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Chapter 5. The theories of
producers’ behaviors
I. The theory of production
II. The theory of cost
III.The theory of profit
1
I. The theory of production
2
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.
• Q= f(X1, X2, ..Xn)
• Q = f (K, L)
• 𝑄 = 𝐴𝐾 % 𝐾& (Cobb Douglass function)
3
3
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Short run vs Long run
• Short-run:
• Period of time in which quantities of one or more production factors cannot be
changed.
• These inputs are called fixed inputs.
• Long-run
• Amount of time needed to make all production inputs variable.
• Short run and long run are not time specific
4
4
L
K
Q
0
10
0
APL
1
10
10
10
2
10
30
15
3
10
60
20
4
10
80
20
5
10
95
19
6
10
108
18
7
10
112
16
8
10
112
14
9
10
108
12
10
10
100
10
0
MPL
10
20
30
20
15
13
4
0
-4
-8
5
Marginal Product and Average Product
• The marginal product of any input is the increase in output
arising from an additional unit of that input, holding all other
inputs constant.
• Marginal product of labor (MPL) =
∆Q
∆L
• Average product of labor (APL) =Q
L
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7
II. The theory of cost
8
Fixed and Variable Costs
• Fixed costs are those costs that do not vary with the quantity of
output produced.
• Variable costs are those costs that do vary with the quantity of
output produced.
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Fixed and Variable Costs
• Total Costs
• Fixed Costs (FC)
• Variable Costs (VC)
• Total Costs (TC)
• TC = FC + VC
10
Costs
Q
FC
VC
TC
$800
FC
$700
VC
TC
$0 $100
$600
1
100
70
170
$500
2
100 120
220
3
100 160
260
4
100 210
310
5
100 280
380
6
100 380
480
7
100 520
620
Costs
0 $100
$400
$300
$200
$100
$0
0
1
2
3
4
5
6
7
Q
11
Fixed and Variable Costs
• Average Costs
• Average costs can be determined by dividing the firm’s costs by the
quantity of output it produces.
• The average cost is the cost of each typical unit of product.
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Fixed and Variable Costs
• Average Costs
• Average Fixed Costs (AFC)
• Average Variable Costs (AVC)
• Average Total Costs (ATC)
• ATC = AFC + AVC
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Average Costs
AFC =
Fixed cost FC
=
Quantity
Q
AVC =
Variable cost VC
=
Quantity
Q
ATC =
Total cost TC
=
Quantity
Q
14
Average Fixed Cost
FC
0 $100
AFC
n/a
1
100
$100
2
100
50
3
100 33.33
4
100
25
5
100
20
6
100 16.67
7
100 14.29
$200
Average
fixed cost (AFC)
is$175
fixed cost divided by the
quantity
of output:
$150
Costs
Q
AFC = FC/Q
$125
$100
Notice
$75 that AFC falls as Q rises:
The firm is spreading its fixed
$50
costs over a larger and larger
$25
number of units.
$0
0
1
2
3
4
Q
5
6
7
15
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Average Variable Cost
0
VC
$200
Average
variable cost (AVC)
is$175
variable cost divided by the
quantity
of output:
$150
AVC
$0
n/a
1
70
$70
2
120
60
3
160 53.33
4
210 52.50
5
280 56.00
6
380 63.33
7
520 74.29
Costs
Q
AVC = VC/Q
$125
$100
As$75
Q rises, AVC may fall initially.
In most cases, AVC will
$50
eventually rise as output rises.
$25
$0
0
1
2
3
4
Q
5
6
7
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Average Total Cost
Q
TC
0 $100
ATC
AFC
Average total cost
(ATC) equals total
cost divided by the
quantity of output:
AVC
n/a
n/a
n/a
1
170
$170
$100
$70
2
220
110
50
60
3
260 86.67 33.33 53.33
4
310 77.50
25 52.50
5
380
76
20 56.00
6
480
80 16.67 63.33
7
620 88.57 14.29 74.29
ATC = TC/Q
Also,
ATC = AFC + AVC
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Average Total Cost
Q
TC
0 $100
ATC
$200
Usually, as in this example,
$175
the ATC curve is U-shaped.
n/a
$150
170
$170
2
220
110
3
260 86.67
4
310 77.50
5
380
76
$25
6
480
80
$0
7
620 88.57
Costs
1
$125
$100
$75
$50
0
1
2
3
4
5
6
7
Q
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Fixed and Variable Costs
• Marginal Cost
• Marginal cost (MC) measures the increase in total cost that arises
from an extra unit of production.
