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Chapter 6
Cost Analysis
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 C C(Q) 270 (30Q .3Q2),
[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 SAC 270/Q (30 .3Q).
[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 average cost curve. Finally, treating cost as a continuous function, we find marginal cost to be SMC dC/dQ 30 .6Q.
[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 difference between total costs and variable costs. We begin our discussion by stressing 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 scale means 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.
