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Problem 1: Alice’s utility function is ?(?, ?) = √?√? where ? is her consumption of...

Problem 1: Alice’s utility function is ?(?, ?) = √?√? where ? is her consumption of good 1 and ? is her consumption of good 2. Denote Alice’s income by ?, and denote the prices of good 1 and 2 by ?? and ?? respectively.

A) Derive the formula for Alice’s marginal rate of substitution.

B) Write down the two equations necessary to solve for Alice’s optimal values of ? and ?.

C) Using the equations from part B, solve for Alice’s demand functions (that is, the optimal values of ? and ? such that the formula for ? does not depend on ?, and the formula for ? does not depend on ?).

D) Let ? = 100, ?1 = 2, and ?2 = 5. What are the optimal values of ? and y

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