Solve for question 2

Question 1 (10 points) Alice enjoys goods :1: and y according to the utility function \"(53, y) = 563/4y1/4- (a) Find Alice's marginal rate of substitution at the point (3, 2). (b) Draw the indifference curve through the point (3, 2). (c) On the same diagram, draw Alice's budget line if 1),, = $4, y = $2, and I = $16. (d) What is the slope of the budget line? Does the budget line have any common points with the indifference curve? How can you interpret your answer to the last question? (8) Find the Marshallian demand functions, a;(pm, pg, I) and y(p$, pg, I) by writing the Lagrangian and nding its critical points. (f) What is Alice's demand for each of the goods at 19,, = $4, 193, = $2, and I = $16? What is the highest utility level, U *, that Alice can achieve if pm = $4, y = $2, and I = $16? (g) Derive Alice's indirect utility function. Question 2 (10 points) Alice enjoys goods :1: and 3; according to the utility function \"(13, 3/) = in?\" 4311/ 4- (a) Using your answer to Question 1(g) and duality between utility maxi mization and expenditure minimization problems, calculate Alice's ex- penditure function for each level of utility, U *. (b) Suppose that the price of good a: becomes p'm = $3.50 and pg remains unchanged. By how much should Alice's income change to provide her the same level of utility as she received when pm was $4? 2 (c) Using your answer to Question 1(e) and duality between utility maxi- mization and expenditure minimization problems, nd the compensated demand functions 2:60.953, pg, U *) and yc(p$, pg, U *) (d) Find the substitution effects for both goods when the price of good :1: drops from 19;, = $4.00 to p3, = $3.50