151ps2ak - Economics 151a Spring 2008 Homework 2 -...

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Economics 151a Spring 2008 Homework 2 - Solutions 4-1. Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 1 machine to do the work of 3 workers. The firm wants to produce 100 units of output. Suppose the price of capital is $750 per machine per week. What combination of inputs will the firm use if the weekly salary of each worker is $300? What combination of inputs will the firm use if the weekly salary of each worker is $225? What is the elasticity of labor demand as the wage falls from $300 to $225? Because labor and capital are perfect substitutes, the isoquants (in bold) are linear and the firm will use only labor or only capital, depending on which is cheaper in producing 100 units of output. The (absolute value of the) slope of the isoquant ( MP E / MP K ) is 1/3 because 1 machine does the work of 3 workers. When the wage is $300 (left panel), the slope of the isocost is 300/750. The isocost curve, therefore, is steeper than the isoquant, and the firm only hires capital (at point A ). When the weekly wage is $225 (right panel), the isoquant is steeper than the isocost and the firm hires only labor (at point B ). Weekly Salary = $300 Weekly Salary = $225 The elasticity of labor demand is defined as the percentage change in labor divided by the percentage change in the wage. Because the demand for labor goes from 0 to a positive quantity when the wage dropped to $225, the (absolute value of the) elasticity of labor demand is infinity.
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4-4. Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r , respectively. Initially the firm faces market prices of w = 6 and r = 4. These prices then shift to w = 4 and r = 2. (a) In which direction will the substitution effect change the firm’s employment and capital stock? Prior to the price shift, the absolute value of the slope of the isocost line ( w/r ) was 1.5. After the price shift, the slope is 2. In other words, labor has become relatively more expensive than capital. As a result, there will be a substitution away from labor and towards capital (the substitution effect). (b) In which direction will the scale effect change the firm’s employment and capital stock?
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This note was uploaded on 10/15/2009 for the course ECON 151A taught by Professor Miller during the Spring '06 term at UC Davis.

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151ps2ak - Economics 151a Spring 2008 Homework 2 -...

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