HW03-solutions

# HW03-solutions - UCLA Economics 11 Microeconomics Theory...

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Unformatted text preview: UCLA Economics 11 Microeconomics Theory Winter 2006 Homework #3 Professor William Zame Prepared by Tzu-Yu Kao February 2, 2006 —————————————————————————————————————— For each of the following, use the marginal utility (slope) method to derive the optimal choice for the given function, prices and income. 1. u 1 x , y x y 1 2 ; p x 10, p y 20; W 400 Step 1: Calculate the MRS (Marginal Rate of Substitution) of the utility function: MRS MU x MU y 1 1 2 y − 1 2 2 y 1 2 Step 2: Calculate the price ratio: P x p y 10 20 1 2 Step 3: Equate MRS Price ratio: 2 y 1 2 1 2 We obatin: y ∗ 1 16 Step 4: Plug this back into the budget constraint: 10 x 20 y 400 We can solve for x ∗ : x ∗ 319 8 Therefore, the optimal choice for this given utility function, prices and income is: x ∗ 319 8 y ∗ 1 16 2. u 2 x , y x y 1 2 ; p x 10, p y 200; W 4000 Step 1: Calculate the MRS (Marginal Rate of Substitution) of the utility function: MRS MU x MU y 1 1 2 y − 1 2 2 y 1 2 Step 2: Calculate the price ratio: P x p y 10 200 1 20 Step 3: Equate MRS Price ratio: 2 y 1 2 1 20 We obatin: y ∗ 1 1600 Step 4: Plug this back into the budget constraint: 10 x 200 y 4000 We can solve for x ∗ : x ∗ 31999 80 Therefore, the optimal choice for this given utility function, prices and income is: x ∗ 31999 80 y ∗ 1 1600 3. u 3 x , y x 1 3 y 1 3 ; p x 100,...
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## This note was uploaded on 04/20/2010 for the course ECON 180052110 taught by Professor Mcdevitt during the Spring '09 term at UCLA.

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HW03-solutions - UCLA Economics 11 Microeconomics Theory...

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