Chapter
13
The Costs of Production
What Does a Firm Do?
• Firm’s Objective
– Firms seek to maximize profits
• Profits = Total Revenues minus Total Costs
• Choose output (Q*) such that
– Max {TR(Q*) –TC{Q*}
• Total revenue
– Revenue received from sale of its output
• Total cost
– Market value of the inputs a firm uses in
production
2
• Total revenue = P*Q
– Revenue received from sale of its output
– Market price for the good
– Perfect Comp -> P-taker
– Firm’s output decision does not affect
market/equilibrium price (too small)
– Price received = market equilib
price; does not change with firm’s
output
– What is then is the firm’s output level that
2-3
• Total cost
– Market value of the inputs a firm uses in
production
– Cost = price(input 1)*Q(input 1) + … +
price(input n)* Q(input n)
𝑛
– C(Q) = 𝑖=1 𝑃𝑖Qi
2-4
K. Translog (Transcendental Logarithmic) Cost Function
2nd order (arbitrary) approximation to a cost function with 3 inputs (K,L<M)
The three factor Translog production function is:
ln(q) = ln(A) + aL*ln(L) + aK*ln(K) + aM*ln(M) + bLL*ln(L)*ln(L) +
bKK*ln(K)*ln(K) + bMM*ln(M)*ln(M)
+ bLK*ln(L)*ln(K) + bLM*ln(L)*ln(M) + bKM*ln(K)*ln(M) = f(L,K,M).
where L = labour, K = capital, M = materials and supplies, and q = product.
Which can be simplified to a linear cost function (when
there are no interaction or higher order terms)
ln(q) = ln(A) + aL*ln(L) + aK*ln(K) + aM*ln(M)
+ = f(L,K,M).
2-5
(*)
Why Are Costs Important to a Firm?
• Primary economic objective of a firm
– Maximize profits
• Total revenues depend on customer demand
• Tot Rev(Q) = Price x Qty Demanded
– Price-taker (competitive world)
»
»
»
»
Initially assume: firm is a Price-taker (competitive world)
Competitors numerous and perfect substitutes
Demand for the firm’s product is perfectly elastic
Price can not be affected/chosen by 1 firm
• Costs {can controlled by p-taking firm}
– Depend on amount supplied (Q*) by the firm
– prices of and amounts used of inputs
6
• Choose Q* such that profits are maximized
• Max {TR(Q*) –TC{Q*}
• 𝑀𝑎𝑥 Π(𝑄∗) = 𝑃 ∗ 𝑄 − 𝑇𝐶{𝑄}
• First order condition δΠ/δQ = 0
• P = δTC{Q}/δQ = 0 or price = marginal cost
• Choose Q* where market price is just equal to
the increase in total costs
(marginal/incremental/additional) costs of
producing 1 more unit of output
2-7
PC Market: Profits Max’ed at Q* where P = MC
In long-run, no economic profit -> produce at Min ATC(Q*)
Marginal Costs
Profits Max’ed
Price does
not change
2-8
Basic Assumptions
•
Atomicity
–
There is a large number of small producers and consumers on a given market,
•
–
•
Any firm may enter or exit the market as it wishes (no barriers to entry).
Individual buyers and sellers act independently
–
•
All firms have access to production technologies, and resources are perfectly mobile.
Free entry
–
•
All firms and consumers know the prices set by all firms
Equal access
–
•
Goods and services are perfect substitutes; that is, there is no product differentiation. (All firms sell an
identical product)
Perfect and complete information
–
•
Firms are price takers, meaning that the market sets the price that they must choose.
Homogeneity
–
•
each so small that its actions have no significant impact on others.
The market is such that there is no scope for groups of buyers and/or sellers to come together to change
the market price (collusion and cartels are not possible under this market structure)
Behavioral assumptions of perfect competition are that:
–
–
Consumers aim to maximize utility/well-being
Producers aim to maximize profits.
9
What are Costs?
• Costs as opportunity costs
– Explicit costs
• Input costs that require an outlay of money by
the firm
• Reflect value of input used by other
producers/markets – price willing to pay
– Implicit costs
• Input costs that do not require an outlay of
money by the firm
• Opportunity costs of time; alternative investment
10
What are Implicit Costs?
