HW_02_Solutions

# HW_02_Solutions - Problem Set 2 Question 1. a) Budget...

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Problem Set 2 Question 1. a) Budget constraint. 120 20 = + M G Where the budget line is given by: G M 20 120 = b) Substitution Method. Get M from the budget constraint: G M 20 120 = Plug it into the objective function: 2 / 1 2 / 1 ) 20 120 ( max G G G F.O.C. 0 ) 20 ( ) 20 120 )( 2 / 1 ( ) 20 120 ( ) 2 / 1 ( 2 / 1 2 / 1 2 / 1 2 / 1 = + G G G G ) 20 ( ) 20 120 ( G G = 120 40 = G 3 * = G and thus 60 * = M c) Marginal utility per dollar method G M G M M G M G 20 20 1 20 2 / 1 2 / 1 2 / 1 2 / 1 = = = G M 6 120

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Substitute for M in the budget constraint: 3 * 120 20 20 = = + G G G and thus 60 * = M d) Lagrangian Method ) 20 120 ( ) ; , ( 2 / 1 2 / 1 M G M G M G L + = λ F.O.C. 0 20 2 1 ) ; , ( 2 / 1 2 / 1 = = M G G M G L 0 2 1 ) ; , ( 2 / 1 2 / 1 = = M G M M G L 0 20 120 ) ; , ( = = M G M G L From the first two equations: G M G M M G M G 20 20 1 20 2 / 1 2 / 1 2 / 1 2 / 1 = = = Plug into the third equation: 3 * 120 20 20 = = + G G G and thus 60 * = M Question 2. a) Budget constraint. 120 20 = + M G G M 6 120
b) Substitution Method. Get M from the budget constraint: G M 20 120 = Plug it into the objective function: ) 20 120 log( 2 log max G G G + F.O.C. 0 20 120 40 1 = + G G ) 40 ( ) 20 120 ( G G = 120 60 = G 2 * = G and thus 80 * = M c) Marginal utility per dollar method G M G M M G 40 20 2 1 20 2 1 = = = Substitute for M in the budget constraint:

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## This note was uploaded on 04/01/2010 for the course ECON 180052110 taught by Professor Mcdevitt during the Winter '09 term at UCLA.

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HW_02_Solutions - Problem Set 2 Question 1. a) Budget...

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