The isocost line through this point represents the sr

Info icon This preview shows pages 12–14. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 12

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 .
Image of page 13
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern