Question: 5. ._' . Tim has the following utility function: U(2:,y) = mn{10:r,5y}. Let Tim's income be I = $300, pa. = $1 be the price

5. ._' . Tim has the following utility function: U(2:,y) =

5. ._' . Tim has the following utility function: U(2:,y) = mn{10:r,5y}. Let Tim's income be I = $300, pa. = $1 be the price of 3:, and pg = $1 be the price of y. (a) (8 points) Find Tim's demand functions 33* (p1. , py, I) and 3;\" (pm, pg, I). How much will Tim consume given the prices and income that he has? (b) (8 points) Suppose now that the price of :1: increases to 103 = $4 and the price of y stays the same. How much of .7; and y will Tim consume now? How much of the change in consumption of a: is due to income effect and how much of it is due to substitution effect? Show your calculations and illustrate the change of a carefully drawn and labeled graph

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