FS09 - Economics 104B Final Exam Spring 2009 1(10pt A firm...

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Unformatted text preview: Economics 104B Final Exam Spring 2009 1. (10pt) A firm is the sole supplier of security systems in the product market and the sole employer of locksmiths in the labor market. The demand curve for security systems is given by P ( Q ) = 100- 1 2 Q , where q is the number of systems installed. The (short run) production function for security systems is given by Q = f ( L ) = 4 L , where L is the number of full-time locksmiths employed. The supply curve for locksmiths is given by w ( L ) = 40 + L , where w is the wage for each locksmith. How many locksmiths will the firm hire, what wage will it pay, what quantity will the firm produce, and how much profit will it make? Answer: The firm is simultaneously a monopolist in the product market (secu- rity systems) and a monopsonist in the factor (locksmiths) market. Thus, by the demand function for security systems, the production function, and the supply function for locksmiths, we get MRP ( L ) = MR ( Q ) MP ( L ) = 4(100- Q ) and MFC ( L ) = 40 + 2 L . Since Q = 4 L , MRP ( L ) = 400- 16 L . By the optimal hiring rule, the number of locksmiths the firm hires is determined by 400- 16 L = 40 + 2 L which implies L * = 20. By inverse supply function for locksmiths, the wage the firm will pay is w * = 40 + L * = 60. Next, from the production function, Q * = 4 L * = 80. Finally, from the inverse demand, p * = 90. Hence, the firm’s= 90....
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FS09 - Economics 104B Final Exam Spring 2009 1(10pt A firm...

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