Schure tests06ans

# The isocost line through this point represents the sr

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The isocost line through this point represents the SR minimum cost level. Remark that the latter isocost line is further away from the origin, so represents higher costs. Question 1-2 A PE allocation between A, B, and C is an allocation between A, B, and C such that it is not possible to re-allocate/re-distribute the available goods X and Y among A, B, and C such that A, B, and C are all better o ff . Question 2-1 (a) Picture as in the labs but the initial allocations di ff ers. The two orange ICs in the picture are those that run through the initial allocation E . Now point to an allocation in the box that is utility improving trades for both agents (it lies in the interior of the set of IR trades). The presence of such an allocation proves that the initial allocation is not Pareto-e cient. [You could also point to the fact that the slopes of the ICs are not identical so that there must be utility improving trades for both A and B.] Some remarks: Here is what I told the TAs regarding grading: “Make sure that students get the box right, with the axes labeled and the lenght of the axis about right (x-axis: 3 units,y- axis 5 units). The initial allocation is of course just a single point. The indi ff erence curves should be bowed inward when your perspective is the origin of each respective agent.” In general, I recommend fi guring out one indi ff curve pretty precisely, while the rest can be sketchy. Find a few easy points. For example, one of Arnold’s ICs is X A Y 1 / 3 A = 1 and the points ( X A , Y A ) = (1 , 1) , (2 , 1 / 8) , (3 , 1 / 27) are on it. From this and your knowledge that this is a convex-shaped function you can graph the IC X A Y 1 / 3 A = 1 “pretty precisely”. With one precise IC you know more or less what the other curves look like as well. Using more colors for your lines works great when working with Edgeworth boxes. (b) Create a new picture. Note that the IR trades are actually a bit tricky. Since Arnold has a zero endowment of good Y, he (weakly) prefers all allocations in the box to his initial 1

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endowment. As a result the set of IR allocation are all allocations that lie “above” (i.e. towards the bottom-left in the E-box) Brigit’s IC that runs through the initial allocation. The exact shape of the contract curve is not so easy to fi gure out, but the picture should made clear that it consists of points for which the ICs of Arnold and Brigit are tangent. The contract curve runs below the diagonal from A to B, by the way. The core is the part of the contract curve that are also in the set of IR allocations. (c) (c1: graphically) First draw the BL in the Edgeworth box. With prices p X = 3 and p Y = 1 the slope of the BL is 3 and it must of course go through the initial allocation E . Next take Arnold’s highest IC that still has a point on the budget line. (c2: mathematically) With prices 3 and 1 we have the following budget restriction (BR) 3 X A + Y A M A = X E A 3 + Y E A 1 = 8 3 3 = 8 , i.e. 3 X A + Y A 8 . One condition for Arnold’s optimum is the budget line, i.e. 3 X A + Y A = 8 .
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