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George is a musician who enjoys playing two different instruments. His utility function is given by U(G,S) = 8G¹/² + S, where G and S denote guitars and sitars, respectively. The prices of guitars and sitars are PG & Ps respectively. For the following consider guitars to be the good on the horizontal axis. a. Set up George's cost minimization problem when he wants to achieve a utility level (ū = 28), which he considers to be consistent with a "reasonable" lifestyle. Be sure to identify what he is minimizing and what is serving as his constraint. b. Given your answer to part (a), find the bundle of goods George would consume to achieve a utility level 28, while minimizing the money he spends (solve this symbolically and then substitute in the numerical values). Also find a symbolic expenditure function, that is, E(PG, Ps, U) for George. What is the minimum amount he needs to spend given the prices PG= $200

George is a musician who enjoys playing two different instruments. His utility function is given by U(G,S) = 8G¹/² + S, where G and S denote guitars and sitars, respectively. The prices of guitars and sitars are PG & Ps respectively. For the following consider guitars to be the good on the horizontal axis. a. Set up George's cost minimization problem when he wants to achieve a utility level (ū = 28), which he considers to be consistent with a "reasonable" lifestyle. Be sure to identify what he is minimizing and what is serving as his constraint. b. Given your answer to part (a), find the bundle of goods George would consume to achieve a utility level 28, while minimizing the money he spends (solve this symbolically and then substitute in the numerical values). Also find a symbolic expenditure function, that is, E(PG, Ps, U) for George. What is the minimum amount he needs to spend given the prices PG= $200

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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1. George is a musician who enjoys playing two different instruments. His utility function is given by U(G,S) = 8G¹/² + S, where G and S denote guitars and sitars, respectively. The prices of guitars and sitars are PG & Ps respectively. For the following consider guitars to be the good on the horizontal axis. a. Set up George's cost minimization problem when he wants to achieve a utility level (Ū = 28), which he considers to be consistent with a "reasonable" lifestyle. Be sure to identify what he is minimizing and what is serving as his constraint. b. Given your answer to part (a), find the bundle of goods George would consume to achieve a utility level 28, while minimizing the money he spends (solve this symbolically and then substitute in the numerical values). Also find a symbolic expenditure function, that is, E(PG, Ps, ū) for George. What is the minimum amount he needs to spend given the prices PG = $200 and Ps= $100? c. Now suppose Apple Records gives George a guaranteed income of $1,800 and the prices of guitars and sitars are still PG= $200 & Ps= $100. Can George sustain his "reasonable" lifestyle, that is, achieve a utility level of 28 or higher? d. Imagine George is currently in the situation from part (b), but the price of a sitar has increased to $150. Does George need an income of $2600, i.e., enough money that he can still afford the optimal bundle he was buying before the price increase, to maintain his preferred lifestyle (U=28)? If he doesn't, what is the least amount of income he would need? Use the consumer's problem diagram to illustrate the logic of your answer.
Transcribed Image Text:1. George is a musician who enjoys playing two different instruments. His utility function is given by U(G,S) = 8G¹/² + S, where G and S denote guitars and sitars, respectively. The prices of guitars and sitars are PG & Ps respectively. For the following consider guitars to be the good on the horizontal axis. a. Set up George's cost minimization problem when he wants to achieve a utility level (Ū = 28), which he considers to be consistent with a "reasonable" lifestyle. Be sure to identify what he is minimizing and what is serving as his constraint. b. Given your answer to part (a), find the bundle of goods George would consume to achieve a utility level 28, while minimizing the money he spends (solve this symbolically and then substitute in the numerical values). Also find a symbolic expenditure function, that is, E(PG, Ps, ū) for George. What is the minimum amount he needs to spend given the prices PG = $200 and Ps= $100? c. Now suppose Apple Records gives George a guaranteed income of $1,800 and the prices of guitars and sitars are still PG= $200 & Ps= $100. Can George sustain his "reasonable" lifestyle, that is, achieve a utility level of 28 or higher? d. Imagine George is currently in the situation from part (b), but the price of a sitar has increased to $150. Does George need an income of $2600, i.e., enough money that he can still afford the optimal bundle he was buying before the price increase, to maintain his preferred lifestyle (U=28)? If he doesn't, what is the least amount of income he would need? Use the consumer's problem diagram to illustrate the logic of your answer.
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