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competitive equilibrium

8. Halloween is an old American tradition. Kids go out dressed in costume and neighbors give them candy when they come to the door. Spike and Cinderella are brother and sister. After a long night collecting candy, they sit down as examine what they have. Spike finds that he has 40 candy bars and 20 packs of gum. His sister finds she has 30 candy bars and 40 packs of gum. Spike likes candy bars exactly twice as much as gum and would always be willing to trade two packs of gum for one candy bar. Cinderella, on the other hand, likes gum exactly twice as much as candy bars and would always be willing to trade two candy bars for one pack of gum. 

a. Illustrate this situation in an Edgeworth box. Let Spike’s origin be in the lower left, and Cinderella’s be in the upper right hand corner. Put candy bars on the horizontal axis and gum on the vertical. 

b. Now draw in indifference curves for the two agents that reflect the description given above. Indicate the endowment point, and the contract curve. Illustrate a competitive equilibrium. Is there more than one competitive equilibrium? 

#10. Ken McSubstitute and Ron O’Complement were flying to a fast food festival in Fiji when an unexpected storm forced their plane to ditch in the middle of the Pacific. Miraculously, they are washed up on a desert island. Ken finds that he has only 5 slightly wet hamburgers and 15 orders of fries in his pockets. Ron discovers he has 15 hamburgers and 5 orders of fries. Ken only cares about how much he gets to eat. His utility function is: Us(H,F) = H+F. On the other hand, Ron believes that it is uncivilized to eat hamburgers without french fries or french fries without hamburgers. His utility function is: Uc(H,F) = min(H,F). 

a. In an Edgeworth box, show the endowment point, the Pareto Opimal Allocations, and the competitive equilibrium 

b. Is the competitive equilibrium Pareto Optimal? 

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