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Production and Costs
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
The Production Function
• Production function– Relationship between
• Quantity of inputs used to make a good• And the quantity of output of that good
– Gets flatter as production rises
• It can be represented by a table, equation, or graph.
• Input sometimes called factors of production to produce output.
THE COSTS OF PRODUCTION
4
0
500
1,000
1,500
2,000
2,500
3,000
0 1 2 3 4 5
No. of workers
Qu
anti
ty o
f ou
tpu
t
Example 1: Farmer Jack’s Production Function
30005
28004
24003
18002
10001
00
Q (bushels of wheat)
L(no. of
workers)
Marginal 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.
• Notation: ∆ (delta) = “change in…”
Examples: ∆Q = change in output, ∆L = change in labor
• Marginal product of labor (MPL) = ∆Q∆L
THE COSTS OF PRODUCTION
6
30005
28004
24003
18002
10001
00
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
THE COSTS OF PRODUCTION
7
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
Qu
anti
ty o
f ou
tpu
t
EXAMPLE 1: MPL = Slope of Prod Function
30005200
28004400
24003600
18002800
100011000
00
MPLQ
(bushels of wheat)
L(no. of
workers)
Production and Costs
• Diminishing marginal product– Marginal product of an input declines as the
quantity of the input increases
• Total-cost curve– Relationship between quantity produced and total
costs
– Gets steeper as the amount produced rises
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
Costs: Explicit vs. Implicit
• Costs as opportunity costs– The cost of something is what you give up to get it
• Firm’s cost of production– Include all the opportunity costs of making its
output of goods and services
– Explicit costs
– Implicit costs
Costs: Explicit vs. Implicit
• Explicit costs– Input costs that require an outlay of money by the
firm
• Implicit costs– Input costs that do not require an outlay of money
by the firm– Ignored by accountants
• Total costs– Explicit costs + Implicit costs
THE COSTS OF PRODUCTION
12
Explicit vs. Implicit Costs: An ExampleYou 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.
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.
14
Economists include all opportunity costs when analyzing a firm, whereas accountants measure only explicit costs. Therefore, economic profit is smaller than accounting profit.
THE COSTS OF PRODUCTION
15
EXAMPLE 1: Farmer Jack’s Costs
$11,000
$9,000
$7,000
$5,000
$3,000
$1,000
Total Cost
30005
28004
24003
18002
10001
$10,000
$8,000
$6,000
$4,000
$2,000
$0
$1,000
$1,000
$1,000
$1,000
$1,000
$1,00000
Cost of labor
Cost of land
Q(bushels of wheat)
L(no. of
workers)
THE COSTS OF PRODUCTION
16
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
To
tal c
ost
Various Measures of Cost
• Fixed costs– Costs that do not vary with the quantity of output
produced
• Variable costs– Costs that vary with the quantity of output
produced
• Total cost– Fixed cost + Variable cost
Costs in Short and Long Run
• Many decisions– Fixed in the short run
– Short run: Some inputs are fixed (e.g., factories, land). The costs of these inputs are FC.
– Variable in the long run
– All inputs are variable (e.g., firms can build more factories, or sell existing ones).
THE COSTS OF PRODUCTION
19
EXAMPLE 2: Costs
7
6
5
4
3
2
1
620
480
380
310
260
220
170
$100
520
380
280
210
160
120
70
$0
100
100
100
100
100
100
100
$1000
TCVCFCQ
$0
$100
$200
$300
$400
$500
$600
$700
$800
0 1 2 3 4 5 6 7
Q
Cos
ts
FC
VC
TC
Marginal cost
• Marginal cost The change in a firm’s total cost from producing one more unit of a good or service.
• MC= ∆TC/ ∆Q
• Rising marginal cost curve– Because of diminishing marginal product
THE COSTS OF PRODUCTION
21
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
6207
4806
3805
3104
2603
2202
1701
$1000
MCTCQ
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
Co
sts
THE COSTS OF PRODUCTION
22
Why Marginal Cost is U-shaped• When the marginal product of labor is raising the
marginal cost of output is falling.
• When the marginal product of labor is falling the marginal cost of production is raising.
