eco204_summer_2009_practice_problem_13

eco204_summer_2009_practice_problem_13 - University of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain Practice Problems 13 Please help improve the course by sending me an email about typos or suggestions for improvements Note: Please don't memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you'll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. In this question you will practice writing down the expressions for profit objectives in terms of output for the four types of firms: competitive, market power, monopsony and dual monopoly. Suppose a firm uses labor and fixed capital to produce output with a CobbDouglas technology: Q = L1/2 k1/2 Note how capital is fixed since K = k. The firm currently has k = 10. For your convenience, here are the profit equations for the four types of firms: notice that the profit equation can be expressed in terms of primitives (wages, capital lease rates, labor and capital) and from that in terms of cost function: Firm Type Competitive Market Power Monopsony Dual Monopoly Equation in Primitives = Pq PK k PL L(q) = P(q) q PK k PL L(q) = P q PK k PL(L) L(q) = P(q) q PK k PL(L) L(q) Equation in Cost Function = PQ TFC TVC(Q) = P(Q) Q TFC TVC(Q) = P Q TFC TVC(Q) = P(Q) Q TFC TVC(Q) Answer each parts (b) (e) independently of other parts. You should really think about what the firm is taking as "given" or exogenous. Think about what sets each type of firm apart from 1 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain others and how you'd go about writing and solving the profit equation. (a) Given a target output q and fixed capital of k = 10, do the Cost Minimization Problem (CMP) to solve for the optimal labor. (b) Suppose the firm is competitive, P = $20, PL = $10 and PK = $10. Write down the profit (c) Suppose the firm has market power where P = 100 20Q, PL = $10 and PK = $10. Write down the profit equation in terms of output. (d) Suppose the firm is a monopsony where P = 20, PK = $10 and wages in the labor market are given by: PL = 100 20 L. Write down the profit equation in terms of output. (e) Suppose the firm is a dual monopoly where P = 100 20Q, PK = $10 and wages in the labor market are given by: PL = 100 20 L. Write down the profit equation in terms of output. 2 ...
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