Exam 30: Exchange-Part A

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?

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.

Every allocation on the contract curve is Pareto optimal.

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.

If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then

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.

In a pure exchange economy with two persons and two goods, one person always prefers more to less of both goods and one person likes one of the goods and hates the other so much that she would have to be paid to consume it.Both are initially endowed with positive amounts of both goods.The competitive equilibrium price of the good that one person hates

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.

In a pure exchange economy, Ollie's utility function is U(x, y)= 3x + y and Fawn's utility function is U(x, y)= xy.Ollie's initial allocation is 1 x and no y's.Fawn's initial allocation is no x's and 2 y's.Draw an Edgeworth box for Fawn and Ollie.Put x on the horizontal axis and y on the vertical axis.Measure goods for Ollie from the lower left and goods for Fawn from the upper right.Mark the initial allocation with the letter W.The locus of Pareto optimal points consists of two line segments.Describe these line segments in words or formulas and show them on your graph.

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?

A small economy has only two consumers, Harold and Irene.Harold's utility function is U(x, y)= x + 50y^1/2.Irene's utility function is U(x, y)= x + 5y.Harold is endowed with 500 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 Harold consume?

A small economy has only two consumers, Nick and Minnie.Nick's utility function is U(x, y)= x + 154y^1/2.Minnie'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 Nick consume?

In a model with two consumers, two goods, and no production, the contract curve must be a line going from one consumer's origin to the other consumer's origin.

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)= 5N_y + B_y.Xavier is endowed with 4 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?

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

If there are consumption externalities, then a competitive equilibrium is not necessarily Pareto optimal.

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 7 units of X.Babettes initial endowment is no units of X and 6 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

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?

Mutt's utility function is U(m, j)= max{3m, j} and Jeff's utility function is U(m, j)= 4m + j.Mutt is initially endowed with 4 units of milk and 2 units of juice and Jeff is initially endowed with 4 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