250
Cost
Solution a. From Equation (6.17), Per-unit labor cost = jQb = 5, 000(120)
ln 0.74 ln 2.5
= $1, 037 per unit
b. The first unit will require $5,000/$15 = 333.33 labor hours.When 120 units are produced, the per-unit labor requirement is $1,037/$15 = 69.13 labor hours.
LONG-RUN COST In the long run all factors of production are assumed to be variable. Since there are no fixed inputs, there are no fixed costs. All costs are variable. Unlike the short-run production function, however, there is little that can be said about production in the long run. There is no long-run equivalent of the law of diminishing marginal product. As in the case of the firm’s short-run cost functions, long-run cost functions are intimately related to the long-run production function. In particular, the firm’s long-run cost functions are related to the concept of returns to scale, which was discussed in Chapter 5. In general, economists have theorized that an increase in the firm’s scale of operations (i.e., a proportional increase in all inputs), is likely to be accompanied by increasing, constant, and decreasing returns to scale. The relation between total output and all inputs, the long-run total product curve (LRTP) is illustrated in Figure 6.4. It will be recalled from Chapter 5 that the coefficient of output elasticity for increasing returns to scale, constant returns to scale, and decreasing returns to scale, which is the sum of the output elasticities of each input, is greater than unity, equal to unity, and less than unity, respectively. Although the shapes of the long-run and short-run total product curves are similar, the reasons are quite different. The short-run total product curve derives
Q LRTP
CRTS IRTS DRTS
6.4 Long-run total product curve: the increase in total output from a proportional increase in all inputs. FIGURE
0
Scale of operations