• Marginal cost helps answer the following question:
• How much does it cost to produce an additional unit of output?
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Marginal Cost
MC =
(change in total cost) DTC
=
(change in quantity)
DQ
20
Marginal Cost
TC
0 $100
1
170
2
220
3
260
4
310
5
380
6
480
7
620
$200
MC
$175
$70
$150
50
$125
40
50
70
100
140
Costs
Q
$100
$75
$50
$25
$0
0
1
2
3
4
5
6
7
Q
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The Various Cost Curves Together
$200
$175
$150
Costs
ATC
AVC
AFC
MC
$125
$100
$75
$50
$25
$0
0
1
2
3
4
5
6
7
Q
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ACTIVE LEARNING
Calculating costs
3
Fill in the blank spaces of this table.
Q
VC
0
1
10
2
30
TC
AFC
AVC
ATC
$50
n/a
n/a
n/a
$10
$60.00
20
36.67
80
3
16.67
4
100
5
150
6
210
150
12.50
8.33
$10
30
37.50
30
260
MC
35
43.33
60
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ACTIVE LEARNING
Answers
3
Use relationship
AFC = TC/Q
ATC
FC/Q
First,
deduce
AVC
VC/Q
FC between
= $50 andMC
useand
FCTC
+ VC = TC.
Q
VC
TC
AFC
AVC
ATC
0
$0
$50
n/a
n/a
n/a
1
10
60
$50.00
$10
$60.00
2
30
80
25.00
15
40.00
3
60
110
16.67
20
36.67
4
100
150
12.50
25
37.50
5
150
200
10.00
30
40.00
6
210
260
8.33
35
43.33
MC
$10
20
30
40
50
60
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When MC < ATC,
$175
$150
ATC is rising.
$125
Costs
When MC > ATC,
The MC curve
crosses the
ATC curve at
the ATC curve’s
minimum.
ATC
MC
$200
ATC is falling.
$100
$75
$50
$25
$0
0
1
2
3
4
5
6
7
Q
25
III. The theory of profit
26
• 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
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Costs: Explicit vs. Implicit
• Explicit costs require an outlay of money,
e.g., paying wages to workers.
• Implicit costs do not require a cash outlay,
e.g., the opportunity cost of the owner’s time.
• Remember one of the Ten Principles:
The cost of something is
what you give up to get it.
• This is true whether the costs are implicit or explicit. Both matter for
firms’ decisions.
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Explicit vs. Implicit Costs: An Example
You need $100,000 to start your business.
The interest rate is 5%.
• Case 1: borrow $100,000
• explicit cost = $5000 interest on loan
• Case 2: use $40,000 of your savings,
borrow the other $60,000
• explicit cost = $3000 (5%) interest on the loan
• implicit cost = $2000 (5%) foregone interest you could have earned on your
$40,000.
In both cases, total (exp + imp) costs are $5000.
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Economic Profit vs. Accounting Profit
• Accounting profit
= total revenue minus total explicit costs
• Economic profit
= total revenue minus total costs (including explicit and implicit
costs)
• Accounting profit ignores implicit costs,
so it’s higher than economic profit.
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Figure 1 Economic versus Accountants
How an Economist
Views a Firm
How an Accountant
Views a Firm
Economic
profit
Accounting
profit
Revenue
Implicit
costs
Explicit
costs
Revenue
Total
opportunity
costs
Explicit
costs
Copyright © 2004 South-Western
31
ACTIVE LEARNING
2
Economic profit vs. accounting profit
The equilibrium rent on office space has just increased
by $500/month.
Compare the effects on accounting profit and economic
profit if
a. you rent your office space
b. you own your office space
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ACTIVE LEARNING
Answers
2
The rent on office space increases $500/month.
a.
You rent your office space.
Explicit costs increase $500/month.
Accounting profit & economic profit each fall
$500/month.
b.
You own your office space.
Explicit costs do not change,
so accounting profit does not change.
Implicit costs increase $500/month (opp. cost
of using your space instead of renting it),
so economic profit falls by $500/month.
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Profit maximization
•
𝜋 = 𝑇𝑅 − 𝑇𝐶
• Profit reaches its maximum when
𝜋′. = 0 ↔ TR3 − TC3 = 0 ↔ 𝑴𝑹 = 𝑴𝑪
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Total revenue maximization
• Total revenue reaches its maximum when
𝑇𝑅′. = 0 ↔ 𝑴𝑹 = 𝟎
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