Question 1 (10 points) Alice enjoys goods x and 3; according to the utility function \"(39, y) = 333/4311\"- (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 pm 2 $4, py = $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? (e) Find the Marshallian demand functions, 23(pm, py, I) and 31(1),, py, I) by writing the Lagrangian and nding its critical points. (f) What is Alice's demand for each of the goods at 19,, = $4, py = $2, and I = $16? What is the highest utility level, U *, that Alice can achieve if 19;, = $4, pg 2 $2, and I = $16? (g) Derive Alice's indirect utility function