• The cost of capital as an opportunity cost
– Implicit cost of investment in firm
• Interest income not earned
– Invested in business
• Not shown as cost by an accountant
– But is an opportunity cost to an economist; the
foregone investment/return
– Key difference between economists/accountants and
treatment of what costs are and how they affect
economic versus accounting profits
11
What are Implicit Costs?
• The cost of your labor as an opportunity cost
– Implicit cost of your labor (owner)
• Wages not earned/paid by someone else
– Do you pay yourself a wage if you own the business?
• If not, then not shown as cost by an accountant
– But is an opportunity cost to an economist; the
foregone salary
– Another example key difference between how costs
are recognized by economists/accountants
12
What are Costs?
• Economic profit
– Total revenue minus total cost
• Including both explicit and implicit costs
• Accounting profit
– Total revenue minus total explicit cost
13
Figure 1
Economists versus accountants
Economists include all opportunity costs when analyzing a firm, whereas
accountants measure only explicit costs. Therefore, economic profit is smaller
than accounting profit
14
Production and Costs
• 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
• Diminishing marginal returns to inputs (e.g., K, L)
• Marginal product
– Increase (change) in output arising from an
additional unit of input (ΔQ/ΔL)
15
Table
1
A production function and total cost: Caroline’s cookie
factory
Number
of workers
Output
(quantity of cookies
produced per hour)
Marginal
product
of labor
0
1
2
3
4
5
6
0
50
90
120
140
150
155
50
40
30
20
10
5
Cost of
factory
Cost of
workers
Total cost of inputs
(cost of factory +
cost of workers)
$30
30
30
30
30
30
30
$0
10
20
30
40
50
60
$30
40
50
60
70
80
90
16
Figure 2
Caroline’s production function and total-cost curve
Quantity
of Output
(cookies
per hour)
(a) Production function
Production
function
$90
160
80
140
70
120
60
100
50
80
40
60
30
40
20
20
10
0
1
2
3
4
5
(b) Total-cost curve
Total
Cost
6 Number of
Workers Hired
0
Total-cost curve
20
40
60
80 100 120 140 160 Quantity
of Output
(cookies per hour)
The production function in panel (a) shows the relationship between the number of workers hired and the quantity of
output produced. Here the number of workers hired (on the horizontal axis) is from the first column in Table 1, and the
quantity of output produced (on the vertical axis) is from the second column. The production function gets flatter as the
number of workers increases, which reflects diminishing marginal product. The total-cost curve in panel (b) shows the
relationship between the quantity of output produced and total cost of production. Here the quantity of output produced
(on the horizontal axis) is from the second column in Table 1, and the total cost (on the vertical axis) is from the sixth
column. The total-cost curve gets steeper as the quantity of output increases because of diminishing marginal product.17
Figure
The Various Measures of Cost
• Fixed costs (short-run)
– Do not vary with the quantity of output
produced
• Variable costs (short and long-run)
– Vary with the quantity of output produced
• Average fixed cost (AFC)
– Fixed cost divided by the quantity of output
• Average variable cost (AVC)
– Variable cost divided by the quantity of
output
19
Table
2
The various measures of cost: Conrad’s coffee shop
Quantity
of coffee
(cups per hour)
Total
Cost
Fixed
Cost
0
1
2
3
4
5
6
7
8
9
10
$3.00
3.30
3.80
4.50
5.40
6.50
7.80
9.30
11.00
12.90
15.00
$3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
Variable
Cost
Average
Fixed
Cost
Average
Variable
Cost
Average
Total
Cost
$0.00
0.30
0.80
1.50
2.40
3.50
4.80
6.30
8.00
9.90
12.00
$3.00
1.50
1.00
0.75
0.60
0.50
0.43
0.38
0.33
0.30
$0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
$3.30
1.90
1.50
1.35
1.30
1.30
1.33
1.38
1.43
1.50
Marginal
Cost
$0.30
0.50
0.70
0.90
1.10
1.30
1.50
1.70
1.90
2.10
20
Figure 3
Conrad’s total-cost curve
Total Cost
$15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0
Total-cost curve
1
2
3
4
5
6
7
8
9
Quantity of Output
10
(cups of coffee per hour)
Here the quantity of output produced (on the horizontal axis) is from the first column in Table 2, and the total
cost (on the vertical axis) is from the second column. As in Figure 2, the total-cost curve gets steeper as the
quantity of output increases because of diminishing marginal product.
