Question

Question 1: Robert and Erin are trapped on a deserted island with only two goods: Wine (W) and Crackers (C). Robert currently has 6 bottles of wine and 9 boxes crackers whereas Erin has 9 bottles of wine and 6 boxes of crackers. Robert's preferences are represented by his utility function UR = W0.6C0.4 and Erin's by UE = W0.400.6. (a) Calculate MRSWc for both Robert and Erin. Are they the same or different given their endowments of W and C? (b) Is the existing allocation of goods Pareto efficient? Explain why or why not. (c) If Robert were to trade 3 boxes of crackers for 3 bottles of wine, would this be a Pareto improvement? Is the new allocation Pareto efficient? Suppose instead that Robert and Erin used a market to trade and that the prices of each good are such that PW = 1. Because it's a market, Robert and Erin can both buy and sell W and C at those prices. (d) What are Robert and Erin's budget constraints? (e) How much W does Robert want to buy or sell? How much W does Erin want to buy or sell? (f) Draw an Edgeworth box with Robert at the bottom left, Erin at the top right, W on the horizontal axis and C on the vertical axis. Note the initial endowment of goods, the bud- get lines of each person, the allocation they trade to, and appropriately draw 2 pairs of indifference curves going through the initial endowment and the final allocation.

Answer 1

zw. -Q) UR = Woocot, UE = wo4c6. then a) MRSR= Mow = 6c = w Moc MRSE - Mow = 4C MWC at initial endowments, eR= (6,9), ef = (9,6) = (W, C) MRSA = 3x2 = 24, MRSE = example two MRS are not equal. Ans b) at Pareto efficiency, MRS RTAMRSE MRs of all agents are same, a but here, MRS R & MRS E, so not Pareto efficient Aus

U C.) New allocations, eR=(6+3,9-3) = 19,6) CE = ( 6,9) Now MRSR= 3x6 = 18 = 1, MRSE = 2 x 9 = 18 = 1 346 To as two MRS are equal, so it is Pareto efficient And d) Boc. Pero wt Pco NG My endowment Income, for Robert, MR= 6+9=15, as P w = Pc = 1 ME = 976 =15 B.C for Both WTC =M =15 W+c=15 | Ang e) Now. at these pruces, demands for Robert WR= 6MR = •6x15 = 90 W, c. Pw 1 (= (9,6) GR = .4MR = .4x15 = 6. J - PC for Erin, WE = .4ME/Pw = 4X15 = 6. } = (619) CE = .6X MP/Pc = 6X15=9 s. 80 Robert will 3W & Sell 3 on eren will sell 3 w & buy 3o. I Ans 12

Mandatorarily Answering only first 4 parts