The Costs of Production
C H A P T E R
13 The Costs of Production
The Costs of Production P R I N C I P L E S O F P R I N C I P L E S O F conomics
E N. Gregory N. Gregory Mankiw Mankiw
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1 A C T I V E L E A R N I N G A C T I V E L E A R N I N G Brainstorming costs Brainstorming costs You run General Motors.
1
§ List 3 different costs you have. § List 3 different business decisions that are affected by your costs.
1 In this chapter, In this chapter,
look for the answers to these questions: 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
§ We assume that the firm’s goal is
Profit = Total revenue – Total cost the amount a firm receives from the sale of its output
THE COSTS OF PRODUCTION
3 Total Revenue, Total Cost, Profit
THE COSTS OF PRODUCTION
4 Costs: Explicit vs. Implicit
In both cases,
Case 2: use $40,000 of your savings, borrow the other $60,000 § explicit cost = $3000 (5%) interest on the loan § implicit cost =
§ explicit cost = §
§ Case 1: borrow $100,000
The interest rate is 5%.
§ This is true whether the costs are implicit or explicit. Both matter for firms’ decisions.
The cost of something is what you give up to get it.
§ Remember one of the Ten Principles:
§ Implicit costs
§ Explicit costs require an outlay of money, e.g., paying wages to workers.
THE COSTS OF PRODUCTION
5 Explicit vs. Implicit Costs: An Example You need $100,000 to start your business.
§ Accounting profit = total revenue minus
§ Economic profit
= total revenue minus § Accounting profit ignores implicit costs, so it’s higher than economic profit.
THE COSTS OF PRODUCTION
6 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 A C T I V E L E A R N I N G A C T I V E L E A R N I N G
2
2 Economic profit vs. accounting profit Economic profit vs. accounting profit
7 THE COSTS OF PRODUCTION
9 The Production Function §
A production function §
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.
Example 1: Farmer Jack’s Production Function L Q
3,000
(no. of (bushels
2,500
workers) of wheat)
ut tp u o 2,000 f o ty
1,500
1 1000
ti n a u 1,000
2 1800
Q 500
3 2400 4 2800
1
2
3
4
5
5 3000
No. of workers
10 THE COSTS OF PRODUCTION M arginal Product
§ If Jack hires one more worker, his output rises by the marginal product of labor.
The marginal product of any input is §
Notation: §
Examples: ∆Q = Marginal product of labor (MPL) =
§
11 THE COSTS OF PRODUCTION EXAM PLE 1: Total & M arginal Product
L Q
(no. of (bushels
MPL
workers) of wheat) 1000
∆L = 1 ∆Q = 1000
1 1000 2 1800 3 2400 4 2800 5 3000
12 THE COSTS OF PRODUCTION
13 MPL equals the slope of the production function.
1000
§ Diminishing marginal product :
§ In general, MPL diminishes as L rises
§ As Jack adds workers,
§ Farmer Jack’s output rises by a smaller and smaller amount for each additional worker. Why?
§ Comparing them helps Jack decide whether he would benefit from hiring the worker.
§ When Farmer Jack
§ Recall one of the Ten Principles: Rational people think at the margin.
(no. of workers)
L
(bushels of wheat)
MPL Q
Notice that MPL diminishes as L increases. This explains why the production function gets flatter as L increases.
1 1000
2 800
5 No. of workers Q u a n ti ty o f o u tp ut EXAM PLE 1: M PL = Slope of Prod Function
500 1,000 1,500 2,000 2,500 3,000
1
2
3
1800
4
3000
5 200
2800
4 400
2400
3 600
THE COSTS OF PRODUCTION
THE COSTS OF PRODUCTION
14 W hy M PL Is Important
THE COSTS OF PRODUCTION
15 W hy M PL Diminishes
§ 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. §
THE COSTS OF PRODUCTION
16 EXAM PLE 1: Farmer Jack’s Costs
(bushels of wheat)
Quantity of wheat T o ta l c o st
1000 2000 3000
$12,000
$0 $2,000 $4,000 $6,000 $8,000 $10,000
$1,000 1000 $3,000 1800 $5,000 2400 $7,000 2800 $9,000 3000 $11,000
(bushels of wheat) Total Cost
Q
(no. of workers)
So Farmer Jack’s costs are related to how much wheat he produces….
