Need help with b-f

Question 1. We reconsider the exchange economy from question 3 in Homework 5 to explore the possibility of price manipulation. Bruce and Sheila both consume the same goods (shrimp and Fosters) in a pure exchange economy. Bruce is originally endowed with 4 units of good 1 (shrimp) and 6 units of good 2 (Fosters). (As usual, think of both shrimp and Fosters as being innitely divisible.) Sheila is originally endowed with 3 shrimp and 4 Fosters. They both have the utility function U (x1, x2) = x1163. Let shrimp be the numeraire, so that p1 = 1. (a) (b) (C) (d) (e) (f) Suppose the Walrasian auctioneer knows the utility functions of Bruce and Sheila, and cal- culates the equilibrium price on the basis of reported endowments. Suppose Bruce and Sheila honestly report their endowments to the Walrasian auctioneer. What price 192 will the auctioneer announce? Which consumer buys shrimp and which consumer sells shrimp (and how much)? [Hint This is easy, and is just to get us started. If it is relevant, you may use the information from the solution to Homework 5.] Suppose Sheila contemplates under-reporting her endowment of shrimp. What would be the resulting announcement of p2 by the auctioneer if Sheila were to report an endowment of 6 shrimp and 4 Fosters? Suppose that Sheila must buy and sell the quantities implied by her endowment report. What will be her trades and nal consumption of shrimp and Fosters when she reports an endowment of 6 shrimp and 4 Fosters? Which does Sheila prefer and why: reporting truth- fully or underreporting shrimp? Suppose (just for this part) that Sheila does not need to buy and sell the quantities implied by her endowment report. Is it consistent with market clearing for Sheila to still believe that she can buy and sell as much as she would like at the announced prices? Now consider the 11 -fold replica economy. In this economy, there are 71 clones of Bruce (with identical endowments and preferences), and n clones of Sheila (with identical endowments and preferences). Suppose all clones of Bruce and all clones of Sheila report their endow- ments truthfully. What price 1}; does the auctioneer announce? Continuing with our analysis of the n-fold replica economy, suppose now that one clone of Sheila reports an endowment of 6 shrimp and 4 Fosters, while all other consumers an- nounce truthfully. What is the resulting announcement of pa by the auctioneer? What hap- pens to this announcement as 11 gets arbitrarily large