homework2Spring2008

homework2Spring2008 - Economics 302 Spring 2008 Homework #2...

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Economics 302 Spring 2008 Homework #2 Homework will be graded for both content and neatness. This homework does not require the use of Microsoft Excel, but you will find Excel speeds up the calculations greatly in this homework. 1) Consider an aggregate production function of the form Y=AK α L 1-α , where A represents the level of technology, L is the level of Labor, and K is the level of capital. Firms operate in a competitive market and therefore take factor prices as given, with W as the wage rate, R the rental rate of capital, and P the output price. a. Write down the firm’s profit function based on the information above, and find the necessary conditions for profit maximization (Hint: These conditions were discussed in class and are the same conditions you would get if you set the derivatives of profit with respect to capital and labor to zero using calculus.) Briefly explain why these conditions must hold if the firm is profit maximizing. b. If the labor income share in production is equal 0.75, find the value of α in the production function using one of the Cobb-Douglas properties discussed in class. c. What is the level of production if 10 units of capital are used in production, the rental rate of capital is 5, and the output price is 2? d. What is the level of labor used in this production function based on the information and answers you have found above if the level of technology is 1? e. What is the wage rate for labor? 2) Assume that the economy’s aggregate production function is 0.4 0.6 ( , , ) Y F A K L AK L = = where A is the level of technology, K is the level of capital and L is the level of labor. The consumption function is equal to C=250+0.7(Y-T). Investment spending is given
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homework2Spring2008 - Economics 302 Spring 2008 Homework #2...

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