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Unformatted text preview: Cornell University Economics 3130 Problem Set 8 Solutions 1. Suppose there are two consumers A and B comprising the entire market for good x 1 . There is also a good x 2 . As consumption bundle is x A = ( x A 1 ,x A 2 ) and Bs is described in similar fashion. Their utility functions are u A 1 = x A 1 + 200 3 x A 2 ( x A 2 ) 2 and u B 2 = x B 1 + 400 3 x B 2 ( x B 2 ) 2 . The price of good x 1 is 1 and the price of good x 2 is p . Individuals have incomes I = ( I A ,I B ) Assume that both individuals have sufficient income so that an interior solution characterizes their optimal choices. (a) What are the (Marshallian) demands for A and B ? What is the market demand X 2 ( p,I )? x A 1 = I A 100 p 3 + p 2 2 x A 2 = 100 3 p 2 x B 1 = I B 200 p 3 + p 2 2 x B 2 = 200 3 p 2 X 1 = I A + I B 100 p + p 2 X 2 = 100 p (b) What are the indirect utility functions for A and B? V A ( p,I A ) = I A 100 3 p + 1 4 ( p ) 2 + 10000 9 V B ( p,I B ) = I B 200 3 p + 1 4 ( p ) 2 + 40000 9 (c) What is As price elasticity of demand for good 2? What is Bs? What is the price elasticity of market demand for good 2? A = x A 2 p p x = 1 2 6 p 200 3 p = 3 p 200 3 p B = 3 p 400 3 p = p 100 p Now, suppose that the supply curve for good 2 is y s 2 = 20 + 2 p and that the market is competitive. (d) What is the equilibrium price p and quantity ( Q )? 100 p = 20 + 2 p p = 40 Q = 60 1 (e) Suppose now that the government introduces a subsidy of $18 per unit and that new firms do not enter. What is the new equilibrium quantity? What is the price paid by consumers? What is the price received by producers?...
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This note was uploaded on 08/29/2009 for the course ECON 3130 taught by Professor Masson during the Spring '06 term at Cornell University (Engineering School).
 Spring '06
 MASSON
 Economics, Microeconomics

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