Surname1Student Name:InstitutionClassDateQuestion 1: Description of an EconomyConsider an endowment economy populated by Ben and Jerry. Their endowments aremeasured by units of apple ( ) and banana ( ). Bens endowment is represented as vector of (,)=(2, 1) whereas Jerrys endowment as ( , )=(1, 2). As for preferences, Bens utility functionis UBen( , ) + and Jerrys utility function is UBen( , ) . Assume that these two guystrade goods without any frictions in perfectly competitive markets. Now, answer the followingquestions based on the descriptions so far.(a) Set up and solve Bens utility maximization program under the market price of (Notethat is a relative market price of X to Y, i.e. = / ). Compare his optimal consumptionplan with his initial endowment.UBen (X, Y) = Log X + Log YU =x yU= 1x 2U= 2Therefore,U (2) = log 2 + log 12Therefore, U = log (2x1)UBen= log 2(b) Set up and solve Jerrys utility maximization program under the market priceof . Compare his optimal consumption plan with his initial endowment.UBen (X, Y) = UBen (1, 2) =12U = U (1, 2)U= 1x2U= 2Surname2U (2)2 = (12)2U (4) =2U= 2/4Uben =0.5(c) By solving (a) and (b), you have derived individual demand functions for Xand Y. Based on your answer to (a) and (b), derive market demands for X andY.Market demand = x/yMarket Demand = log 2/0.5Market demand = log 4Market demand = 0.60(d) Set the market demand ...
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