ajaz_eco204_2009_chapter_4.2

ajaz_eco204_2009_chapter_4.2 - University of Toronto...

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ECO 204 2009 2010 S. Ajaz Hussain (Draft) Chapter 4.2: Long Run CMP; Cobb Douglas CMP 1 Please help improve the course by sending me an e mail about typos or suggestions for improvements In this chapter, we model the optimal choice of inputs for a firm that produces a single product (good or service) in the long run and hires inputs as a price taker. The price taking assumption means that the firm’s demand for inputs (say labor) does not impact the input prices (such as wages), just as a perfectly competitive firm’s output does not affect the price of output. For example, there is no impact on waiters’ wages when a restaurant in a large city hires more waiters. On the other hand, when a ski resort ‐‐ typically the largest employer in the area ‐‐ hires more workers, it does impact wage rates 2 . L L P L P L Input “Price Taking” Firm Input “Price Making” Firm Demand for Labor Demand for Labor 1 Thanks: Patrick Gilmour, Sijin Jason Park Note to self: next semester: model technology in 4.1 and introduce choice of inputs for an inputs price making firm. 2 A monopolist charges a higher price than competition. Similarly, a monopsonist pays a lower price than competition. 1 ECO 204 (Draft) Chapter 4.2
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2010 S. Ajaz Hussain The focus of this chapter is on the long run optimal choice of inputs required to produce an exogenously given target level of output. For tractability, assume that the production function is: ܳൌܣ ݂ሺܮ, ܭሻ Observe labor and capital are the only inputs and are both variable. 1. Cost Minimization Problem (CMP) We assume the firm’s objective is to maximize profits. Of course, the firm may pursue other objectives such as maximizing revenue, expanding market share, minimizing average cost, etc. but arguably, the most plausible objective is profit maximization. The firm’s profits are: Profits = Revenues Cost ߎൌܴെܥൌܲܳെ ܥ If labor and capital are the only inputs, the cost of production (“expenditure”, “budget”) is: ܥൌܲ ܭ൅ܲ ܮ Thus, profits become: ߎൌܴെܥൌܲܳെ ሾܲ ܭ ൅ ܲ ܮሿ From chapter 4, recall that the firm has target output ݍ . If the firm produces this output ݍ its revenues are (a constant) and profits will be: ܴൌܲݍ ߎൌܲݍെܥൌܲݍെ ሾܲ ܭ ൅ ܲ ܮሿൌConstant െሾܲ ܭ൅ܲ ܮሿ Since revenues are constant, maximizing profits is equivalent to minimizing total cost. Since ܲ are exogenous parameters the firm’s cost minimization problem (CMP) is to choose labor and capital to minimize cost subject to constraint that output target output ݍ : min ௅,௄ ܥൌܲ ܭ൅ܲ ܮ s.t. Output ൒ ݍ The company’s output is given by the production function
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto.

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ajaz_eco204_2009_chapter_4.2 - University of Toronto...

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