Costs
21. THE COSTS OF PRODUCTION 29
EXAMPLE 2: Average Total Cost
88.57
80
76
77.50
86.67
110
$170
n/a
ATC
620
7
480
6
380
5
310
4
260
3
220
2
170
1
$100
0
74.29
14.29
63.33
16.67
56.00
20
52.50
25
53.33
33.33
60
50
$70
$100
n/a
n/a
AVC
AFC
TC
Q Average total cost
(ATC) equals total
cost divided by the
quantity of output:
ATC = TC/Q
Also,
ATC = AFC + AVC
22. THE COSTS OF PRODUCTION 30
Usually, as in this example,
the ATC curve is U-shaped.
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Costs
EXAMPLE 2: Average Total Cost
88.57
80
76
77.50
86.67
110
$170
n/a
ATC
620
7
480
6
380
5
310
4
260
3
220
2
170
1
$100
0
TC
Q
23. THE COSTS OF PRODUCTION 31
EXAMPLE 2: The Various Cost Curves Together
AFC
AVC
ATC
MC
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Costs
24. A C T I V E L E A R N I N G 3
Calculating costs
32
Fill in the blank spaces of this table.
210
150
100
30
10
VC
43.33
35
8.33
260
6
30
5
37.50
12.50
150
4
36.67
20
16.67
3
80
2
$60.00
$10
1
n/a
n/a
n/a
$50
0
MC
ATC
AVC
AFC
TC
Q
60
30
$10
25. A C T I V E L E A R N I N G 3
Answers
33
Use AFC = FC/Q
Use AVC = VC/Q
Use relationship between MC and TC
Use ATC = TC/Q
First, deduce FC = $50 and use FC + VC = TC.
210
150
100
60
30
10
$0
VC
43.33
35
8.33
260
6
40.00
30
10.00
200
5
37.50
25
12.50
150
4
36.67
20
16.67
110
3
40.00
15
25.00
80
2
$60.00
$10
$50.00
60
1
n/a
n/a
n/a
$50
0
MC
ATC
AVC
AFC
TC
Q
60
50
40
30
20
$10
26. THE COSTS OF PRODUCTION 35
EXAMPLE 2: ATC and MC
ATC
MC
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Costs
When MC < ATC,
ATC is falling.
When MC > ATC,
ATC is rising.
The MC curve
crosses the
ATC curve at
the ATC curve’s
minimum.
27. THE COSTS OF PRODUCTION 48
The Complete Data for Example 2
720
100
8
88.57
74.29
620
7
80
480
100
6
56.00
20
380
280
5
52.50
25
310
4
86.67
160
100
3
110
60
50
120
2
$170
$100
170
100
1
n/a
n/a
n/a
$100
$0
$100
0
MC
ATC
AVC
AFC
TC
VC
FC
Q
200
140
100
70