econ11_08_hw3_sol

Econ11_08_hw3_sol - Eco11 Fall 2008 Simon Board Economics 11 Solutions to Homework 3 Due date Tuesday 25th November Instructions You are required

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Unformatted text preview: Eco11, Fall 2008 Simon Board Economics 11: Solutions to Homework 3 November 25, 2008 Due date: Tuesday 25th November. Instructions: You are required to write up your solution separately and independently, al- though you are encouraged to discuss and work in groups. Please write your name, student ID number, and the name of your TA on the front page of the assignment that you hand in. Also, please put boxes around your final answer to each part. 1. Consumer Surplus with CES utility An agent has utility u ( x 1 ,x 2 ) = x 1 / 2 1 + x 1 / 2 2 , income m = 4 and faces prices p 1 = 2 and p 2 = 2. Suppose the price of good 1 rises to p 1 = 3. Calculate the increase in the agent’s income required to compensate her for this price rise. Solution We derived the Marshallian demand and indirect utility function in PS4. The indirect utility function is v ( p 1 ,p 2 ,m ) = • m p 1 + p 2 p 1 p 2 ‚ 1 / 2 Plugging in the parameters, we see v ( p 1 ,p 2 ,m ) = 2. Inverting the indirect utility function we obtain the expenditure function, e ( p 1 ,p 2 , u ) = u 2 p 1 p 2 p 1 + p 2 Letting, u = 2, the compensating variation is CV = e ( p 1 ,p 2 , u )- e ( p 1 ,p 2 , u ) = u 2 p 1 p 2 p 1 + p 2- u 2 p 1 p 2 p 1 + p 2 = 4 5 1 Eco11, Fall 2008 Simon Board 2. Cost Minimisation with Quasilinear Production A firm has production function f ( z 1 ,z 2 ) = 2 z 1 / 2 1 + z 2 The firm’s inputs cost r 1 and r 2 ....
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This note was uploaded on 04/25/2009 for the course ECON 11 taught by Professor Cunningham during the Fall '08 term at UCLA.

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Econ11_08_hw3_sol - Eco11 Fall 2008 Simon Board Economics 11 Solutions to Homework 3 Due date Tuesday 25th November Instructions You are required

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