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Question 1: You offer Donny the choice between two bundles of Coffee (C) and Muffins (M). Theoptions are (C,M) = (6, 4) and (C,M) = (8, 2), and Donny indicates he prefers the second option.(a) Write a utility function for Donny that is consistent with his choice.Suppose you offer him a third option of (C,M) = (7, 6) in addition to the original two, and thatDonny indicates he prefers this third option to the first two.(b) Write a utility function for Donny that is consistent with his choice. It is possible it may bethe same as your answer from part (a).Question 2: Donny’s monthly budget for Coffee and Muffins is 60 and the prices of those twogoods are pC = 2 and pM = 4, respectively.(a) Make a properly labeled diagram illustrating Donny’s budget constraint with C on thehorizontal axis and M on the vertical axis. Indicate the area corresponding to the set ofbundles (C,M) that Donny can afford.(b) On the same diagram, illustrate Donny’s budget constraint if pM falls from 4 to 2.Up until this point it is impossible to predict what Donny will purchase without knowing hispreferences.(c) Suppose Donny views Coffee and Muffins as perfect substitutes (he is always willing totrade one C for one M). Which bundle of the two goods will he purchase, assuming pC = 2and pM = 4?(d) Suppose Donny views Coffee and Muffins as perfect complements (he always has to consumeone C with one M to obtain any utility). Which bundle of the two goods will hepurchase, assuming pC = 2 and pM = 4?(e) In which case of preferences (perfect substitutes or perfect complements) would Donnybenefit more from the price decrease of pM = 4 to pM = 2?Question 3: Dave is on the keto diet so he only obtains utility from two products, Avocados (A)and Beef (B). His utility function representing his preferences is U(A, B) = 5A0.2B0.8. His incomeis 180. The prices are pA = 2, pB = 2.(a) What is Dave’s marginal rate of substitution, MRSAB? Interpret it. Does it depend on howmuch A or B he already has, and if so, how?(b) Which bundle will Dave consume? How much utility will he get?(c) Draw Dave’s budget constraint and indicate his bundle choice on your diagram. Draw arepresentative indifference curve going through that point. Label it appropriately.1Question 4: Dina views Apples (A) and Bananas (B) as imperfect substitutes. Her utility functionfor the two products is U(A, B) = A0.5B0.5. The prices of the two products are pA = 1, pB = 4.(a) What is MRSAB?(b) Consider the bundle (A, B) = (8, 8). Without knowing Dina’s income, is it possible toconclude whether this bundle maximizes Dina’s utility? Explain.(c) Suppose Dina’s income is 80. What is her optimal consumption bundle?(d) Draw a diagram with Dina’s budget constraint, the bundle (16, 16), her optimal consumptionbundle, and a representative indifference curve going through her optimal consumptionbundle.Question 5: Denny views Scotch (S) and Cigars (C) as perfect complements. He always consumesthem in equal proportions. One without the other gives him no utility. As such, his utility functionis given by U = min[S, C]. His income is 100 and prices are pC = pS = 5.(a) What is Denny’s optimal consumption bundle? How much utility does he obtain from it?(b) Would Denny prefer all prices fall to 1 or that his income be increased to 500? Explain.Suppose Denny’s income remains at 100 but you do not know what the prices of scotch and cigarsare.(c) Find Denny’s demand function for Scotch, qS, and cigars, qC. [Hint: You are solving forhow much C and S Denny would purchase for any possible prices pS and pC.]Question 6: Danielle’s utility function for two products is given by U = A0.6B0.4. She has incomeY and the prices of the goods are pA and pB.(a) Calculate Danielle’s demand function for good A, qA. Is it increasing or decreasing in Y?Increasing or decreasing in pA? Show your answers formally (using calculus).
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