Chapter

The Costs of Production

13

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

production2

2-3

• 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 maximizes profits?

2-4

• 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)– C(Q) = Qi

2-5

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).

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

2-7

• Choose Q* such that profits are maximized• Max {TR(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

2-8

PC Market: Profits Max’ed at Q* where P = MCIn long-run, no economic profit -> produce at Min ATC(Q*)

Price does not change

Marginal Costs

Profits Max’ed

• Atomicity – There is a large number of small producers and consumers on a given market,

• each so small that its actions have no significant impact on others. – Firms are price takers, meaning that the market sets the price that they must choose.

• Homogeneity – Goods and services are perfect substitutes; that is, there is no product differentiation. (All firms sell an

identical product) • Perfect and complete information

– All firms and consumers know the prices set by all firms• Equal access

– All firms have access to production technologies, and resources are perfectly mobile. • Free entry

– Any firm may enter or exit the market as it wishes (no barriers to entry). • Individual buyers and sellers act independently

– 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

Basic Assumptions

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

Economists versus accountants

1

14

Economists include all opportunity costs when analyzing a firm, whereas accountants measure only explicit costs. Therefore, economic profit is smaller than accounting profit

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

A production function and total cost: Caroline’s cookie factory

1

16

Number of workers

Output(quantity of cookies produced per hour)

Marginal product of labor

Cost of factory

Cost of workers

Total cost of inputs(cost of factory + cost of workers)

0123456

05090

120140150155

$30303030303030

$0102030405060

$30405060708090

50403020105

Figure

TotalCost

50

40

30

20

10

80

70

60

$90

Quantityof Output(cookies

per hour)

100

80

60

40

20

160

140

120

Caroline’s production function and total-cost curve

2

17

(a) Production function

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.

(b) Total-cost curve

Number of Workers Hired

0 1 2 3 4 5 6

Productionfunction Total-cost curve

Quantityof Output

(cookies per hour)

0 20 40 60 80 100 120 140 160

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

The various measures of cost: Conrad’s coffee shop

2

20

Quantityof coffee

(cups per hour)TotalCost

FixedCost

VariableCost

AverageFixedCost

AverageVariable

Cost

AverageTotalCost

MarginalCost

0123456789

10

$3.003.303.804.505.406.507.809.30

11.0012.9015.00

$3.003.003.003.003.003.003.003.003.003.003.00

$0.000.300.801.502.403.504.806.308.009.90

12.00

-$3.001.501.000.750.600.500.430.380.330.30

-$0.300.400.500.600.700.800.901.001.101.20

-$3.301.901.501.351.301.301.331.381.431.50

$0.300.500.700.901.101.301.501.701.902.10

Figure

Total Cost

5.004.003.002.001.00

8.007.006.00

9.0010.0011.0012.0013.0014.00

$15.00

Conrad’s total-cost curve

3

21

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.

Quantity of Output(cups of coffee per hour)

0 1 2 3 4 5 6 7 8 9 10

Total-cost curve

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 5.1Daily Costs of Manufacturing Pine Lumber

5-24

EXHIBIT 5.2The Marginal Cost of Manufacturing Pine

Lumber

5-25

EXHIBIT 5.1Daily Costs of Manufacturing Pine Lumber

5-26

EXHIBIT 5.3The 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 average-

total-cost curve at its minimum

29

Figure

Cost curves for a typical firm

5

30

Costs

1.00

0.50

2.00

1.50

2.50

$3.00

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 average variable cost fall for a while before starting to rise.

Quantity of Output

0 2 4 6 8 10 12 14

MC

ATC

AVC

AFC

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

Average total cost in the short and long runs

6

33

AverageTotalCost

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 shortrun with

small factory

ATC in shortrun with

medium factory

ATC in shortrun with

large factory

ATC in long run

10,000

$12,000

1,000 1,200

Economiesof scale

Diseconomiesof scaleConstant returns to scale

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

The many types of cost: A summary

3

37

Term Definition MathematicalDescription

Explicit costs

Implicit costs

Fixed costs

Variable costs

Total cost

Average fixed cost

Average variable cost

Average total cost

Marginal cost

Costs that require an outlay of money by the firm

Costs that do not require an outlay of money by the firm

Costs that do not vary with the quantity of output produced

Costs that vary with the quantity of output produced

The market value of all the inputs that a firm uses in production

Fixed cost divided by the quantity of output

Variable cost divided by the quantity of output

Total cost divided by the quantity of output

The increase in total cost that arises from an extra unit of production

FC

VC

TC = FC + VC

AFC = FC / Q

AVC = VC / Q

ATC = TC / Q

MC = ΔTC / ΔQ