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Chapter 7: Problem 12

A computer company's cost function, which relates its average cost of production AC to its cumulative output in thousands of computers \(Q\) and its plant size in terms of thousands of computers produced per year \(q\) (within the production range of 10,000 to 50,000 computers \(),\) is given by \\[ \mathrm{AC}=10-0.1 \mathrm{Q}+0.3 \mathrm{q} \\] a. Is there a learning-curve effect? b. Are there economies or diseconomies of scale? c. During its existence, the firm has produced a total of 40,000 computers and is producing 10,000 computers this year. Next year it plans to increase production to 12,000 computers. Will its average cost of production increase or decrease? Explain.

Short Answer

Expert verified
a) Yes, there is a learning-curve effect in this problem as the coefficient of Q is negative in the cost function. b) The company experiences diseconomies of scale as the coefficient of q in the cost function is positive. c) The company's average cost of production decreases from 6 to 5.6 as it increases its annual production from 10,000 to 12,000 computers.

Step by step solution

01

Identify Learning Curve Effect

The learning curve effect is represented by the output in the cost function (Q). If the coefficient of Q is negative then it indicates a learning curve effect because costs decrease with increased production. In this case the coefficient of Q is -0.1, which is negative, so there is a learning curve effect.
02

Economies or Diseconomies of Scale

Looking at the cost function, we observe that the coefficient of the plant size (q) is positive or negative, that determines the economies or diseconomies of scale. If it is positive, then there are diseconomies of scale (costs rise as size increases) and if it is negative then there are economies of scale (costs decrease as size increases). Here the coefficient is 0.3 which is positive, so there are diseconomies of scale.
03

Average Cost of Production Increase or Decrease

Average Cost of production when the firm has produced a total of 40,000 computers and is producing 10,000 computers this year is calculated as: \[AC = 10-0.1(40)+0.3(10) = 6\]. Next year it plans to increase production to 12,000 computers so the average cost of production will be: \[ AC = 10-0.1(52)+0.3(12) = 5.6\]. The average cost of production decreases as the firm increase its production from 10,000 to 12,000.

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Most popular questions from this chapter

Suppose the long-run total cost function for an industry is given by the cubic equation \(\mathrm{TC}=\mathrm{a}+\mathrm{bq}+\mathrm{cq}^{2}+\mathrm{d} q^{3}\) Show (using calculus) that this total cost function is consistent with a U-shaped average cost curve for at least some values of \(a, b, c,\) and \(d\).

Suppose the economy takes a downturn, and that labor costs fall by 50 percent and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm's expansion path.

A recent issue of Business Week reported the following: During the recent auto sales slump, GM, Ford, and Chrysler decided it was cheaper to sell cars to rental companies at a loss than to lay off workers. That's because closing and reopening plants is expensive, partly because the auto makers' current union contracts obligate them to pay many workers even if they're not working. When the article discusses selling cars "at a loss," is it referring to accounting profit or economic profit? How will the two differ in this case? Explain briefly.

A computer company produces hardware and software using the same plant and labor. The total cost of producing computer processing units \(H\) and software programs \(S\) is given by \\[ \mathrm{TC}=a H+b S-\mathrm{cHS} \\] where \(a, b,\) and \(c\) are positive. Is this total cost function consistent with the presence of economies or diseconomies of scale? With economies or diseconomies of scope?

A chair manufacturer hires its assembly-line labor for \(\$ 30\) an hour and calculates that the rental cost of its machinery is \(\$ 15\) per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. If the firm is currently using 3 hours of labor for each hour of machine time, is it minimizing its costs of production? If so, why? If not, how can it improve the situation? Graphically illustrate the isoquant and the two isocost lines for the current combination of labor and capital and for the optimal combination of labor and capital.
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