Exam 32:Exchange-Part A

Colette and Boris both consume the same goods in a pure exchange economy.Colette is originally endowed with 9 units of good 1 and 6 units of good 2.Boris is originally endowed with 18 units of good 1 and 3 units of good 2.They both have the utility function U(x₁,x₂)= x^1/3₁x^2/3₂.If we let good 1 be the numeraire,so that p₁ =$1,then what will be the equilibrium price of good 2?

Professor Nightsoils utility function is U N (B N,P N)=B_N+4P^1/2_N and Dean Interfaces utility function is U I (B I,P I)= B_I+2P^1/2_I,where B N and B I are the number of bromides and P N and P I are the number of platitudes consumed by Nightsoil and Interface respectively.If Nightsoils initial endowment is 4 bromides and 10 platitudes and if Interfaces initial endowment is 3 bromides and 15 platitudes,then at any Pareto efficient allocation in which both consume positive amounts of both goods,

If two people have identical Cobb-Douglas utility functions,then in every Pareto optimal allocation,they must consume all goods in the same proportions as each other.

Eduardo and Francisca participate in an economy that is in competitive equilibrium.Although they are unacquainted with each other,both purchase strawberries and champagne.Edouardo's utility function is U(s,c)=2s +c,where s is the number of boxes of strawberries he consumes per month and c is the number of bottles of champagne.Francisca's utility function is U(s,c)= sc.

Astrids utility function is U(H A,C A)= H A C A.Birgers utility function is min{H B,C B}.If Astrids initial endowment is no cheese and 5 units of herring and if Birgers initial endowments are 6 units of cheese and no herring,then where p is a competitive equilibrium price of herring and cheese is the numeraire,it must be that demand equals supply in the herring market.This implies that

A small economy has only two consumers,Boris and Vanessa.Boris's utility function is U(x,y)= x +16y^1/2.Vanessa's utility function is U(x,y)= x + 2y.Boris is endowed with 160 units of x and 60 units of y.They make trades to reach a Pareto optimal allocation of resources in which both persons consume positive amounts.How much y does Boris consume?

The second welfare theorem of economics states that if preferences are convex,then any Pareto optimal allocation could be achieved as a competitive equilibrium after some reallocation of initial endowments.

Pete and Dud live in a two-commodity world.Pete's utility function is U ^P(x ^P₁,x ^P₂)= x ^P₁x ^P₂.Dud's utility function is U ^D(x ^D₁,x ^D₂)=min{x ^D₁,x ^D₂}.Pete is initially endowed with 3 units of commodity 1 and 4 units of commodity 2.Dud is initially endowed with 7 units of commodity 1 and 6 units of commodity 2.

A small economy has only two consumers,Ivan and Marilyn.Ivan's utility function is U(x,y)= x + 18y^1/2.Marilyn's utility function is U(x,y)= x + 3y.Ivan is endowed with 135 units of x and 60 units of y.They make trades to reach a Pareto optimal allocation of resources in which both persons consume positive amounts.How much y does Ivan consume?

Morris has the utility function U(b,w)= 4b +4w and Philip has the utility function U(b,w)= bw,where b is the number of books consumed per month and w is bottles of wine consumed per month.If we draw an Edgeworth box with books on the horizontal axis and wine on the vertical axis and if we measure Morris's consumptions from the lower left corner of the box,then the contract curve contains

In a competitive pure exchange economy,if the initial endowment is on the diagonal line between the two origins,then,according to the first welfare theorem of economics,there must always be a competitive equilibrium in which no trade takes place.

Arturo and Belen consume only two goods,X and Y.They have strictly convex preferences and no kinks in their indifference curves.At the initial allocation,the ratio of Arturo's marginal utility of X to his marginal utility of Y is A and the ratio of Belen's marginal utility of X to his marginal utility of Y is B,where A $\lt$ B.The competitive equilibrium price ratio is p_x/p_y = C.