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Chapter 7: Problem 6

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.

Short Answer

Expert verified
The decrease in labor costs shifts the isocost line outwards reflecting more affordability of labor for the same amount of capital. This in turn shifts the firm's equilibrium point along the isoquant. Consequently, the firm's expansion path, represented by the line joining these equilibrium points, changes.

Step by step solution

01

Understanding the Context

Initially, the firm is in equilibrium at some point on its expansion path. The expansion path of a firm is the path traced out by the tangency points of isoquants and isocost lines as the firm expands its output level. Here, we use the labor market as an example, where capital is maintained constant and labor and the output vary.
02

Analyzing the Shift

A decrease in labor costs implies that for the same amount of capital, a firm can now afford more labor. This shifts the isocost line outwards. The isocost line will now intersect the isoquant at a different point.
03

Graphically Representing the Shift

On graph, draw the original isocost line and the isoquant curve with their tangency representing the firm's equilibrium. Then, show the reduction in labor cost by drawing a new isocost line to the right of the original one, indicating more labor can be afforded. Mark the new tangency point with the isoquant.
04

Indicating the New Expansion Path

The expansion path changes because the new equilibrium point is different from its previous one. The new expansion path will now be the line joining all such new equilibrium points for different levels of output. On the graph, draw this new expansion path.

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Most popular questions from this chapter

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.

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.

You manage a plant that mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function \\[ q=5 K L \\] where \(q\) is the number of engines per week, \(K\) is the number of assembly machines, and \(L\) is the number of labor teams. Each assembly machine rents for \(r=\$ 10,000\) per week, and each team costs \(w=\$ 5000\) per week. Engine costs are given by the cost of labor teams and machines, plus \(\$ 2000\) per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design. a. What is the cost function for your plant-namely, how much would it cost to produce \(q\) engines? What are average and marginal costs for producing \(q\) engines? How do average costs vary with output? b. How many teams are required to produce 250 engines? What is the average cost per engine? c. You are asked to make recommendations for the design of a new production facility. What capital/ labor \((K / L)\) ratio should the new plant accommodate if it wants to minimize the total cost of producing at any level of output \(q ?\)

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 \(d\).

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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