Exam 32:Exchange-Part A

An economy has 2,000 people.1,000 of them have utility functions U(x,y)= x + y and 1,000 of them have utility functions U(x,y)=min{2x,y}.Everybody has an initial allocation of 1 unit of x and 1 unit of y.Find the competitive equilibrium prices and consumptions for each type of person.

Colette and Hans both consume the same goods in a pure exchange economy.Colette is originally endowed with 15 units of good 1 and 12 units of good 2.Hans is originally endowed with 97 units of good 1 and 4 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?

An economy has two people,Charlie and Doris.There are two goods,apples and bananas.Charlie has an initial endowment of 3 apples and 10 bananas.Doris has an initial endowment of 6 apples and 5 bananas.Charlie's utility function is U(A C,B C)=A C B C,where A C is his apple consumption and B C is his banana consumption.Doris's utility function is U(A D,B D)=A D B D,where A D and B D are her apple and banana consumptions.At every Pareto optimal allocation,

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 25 platitudes and if Interfaces initial endowment is 2 bromides and 20 platitudes,then at any Pareto efficient allocation in which both consume positive amounts of both goods,

Astrid's utility function is U(H_A,C_A)=H_AC_A.Birger's utility function is min{H_B,C_B}.If Astrid's initial endowment is no cheese and 13 units of herring and if Birger's initial endowments are 8 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

Jack Spratt's utility function is U(F,L)= L.His wife's utility function is U(F,L)= F.If Jack's initial endowment is 10 units of F and 5 units of L and if Jack's wife's initial endowment is 6 units of F and 10 units of L,then in an Edgeworth box for Jack and his wife,an allocation of F and L will be Pareto optimal only if it is at a corner of the box.

A small economy has only two consumers,Charlie and Doreen.Charlie's utility function is U(x,y)= x+154y^1/2.Doreen's utility function is U(x,y)= x + 7y.At a Pareto optimal allocation in which both individuals consume some of each good,how much y does Charlie consume?

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 11 units of herring and if Birgers initial endowments are 4 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

Will likes apples and hates bananas.Wanda likes both apples and bananas.Both of them have convex preferences.Will's initial endowment is 10 apples and 5 bananas.Wanda's initial endowment is 5 bananas and 10 apples. a.Draw an Edgeworth box with apples on the horizontal axis.Label the initial endowment point W. b.Show two indifference curves for each person. c.Show where on your diagram the Pareto optimal allocations are.

Amaranda and Bartolo consume only two goods,X and Y.They can trade only with each other and there is no production.The total endowment of good X equals the total endowment of good Y.Amaranda's utility function is U(x_A,y_A)=min{x_A,y_A}and Bartolo's utility function is U(x_B,y_B)=max{x_B,y_B}.In an Edgeworth box for Amaranda and Bartolo,the set of Pareto optimal allocations is

Irene and Orville live in an isolated valley and trade with no one but each other.They consume only cantaloupes and grapefruits.Irene has an initial endowment of 5 cantaloupes and 12 grapefruits.Orville has an initial endowment of 19 cantaloupes and 25 grapefruits.For Irene,the two goods are perfect substitutes,one for one.For Orville,they are perfect complements,one for one.At all Pareto efficient allocations,

Abduls utility is U(X A,Y A)=min{X A,Y A},where X A,and Y A are his consumptions of goods X and Y respectively.Babettes utility function is U(X B,Y B)= X B Y B,where X B and Y B are her consumptions of goods X and Y.Abduls initial endowment is no units of Y and 6 units of X.Babettes initial endowment is no units of X and 10 units of Y.If X is the numeraire good and p is the price of good Y,then supply will equal demand in the market for Y if

Mutt's utility function is U(m,j)=max{3m,j}and Jeff's utility function is U(m,j)= 2m + j.Mutt is initially endowed with 3 units of milk and 2 units of juice and Jeff is initially endowed with 5 units of milk and 6 units of juice.If we draw an Edgeworth box with milk on the horizontal axis and juice on the vertical axis and if we measure goods for Mutt by the distance from the lower left corner of the box,then the set of Pareto optimal allocations includes the

If allocation x is a competitive equilibrium at prices p and if everybody likes his bundle in allocation y better than his bundle in allocation x,then the total value of allocation y at prices p exceeds the total value of allocation x at prices p.

Xavier and Yvette are the only two persons on a desert island.There are only two goods,nuts and berries.Xavier's utility function is U(N_x,B_x)=N_xB_x.Yvette's utility function is U(N_y,B_y)=2N_y + B_y.Xavier is endowed with 5 units of berries and 13 units of nuts.Yvette is endowed with 6 units of berries and 8 units of nuts.In a competitive equilibrium for this economy,how many units of berries does Xavier consume?

Marilyn and Chen live in an isolated valley and trade with no one but each other.They consume only bananas and tomatoes.Marilyn has an initial endowment of 4 bananas and 11 tomatoes.Chen has an initial endowment of 20 bananas and 27 tomatoes.For Marilyn,the two goods are perfect substitutes,one for one.For Chen,they are perfect complements,one for one.At all Pareto efficient allocations,

In a competitive pure exchange economy,if the total value of excess demand for all types of food is zero,then the total value of excess demand for all nonfood commodities must be zero.

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 5 bromides and 20 platitudes and if Interfaces initial endowment is 3 bromides and 20 platitudes,then at any Pareto efficient allocation in which both consume positive amounts of both goods,

Adelino and Benito consume only two goods,X and Y.They trade only with each other and there is no production.Adelino's utility function is given by U(x_A,y_A)=2x_A + 5y_A and Benito's utility function is given by U(x_B,y_B)=2(6x_B +15y_B)^1/2.In the Edgeworth box constructed for Adelino and Benito,the set of Pareto optimal allocations is

A pure exchange economy is an economy where goods are traded but there is no production.