S - HW2 - University of Illinois at Urbana-Champaign...

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University of Illinois at Urbana-Champaign Professor Ron Laschever, ECON 440, Spring 2010 1 Problem set #2 Answer Key 1. Indicate whether the statement is true or false, and support your answer with a 1-3 sentence explanation. If part of a statement is false, then the whole statement is false. Firms’ demand for labor is more sensitive to wage rates in the short-run than in the long-run. Explain whether this statement is true or false and draw a graph of the long run and short-run demand for labor to illustrate your answer. [10 Pts] False. The demand for labor is more elastic in the long run than in the short run. In the long run, firms can adjust their capital stock to changes in the price of labor, allowing them to be more flexible in their use of labor. See the graph below and page 124 in the textbook. If women’s labor supply is more elastic than men’s, it will be more efficient to tax the labor income of men than to tax that of women. (Assume that the firm demand curves for labor supplied by women and men are the same.) [10 Pts] True. The more efficient outcome is the one that minimizes Deadweight Loss due caused by taxation. From the figures below, we can see that there is less DWL when labor supply is more inelastic.
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University of Illinois at Urbana-Champaign Professor Ron Laschever, ECON 440, Spring 2010 2 2. Consider a firm that uses both labor and capital in production. The price of capital is $20 per unit and the wage rate is $10 per hour. [10X3=30 Pts] a. Draw the firm’s isocost line assuming a total production cost of $100. How steep is this line (that is, what is its slope)? Be sure to clearly label the axis. Total costs = $100 = w*L + r*K, where w is the wage rate, r is the price of capital, and L and K are the quantities of labor and capital used by the firm. We can rearrange this to get the isocost line of K = (100/r) – (w/r)*L. Thus, the slope of the isocost line is –w/r. See page 116 in the textbook. b. If the firm chooses its labor and capital combination to minimize its production costs, will the marginal product of labor be higher than, lower than, or equal to the marginal product of capital? Why? The slope of the isocost curve is –w/r, which is equal to –½ in this case. The slope of the isoquant is equal to –MP L /MP K , the ratio of the marginal product of labor to the marginal product of capital (with a minus sign in front). At the firm’s optimal use of capital and labor, the isoquant is tangent to the
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S - HW2 - University of Illinois at Urbana-Champaign...

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