## (solution) BC3035: Microeconomic Theory, Problem Set #5 1. Jack Sprat can

Question 4 on attached doc. Consider an exchange economy in which there are exactly 1000 soft drinks(x) and 1000 hamburgers (y).  Each individual has an initial endowment of 500 units of each good.a. Express the demand for Smith and Jones for goods x and y as functions of PX, PY and their initial endowments.b. Use the demand functions from part (a) together with the observation that total demand for each good must be 1000 to calculate the equilibrium price ratio, PX /PY, in this situation. What are the equilibrium consumption levels of each good by each person?c. How would the answers to this problem change for the following initial endowments?

BC3035: Microeconomic Theory, Problem Set #5 1. Jack Sprat can eat no fat, his wife can eat no lean.? Construct an Edgeworth box diagram for this pair (assuming fixed quantities of ?fat? and ?lean?) and indicate the contract curve. 2. Nothing in our analysis of exchange requires that the equilibrium be unique. Draw an example of an Edgeworth box diagram in which there are two different, interior equilibria arising from the same initial endowments. Explain intuitively why can these occur. 3. Suppose there are only two individuals (Sally and Jenny) and two goods (ham and cheese) in an exchange economy. Sally chooses to consume ham and cheese in fixed proportions of 2 C and 1 H. Sally?s utility function is therefore ! = min (, /2). Jenny has flexible preferences and utility is given by ! = 4 + 3. Initial endowments for Sally are H = 60, C = 80 and for Jenny H = 40, C = 120. a. Graph the Edgeworth box diagram for this exchange economy and indicate the core of the economy given the initial endowments specified b. At the competitive equilibrium, what will be the equilibrium price ratio? Who will obtain the gains from Trade? 4. Consider an exchange economy in which there are exactly 1000 soft drinks (x) and 1000 hamburgers (y). Let Smith?s utility be represented by ! ! ! ! ! ! , ! = ! ! ! ! . And Jones? utility by ! ! , ! = ! ! ! ! . Each individual has an initial endowment of 500 units of each good. a. Express the demand for Smith and Jones for goods x and y as functions of PX, PY and their initial endowments. b. Use the demand functions from part (a) together with the observation that total demand for each good must be 1000 to calculate the equilibrium price ratio, PX /PY, in this situation. What are the equilibrium consumption levels of each good by each person? c. How would the answers to this problem change for the following initial endowments?

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