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We have described the firm’s short-run cost function in tabular and graphic

forms. The cost function also can be represented in equation form. The repair

company’s short-run cost function is

[6.2]

where output is measured in thousands of units and costs are in thousands of

dollars. (You should check this equation against Figure 6.1 for various outputs.)

The first term is the firm’s fixed costs; the term in parentheses encompasses its

variable costs. In turn, short-run average cost is SAC C/Q, or

[6.3]

The first term usually is referred to as average fixed cost(fixed cost divided

by total output); the term in the parentheses is average variable cost (variable

cost divided by total output).According to Equation 6.3, as output increases,

average fixed cost steadily declines while average variable cost rises. The first

effect dominates for low levels of output; the second prevails at sufficiently

high levels. The combination of these two effects explains the U-shaped aver-

age cost curve. Finally, treating cost as a continuous function, we find mar-

ginal cost to be

[6.4]

We observe that marginal cost rises with the level of output.

Long-Run Costs

In the long run, the firm can freely vary all of its inputs. In other words, there

are no fixed inputs or fixed costs; all costs are variable.Thus, there is no differ-

ence between total costs and variable costs. We begin our discussion by stress-

ing two basic points. First, the ability to vary all inputs allows the firm to

produce at lower cost in the long run than in the short run (when some inputs

are fixed). In short, flexibility is valuable. As we saw in Chapter 5, the firm still

faces the task of finding the least-cost combination of inputs.

Second, the shape of the long-run cost curve depends on returns to scale.

To see this, suppose the firm’s production function exhibits constant returns

to scale. Constant returns to scalemeans that increasing all inputs by a given

percentage (say, 20 percent) increases output by the same percentage.

Assuming input prices are unchanged, the firm’s total expenditure on inputs

also will increase by 20 percent. Thus, the output increase is accompanied by

an equal percentage increase in costs, with the result that average cost is

unchanged. As long as constant returns prevail, average cost is constant.

SMCdC/dQ 30 .6Q.

SAC270/Q(30.3Q).

CC(Q) 270 (30Q.3Q^2 ),

242 Chapter 6 Cost Analysis

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