Econ 339 Winter 2008 Problem Set 3-4 - Solutions

Econ 339 Winter 2008 Problem Set 3-4 - Solutions - Econ 339...

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Econ 339 Winter Quarter 2008 Problem Set 3-4 - Due Date: 2/4/2008 Solve the following Problems. Show your work. 1. Problems: 4-1, 4-2, 4-4, 4-7, 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. 4-2. (a) What happens to the long-run demand curve for labor if the demand for the firm’s output increases? Labor Capital slope = w/r =300/750 slope=MP E /MP K =1/3 A Labor Capital slope = w/r =225/750 slope =MP E / MP K =1/3 B
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The labor demand curve is given by VMP E = MR x MP E . As demand for the firm’s output increases, its marginal revenue also increases. Thus, an increase in demand for the firm’s output shifts the labor demand curve to the right. (b) What happens to the long-run demand curve for labor if the price of capital increases? To determine how an increase in the price of capital changes the demand for labor, suppose initially that the firm is producing 200 units of output at point P in the figure. The increase in the price of capital (assuming capital is a normal input) increases the marginal costs of the firm and will reduce the profit-maximizing level of output to say 100 units. The increase in the price of capital also flattens the isocost curve, moving the firm to point R . The move from point P to point R can be decomposed into a substitution effect ( P to Q ) which reduces the demand for capital, but increases the demand for labor, and a scale effect ( Q to R ) which reduces the demand for both labor and capital. The direction of the shift in the demand curve for labor, therefore, will depend
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This note was uploaded on 12/04/2008 for the course ECONOMICS 339 taught by Professor Habermalz during the Winter '07 term at Northwestern.

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Econ 339 Winter 2008 Problem Set 3-4 - Solutions - Econ 339...

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