L
Q
Cost of labor Cost of land
$0 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000
$8,000 $6,000 $4,000 $2,000
1 $10,000
2 1000
3 1800
4 2400
5 2800
3000
Total Cost
$11,000 $9,000 $7,000 $5,000 $3,000 $1,000
THE COSTS OF PRODUCTION
17 EXAM PLE 1: Farmer Jack’s Costs
THE COSTS OF PRODUCTION
18 EXAM PLE 1: Farmer Jack’s Total Cost Curve
M arginal Cost § Marginal Cost (MC)
19 THE COSTS OF PRODUCTION EXAM PLE 1: Total and M arginal Cost
Q
Total Marginal (bushels
Cost Cost (MC) of wheat) $1,000
$2.00
∆Q = 1000 ∆TC = $2000
1000 $3,000 1800 $5,000 2400 $7,000 2800 $9,000 3000 $11,000
20 THE COSTS OF PRODUCTION EXAM PLE 1: The M arginal Cost Curve
$12 Q
(bushels TC MC
$10 MC usually rises
of wheat)
as Q rises, ($)
$8 t as in this example.
$1,000 s
o
$2.00 C
l $6 a
1000 $3,000
in
$2.50
rg $4 a
1800 $5,000
M
$3.33
$2
2400 $7,000 $5.00 2800 $9,000
$0
$10.00
1,000 2,000 3,000
3000 $11,000
Q
21 THE COSTS OF PRODUCTION
W hy M C Is Important Farmer Jack is rational and wants to maximize
§ his profit. To increase profit, should he produce more or less wheat? To find the answer, Farmer Jack needs to
§ “think at the margin.”
22 THE COSTS OF PRODUCTION Fixed and Variable Costs
§ Fixed costs (FC) § For Farmer Jack, § Other examples:
§ Variable costs (VC) For Farmer Jack, VC =
§ § Other example: § Total cost (TC) =
23 THE COSTS OF PRODUCTION EXAM PLE 2 Our second example is more general,
§ applies to any type of firm producing any good with any types of inputs.
24 THE COSTS OF PRODUCTION
EXAM PLE 2: Costs $800
FC Q FC
VC TC
VC $700
TC
$100 $0 $100
$600
1 100 70 170
$500 ts
2 100 120 220
s $400 o C
3 100 160 260
$300
4 100 210 310
$200
5 100 280 380
$100
6 100 380 480
$0
7 100 520 620
1
2
3
4
5
6
7 Q
25 THE COSTS OF PRODUCTION EXAM PLE 2: M arginal Cost
$200
Q TC MC Recall, Marginal Cost (MC)
$175
is the change in total cost from
$100 $70 producing one more unit: $150 1 170
$125 ∆TC
50
ts MC = s
2 220
o $100 ∆Q
40 C 3 260 Usually, MC rises as Q rises, due $75
50 to diminishing marginal product. 4 310 $50
70 Sometimes (as here), MC falls
$25 5 380 100 before rising.
$0 6 480 140 (In other examples, MC may be
1
2
3
4
5
6
7 7 620
constant.) Q
26 THE COSTS OF PRODUCTION
EXAM PLE 2: A verage Fixed Cost
$200
Q FC AFC Average fixed cost (AFC) is fixed cost divided by the $175
$100 n/a
quantity of output:
$150 1 100 $100
AFC = FC/Q
$125
ts
2 100
50
s o
$100
C
3 100
33.33 Notice that AFC falls as Q rises:
$75 4 100
25 The firm is spreading its fixed
$50
costs over a larger and larger
5 100
20 $25 number of units.
