Suppose you are deciding how many pounds of spaghetti (x), and how many blocks of pecorino Romano cheese to buy (y). Your utility over these two products is u(x, y) = xy5. Let the price of spaghetti be p = $3, and the price of cheese be py = $5. Your budget is $40. (a) Why is a Cobb-Douglas utility function (like the one we have for this question) an appro- priate way to represent preferences over spaghetti and cheese? (b) Draw a graph showing how we would find the optimal quantities for spaghetti and cheese. (You do not need to do any math for this step.) (c) Calculate the optimal quantities of spaghetti and cheese. (d) Now suppose the price of cheese doubled to Py = $10. How would your consumption of spaghetti and cheese change? (e) What is your demand curve for spaghetti, and your demand curve for cheese?