21
The Various Measures of Cost
• Average total cost (ATC)
– Total cost divided by the quantity of output
– Average total cost = Total cost / Quantity
ATC = TC / Q
• Marginal cost (MC)
– Increase in total cost
• Arising from an extra unit of production
– Marginal cost = Change in total cost / Change
in quantity
MC = ΔTC / ΔQ
22
The Various Measures of Cost
• Average total cost = Total Costs(Q) ÷Q
– Cost of a typical unit of output
• Average Fixed Costs = Total Fixed Costs ÷ Q
• Average Variable Costs = Total Var Costs ÷ Q
• Marginal cost = ΔTC(Q+1 – Q)/ΔQ
– Increase in total cost from producing an
additional unit of output
23
EXHIBIT 5.1
Daily Costs of Manufacturing Pine Lumber
5-24
EXHIBIT 5.2
The Marginal Cost of Manufacturing Pine
Lumber
5-25
EXHIBIT 5.1
Daily Costs of Manufacturing Pine Lumber
5-26
EXHIBIT 5.3
The Cost Curves
5-27
The Various Measures of Cost
• Cost curves and their shapes
• U-shaped average total cost: ATC = AVC + AFC
– AFC – always declines as output rises
– AVC – typically rises as output increases
• Diminishing marginal product
• At the minimum of ATC or AVC
– The bottom (lowest point) of the U-shaped
curve
– MC = min(ATC) and MC = min(AVC)
28
The Various Measures of Cost
• Cost curves and their shapes
• Efficient scale
– Quantity of output that minimizes average
total cost
• 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 averagetotal-cost curve at its minimum
29
Figure 5
Cost curves for a typical firm
Costs
$3.00
2.50
MC
2.00
1.50
ATC
1.00
AVC
0.50
AFC
0
2
4
6
8
Quantity of Output
10
12
14
Many 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
30
average variable cost fall for a while before starting to rise.
Figure
 FIGURE 9.2 Short-Run Supply Curve of a Perfectly Competitive Firm
At prices below average variable cost, it pays a firm to shut down rather than continue
operating.
Thus, the short-run supply curve of a competitive firm is the part of its marginal cost curve
that lies above its average variable cost curve.
Costs in Short Run and in Long Run
• Many decisions
– Some inputs are fixed (unalterable)in the
short run
– All inputs are variable in the long run,
• Firms – greater flexibility in the long-run
– Long-run cost curves
• Differ from short-run cost curves
• Much flatter than short-run cost curves
– Short-run cost curves
• Lie on or above the long-run cost curves
32
Figure 6
Average total cost in the short and long runs
Average
Total
Cost
ATC in short
run with
small factory
ATC in short
run with
medium factory
ATC in short
run with
large factory
ATC in long run
$12,000
10,000
Economies
of scale
0
Constant returns to scale
1,000
1,200
Diseconomies
of scale
Quantity of Cars per Day
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.
33
Figure
Costs in Short Run and in Long Run
• Economies of scale
– Long-run average total cost falls as the
quantity of output increases
– Increasing specialization
• Constant returns to scale
– Long-run average total cost stays the same as
the quantity of output changes
35
Costs in Short Run and in Long Run
• Diseconomies of scale
– Long-run average total cost rises as the
quantity of output increases
– Increasing coordination problems
36
Table
3
The many types of cost: A summary
Mathematical
Description
Term
Definition
Explicit costs
Costs that require an outlay of money by the firm
Implicit costs
Costs that do not require an outlay of money by the firm
Fixed costs
Costs that do not vary with the quantity of output produced
FC
Variable costs
Costs that vary with the quantity of output produced
VC
Total cost
The market value of all the inputs that a firm uses in
production
TC = FC + VC
Average fixed cost
Fixed cost divided by the quantity of output
AFC = FC / Q
Average variable cost
Variable cost divided by the quantity of output
AVC = VC / Q
Average total cost
Total cost divided by the quantity of output
ATC = TC / Q
Marginal cost
The increase in total cost that arises from an extra unit of
production
MC = ΔTC / ΔQ
37