HW3 - Intermediate Microeconomics Spring 2011 Homework 3:...

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Economics 1110 Intermediate Microeconomics Spring 2011 Homework 3: Choice and Demand Instructors: Dror Brenner and Ryan Miller The purpose of this homework is to: (i)derive optimal consumption bundles for di/erent preference relations (ii) compute and graph demand functions (iii) compute and graph income and price o/er curves (iv) compute and graph Engel curves. 1. For each of the following utility functions, prices and incomes derive the optimal bundle for the con- sumer: a: U ( X 1 ;X 2 ) = X 2 1 X 3 2 P 1 = 4 ; P 2 = 6 ; M = 200 b: U ( X 1 ;X 2 ) = X 1 + X 1 X 2 + 3 X 2 P 1 = 3 ; P 2 = 2 ; M = 97 c: U ( X 1 ;X 2 ) = min 2 X 1 ; X 2 3 ± P 1 = 4 ; P 2 = 1 ; M = 50 d: U ( X 1 ;X 2 ) = 6 X 1 + X 1 = 2 2 P 1 = 3 ; P 2 = 2 ; M = 154 2. P 1 = 4 ; P 2 = 1 ; M = 1000 : U ( X 1 ;X 2 ) = X 2 1 + X 2 2 is U ( X 1 ;X 2 ) = X 1 = 2 1 + X 1 = 2 2 a: Compute the optimal consumption bundles for Bob and Mark. b:
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