Assignment Task: Jesse Marsch, coach of Leeds United soccer club wants to transfer some forwards on his club roster in exchange for some additional defenders. Graham Potter, the coach of Chelsea, is interested in transferring some defenders in exchange for some additional forwards. Currently, Leeds United have a total of 70 forwards and 30 defenders on their club roster, while Chelsea, have a total of 50 defenders and 35 forwards. Both Potter and Marsch have well-behaved preferences. Given the initial endowment of players, at that point Marsch is willing to trade 1 forward for 4 defenders, while Potter is willing to trade 6 defenders for 4 forwards.
Based on this information, answer the following:
(a) Using appropriate scaling, draw the Edgeworth Box based on the information given above.
(b) What would happen to the dimensions of the Edgeworth Box to if Marsch were to lose 10 defenders to serious injuries, and Potter were to receive 6 additional forwards from Chelsea's youth soccer academy?
(c) At the initial endowment point, what are the marginal rates of substitution for Marsch and Potter? Given their marginal rates of substitution, is the initial endowment point Pareto efficient? Why or why not? Could a Pareto improvement be made? Do you have enough information in the question to draw their indifference curves at the initial endowment? If not, what additional information would you need?
(d) Suppose the transfer market for soccer players sets the price for forwards at $5 million/player, and defenders at $3 million/player. Given these prices, calculate the wealth of Marsch's club Leeds United and Potter's club Chelsea based on their initial endowments of players, and derive the value of the slope of their wealth/budget line(s). If these prices eventually result in there being a competitive equilibrium, does their wealth change compared to that at their initial endowment? With this information on prices, what will the marginal rates of substitution have to be for Marsch and Potter at the competitive equilibrium?
(e) If these transfer prices do not result in competitive equilibrium, there being an excess demand for forwards and an excess supply of defenders, what will have to happen to relative transfer prices to bring about competitive equilibrium in the transfer market?