6 100
16.67 $0
1
2
3
4
5
6
14.29 Q
7 7 100
27 THE COSTS OF PRODUCTION
A verage Variable Cost
THE COSTS OF PRODUCTION
28 EXAM PLE 2:
33.33
2
1
$100 $125 $150 $175 $200
$0 $25 $50 $75
AVC AFC TC Q Average total cost (ATC) Also,
50 $70 $100 n/a n/a
60
25
53.33
4
52.50
20
56.00
16.67
63.33
14.29
74.29
3
6
5
7 480
TC Q
1 $100
2 170
3 220
4 260
5 310
6 380
620
2 170
ATC
$170 n/a
86.67 110
77.50
76
80
88.57
7 Q C o s ts EXAM PLE 2: A verage Total Cost
520
1 $100
3 220
63.33
AVC = VC/Q As Q rises, AVC may fall initially.
VC Q Average variable cost (AVC) is variable cost divided by the quantity of output:
AVC
$0 n/a
60 $70
53.33
52.50
56.00
74.29
$0 $25 $50 $75
1
70
2
3 120
4 160
5 210
6 280
7 380
4 260
In most cases, AVC will eventually rise as output rises.
$100 $125 $150 $175 $200
76
5 310
6 380
7 480
620
ATC
$170 n/a
86.67 110
1
77.50
80
88.57
C o s ts
7 Q
6
5
4
3
2
THE COSTS OF PRODUCTION
29 EXAM PLE 2: A verage Total Cost
THE COSTS OF PRODUCTION
30 Usually, as in this example, the ATC curve is U-shaped.
The Various Cost Curves Together EXAM PLE 2: $200 $175 $150
ATC $125 ts
AVC s o
$100 AFC C
$75 MC
$50 $25 $0
1
2
3
4
5
6
7 Q
31 THE COSTS OF PRODUCTION
3 A C T I V E L E A R N I N G A C T I V E L E A R N I N G
3
Calculating costs Calculating costs Fill in the blank spaces of this table.
Q
VC TC AFC AVC ATC MC
$50 n/a n/a n/a $10 1 10 $10 $60.00
2
30
80
30
3
16.67
20
36.67 4 100 150
12.50
37.50 5 150
30
60 6 210 260
8.33
35
43.33
32 EXAM PLE 2:
W hy ATC Is Usually U-Shaped As Q rises:
$200 Initially,
$175 $150 $125 ts
Eventually, s o $100 C
$75 $50 $25
Efficient scale : $0
1
2
3
4
5
6
7 Q
34 THE COSTS OF PRODUCTION
EXAM PLE 2: A TC and MC When MC < ATC,
ATC $200
MC $175 $150
When MC > ATC, $125 ts s o
$100 C
$75 The MC curve
$50 crosses the ATC curve at $25
$0
1
2
3
4
5
6
7 Q
35 THE COSTS OF PRODUCTION Costs in the Short Run & Long Run
Short run: §
Long run: §
In the long run, § (e.g., the factory size with the lowest ATC).
36 THE COSTS OF PRODUCTION EXAM PLE 3: LRA TC with 3 factory Sizes
Firm can choose Avg from 3 factory Total sizes: S, M, L.
Cost Each size has its own SRATC curve.
Q
37 THE COSTS OF PRODUCTION
LRA TC with 3 factory Sizes ATC S ATC M ATC L Q
Avg Total Cost
THE COSTS OF PRODUCTION
38 EXAM PLE 3:
LRATC
40 Q ATC How ATC Changes as the Scale of Production Changes Economies of scale : Constant returns to scale : Diseconomies of scale :
So a typical LRATC curve looks like this:
Q ATC In the real world, factories come in many sizes, each with its own SRATC curve.
, firm will choose
To produce more than Q B
B , firm will choose
To produce between Q A and Q
A , firm will choose
Q A Q B To produce less than Q
THE COSTS OF PRODUCTION
39 A Typical LRA TC Curve
THE COSTS OF PRODUCTION
How ATC Changes as the Scale of Production Changes Economies of scale occur when
§ Diseconomies of scale are due to
§
41 THE COSTS OF PRODUCTION CONCLUSION Costs are critically important to many business
§ decisions, including production, pricing, and hiring.
§ This chapter has introduced the various cost concepts.
The following chapters will show how firms use § these concepts to maximize profits in various market structures.