Labour Quantity Marginal Product of Labour (MPL)
Total Cost Marginal Cost (MC) $
0 0 - 800 -
1 200 200 1450 3.25
2 450 250 2100 2.60
3 550 100 2750 6.50
4 600 50 3400 13.00
Various Measures of Cost
• Average total cost (ATC) equals total cost divided by the quantity of output:
• ATC = TC/Q– Cost of a typical unit of output
• ATC = AFC + AVC• Average fixed cost (AFC), Fixed cost divided by
the quantity of output produced= FC/Q• Average variable cost (AVC), Variable cost
divided by the quantity of output produced=VC/Q
Various Measures of Cost
• U-shaped average total cost curveATC = AVC + AFC
– AFC – always declines as output rises
– AVC – typically rises as output increases • Because of diminishing marginal product
– The bottom of the U-shape• At quantity that minimizes average total cost
25© 2012 Cengage Learning. All Rights
Reserved.
Cost Curves for a Typical Firm
Costs
1.00
0.50
2.00
1.50
2.50
$3.00Many firms experience increasing marginal product before diminishing marginal product. As a result, they have cost curves shaped like those in this figure. Notice that marginal cost and average variable cost fall for a while before starting to rise.
Quantity of Output0 2 4 6 8 10 12 14
MC
ATC
AVC
AFC
Various Measures of Cost
• Efficient scale– Quantity of output that minimizes ATC
• Relationship between MC and ATC – When MC < ATC: average total cost is falling
– When MC > ATC: average total cost is rising
– The marginal-cost curve crosses the average-total-cost curve at its minimum
THE COSTS OF PRODUCTION
27
EXAMPLE 2: ATC and MC
ATCMC
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Cos
ts
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.
Costs in Long Run
• Long-run average cost curve A curve showing the lowest cost at which a firm is able to produce a given quantity of output in the long run, when no inputs are fixed.
• In the long run, ATC at any Q is cost per unit using the most efficient mix of inputs for that Q (e.g., the factory size with the lowest ATC).
© 2012 Cengage Learning. All Rights Reserved.
Average Total Cost in the Short and Long RunsAverage
TotalCost
Because fixed costs are variable in the long run, the average-total-cost curve in the short run differs from the average-total-cost curve in the long run.
Quantity of Cars per Day0
ATC in short run with small factory
ATC in short runwith medium factory ATC in short run
with large factory
ATC in long run
10,000
$12,000
1,000 1,200
Economiesof scale
Diseconomiesof scale
Constant returns to scale
THE COSTS OF PRODUCTION
30
How ATC Changes as the Scale of Production Changes
Economies of scale: ATC falls as Q increases.
Constant returns to scale: ATC stays the same as Q increases.
Diseconomies of scale: ATC rises as Q increases.
LRATC
Q
ATC
Costs in Long Run• Economies of scale The situation when a firm’s
long-run average total costs fall as it increases output– Increasing specialization among workers .
• Constant returns to scale– Long-run average total cost stays the same as the
quantity of output changes
Diseconomies of scale
– The situation when a firm’s long-run average costs rise as the firm increases output.
– Increasing coordination problems
TERM DEFINITIONSYMBOLS AND EQUATIONS
Total cost The cost of all the inputs used by a firm, or fixed cost plus variable cost
TC
Fixed costs Costs that remain constant when a firm’s level of output changes
FC
Variable costs Costs that change when the firm’s level of output changes
VC
Marginal cost Increase in total cost resulting from producing another unit of output
Average total cost Total cost divided by the quantity of output produced
Average fixed cost Fixed cost divided by the quantity of output produced
Average variable cost Variable cost divided by the quantity of output produced
Implicit cost A nonmonetary opportunity cost ―
Explicit cost A cost that involves spending money ―
Q
TCATC
Q
FCAFC
Q
VCAVC
Q
TCMC
Table 10-4A Summary of Definitions of Cost
Conclusion
EXERCISE• Table 13-1• Listed in the table are the long-run total costs for three
different firms.
• Refer to Table 13-1. Firm A is experiencing economies of scale.• ANS: T/F
•
Quantity 1 2 3 4 5
Firm A 100 100 100 100 100
Firm B 100 200 300 400 500
Firm C 100 300 600 1,000 1,500
