Sample Final Questions - Intermediate Microeconomic Theory | ECON 3070, Exams of Microeconomics

Download Sample Final Questions - Intermediate Microeconomic Theory | ECON 3070 and more Exams Microeconomics in PDF only on Docsity! Econ 3070-004: solutions to some sample final questions December 14, 2007 Question 3 Consider an economy with two individuals (Adam, Eve) each endowed with 100 units of different goods (Adam has 100 tomatoes, x and Eve has 100 pounds of goat cheese, y). Eve’s utility is UE ¡ xE, yE ¢ = xE + yE and Adam’s utility is UA ¡ xA, yA ¢ = xAyA 1. Depict the endowment in an Edgeworth box 0 20 40 60 80 100 y 20 40 60 80 100x 2. Draw the indifference curves through the initial endowment. Is this allocation Pareto efficient? No, any allocation below the diagonal (IC) 1 of Eve and above the IC of Adam, which coincides with his axis is preferred by both. 3. Calculate the set of Pareto Efficient allocations. 4. A Pareto Efficient allocation satisfies the following conditions: (a) MRSA ¡ xA, yA ¢ =MRSE ¡ xE, yE ¢ , (b) xA + xE = 100; yA + yE = 100 Condition a implies yA xA = 1, so yA = xA. Condition b restricts yA, xA to be between zero and 100. So the set of Pareto efficient allocations in this case is a diagonal connecting the bottom-left corner and the upper-right one. 5. Assume after an exchange (with an auctioneer announcing prices) Eve has 30 tomatoes and 70 pounds of cheese, while Adam has 70 tomatoes and 30 pounds of cheese. Can this be a ‘competitive market allocation’ with both Adam and Eve taking prices as given? Why? MRSE ¡ xE, yE ¢ = 1 for all xE, yE.On the other hand,MRSA (70, 30) = 3 7 < 1 =MRSE ¡ xE, yE ¢ and that is why the allocation is not efficient: Adam values tomatoes relatively less than Eve. 6. Extra credit (10%) Compute Walrasian equilibrium (allocation and prices) for this economy. Walrasian equilibrium is an allocation and prices such that (a) Consumers choose the best affordable bundle taking prices as given (b) Prices are such that the markets clear. Eve’s preference is linear, so her best affordable bundle is just tomatoes ³ 100py px , 0 ´ if the price of tomatoes is smaller than that of cheese, or just cheese (0, 100) if the opposite is true. If px py = 1, then any combination of cheese and tomatoes satisfying xE+yE = 100. Adam: max xA,yA xAyA pxx A + pyy A = 100px 2