8Short-Run Costs andOutput Decisions

CHAPTER OUTLINE

Costs in the Short RunFixed CostsVariable CostsTotal CostsShort-Run Costs: A Review

Output Decisions: Revenues, Costs, and Profit Maximization

Perfect CompetitionTotal Revenue and Marginal RevenueComparing Costs and Revenues to Maximize ProfitThe Short-Run Supply Curve

Looking Ahead

In their quest for profits, firms make three specific decisions involving their production.

FIGURE 8.1 Decisions Facing Firms

fixed cost Any cost that does not depend on the firms’ level of output. These costs are incurred even if the firm is producing nothing. There are no fixed costs in the long run.

variable cost A cost that depends on the level of production chosen.

total cost (TC) Total fixed costs plus total variable costs.

TC = TFC + TVC

Costs in the Short Run

A production function and Fixed Costs

1

4

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

$100100100100100100100

$0102030405060

$100110120130140150160

50403020105

total fixed costs (TFC) or overhead The total of all costs that do not change with output even if output is zero. (Typically Capital)

TABLE 8.1 Short-Run Fixed Cost (Total and Average) of a Hypothetical Firm

(1)q

(2)TFC

(3)AFC (TFC/q)

012345

$100100100100100100

$ -100

50332520

Fixed Costs

Total Fixed Cost (TFC)

FIGURE 8.2 Short-Run Fixed Cost (Total and Average) of a Hypothetical Firm

Average fixed cost is simply total fixed cost divided by the quantity of output.As output increases, average fixed cost declines because we are dividing a fixed number ($1,000) by a larger and larger quantity.

Average Fixed Cost (AFC)

average fixed cost (AFC) Total fixed cost divided by the number of units of output; a per-unit measure of fixed costs.

spreading overhead The process of dividing total fixed costs by more units of output. Average fixed cost declines as quantity rises.

TFCAFC

q

A production function and variable costs

1

7

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

$100100100100100100100

$0102030405060

$100110120130140150160

50403020105

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

8

(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

marginal cost (MC) The increase in total cost that results from producing 1 more unit of output. Marginal costs reflect changes in variable costs.

TABLE 8.3 Derivation of Marginal Cost from Total Variable Cost

Units of Output Total Variable Costs ($) Marginal Costs ($)

0123

0203853

20 18 15

Marginal Cost (MC)

FIGURE 8.4 Declining Marginal Product Implies That Marginal Cost Will Eventually Rise with Output

In the short run, every firm is constrained by some fixed factor of production.A fixed factor implies diminishing returns (declining marginal product) and a limited capacity to produce. As that limit is approached, marginal costs rise.

The Shape of the Marginal Cost Curve in the Short Run

In the short run, every firm is constrained by some fixed input that (1) leads to diminishing returns to variable inputs and (2) limits its capacity to produce. As a firm approaches that capacity, it becomes increasingly costly to produce successively higher levels of output. Marginal costs ultimately increase with output in the short run.

FIGURE 8.5 Total Variable Cost and Marginal Cost for a Typical Firm

Total variable costs always increase with output.Marginal cost is the cost of producing each additional unit. Thus, the marginal cost curve shows how total variable cost changes with single-unit increases in total output.

MCTVCTVC

q

TVCTVC

1Δ of slope

Graphing Total Variable Costs and Marginal Costs

FIGURE 8.6 More Short-Run Costs

When marginal cost is below average cost, average cost is declining. When marginal cost is above average cost, average cost is increasing.Rising marginal cost intersects average variable cost at the minimum point of AVC.

Graphing Average Variable Costs and Marginal Costs

FIGURE 8.7 Total Cost = Total Fixed Cost + Total Variable Cost

Adding TFC to TVC means adding the same amount of total fixed cost to every level of total variable cost.Thus, the total cost curve has the same shape as the total variable cost curve; it is simply higher by an amount equal to TFC.

Total Costs

average total cost (ATC) Total cost divided by the number of units of output.

q

TCATC

AVCAFC ATC

Average Total Cost (ATC)

FIGURE 8.8 Average Total Cost = Average Variable Cost + Average Fixed Cost

To get average total cost, we add average fixed and average variable costs at all levels of output.Because average fixed cost falls with output, an ever-declining amount is added to AVC. Thus, AVC and ATC get closer together as output increases, but the two lines never meet.

If marginal cost is below average total cost, average total cost will decline toward marginal cost. If marginal cost is above average total cost, average total cost will increase. As a result, marginal cost intersects average total cost at ATC’s minimum point for the same reason that it intersects the average variable cost curve at its minimum point.

The relationship between average total cost and marginal cost is exactly the same as the relationship between average variable cost and marginal cost.

The Relationship Between Average Total Cost and Marginal Cost

What Does a Firm Do?

• Firm’s Objective– Firms seek to maximize profits

• Profits = Total Revenues minus Total Costs• Choose 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

16

2-17

• 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 price: P does not depend on Q

– Revenues only affected then by quantity supplied/produced

– What can be produced profitably at the given market price?

2-18

• 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