Edgeworth Box Problem solutions Live 5 PDF

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Edgeworth Box Problem solutions...

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Problem Solutions Bill and Ernie live in a two good economy (food and clothing), and they can trade with each other. A. Bill has an initial endowment consisting of 10 units of food and 10 units of clothing. Ernie has an initial endowment of 10 units of food and 20 units of clothing. Draw an Edgeworth Box for these consumers. Answer The box should be 20 units high by 30 units wide, assuming that you put food on the vertical axis and clothing on the horizontal. Let’s assume that you decide to put Bill’s origin at the bottom left and Ernie’s origin at the top right. Mark amounts of food and clothing on the axes so that Bill measures increasing amounts of food in an upward direction and increasing amounts of clothing in a rightward direction. Ernie will then measure increasing amounts of food in a downward direction and increasing amounts of clothing in a leftward direction.

B. Bill regards food and clothing as perfect one-for-one substitutes, while Ernie regards them as perfect complements but in a ratio of 3 units of clothing for 2 units of food. a. On your diagram, indicate the area which represents the set of allocations that are Pareto-preferred or Pareto superior to the original endowment given above.

Answer Perfect one-for-one substitutes means that Bill’s indifference curves are straight lines joining equal amounts of food and clothing along the axes. One indifference curve is a straight line joining the point representing 20 units of food and no clothing to the point representing 20 units of clothing and no food—this means that Bill gets equal amounts of utility from 20 units of food or 20 units of clothing or any linear combination of these two. In contrast, Ernie’s indifference curves are L-shaped (upside-down L-shaped since his origin is in the northeast corner of the Edgeworth Box). The vertex of the L always has an allocation of food and clothing to Ernie in the ratio of 3 units of clothing to 2 units of food. Any other ratio involves either excess clothing or excess food, in the sense that Ernie gets no additional utility from the excess food which is above a ratio of 2 to 3, and no additional utility from the excess clothing which is above a ratio of 3 to 2. Any point on the lens formed by the two indifference curves that pass through the initial endowment will be Pareto superior (except for the one exception of the allocation at the extreme opposite end of the lens). The area of allocations that are Pareto superior to the initial endowment is thus given by the grey triangle in the diagram below.

b. Find the Pareto-optimal allocation Answer The initial endowment gives Ernie 10 units of food and 20 units of clothing. This implies that Ernie has 5 units of excess clothing at this initial endowment. He is therefore willing to trade away clothing in exchange for food. On the other hand, Bill gets equal utility from a unit of food or a unit of clothing (they are perfect substitutes). So, for instance, if Ernie were to trade 2 units of clothing and get 2 units of food in return, he would be better off and Bill would be no worse off, so this would be a Pareto superior move. In fact, this allocation would be Pareto optimal since Ernie’s allocation cannot be further improved without making Bill worse off. The Pareto-optimal allocation thus occurs where Bill has 8 units of food and 12 units of clothing and Ernie has 12 units of food and 18 units of clothing. At this point, the indifference curves of the two agents are tangent to each other. c. What price ratio would allow this Pareto-optimal trade to take place? Answer A competitive price ratio of 1-1 (i.e. PF/PC = 1)....