Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportions of 2 slices of cheese to each slice of ham. Her utility function is given by US = Min(10H; 5C). Jones, on the other hand, regards ham and cheese as perfect substitutes—she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese.
a) Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy?
b) Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones gets the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades?
c) Suppose that 20 slices of ham could be transferred without cost from Jones’ to Smith’s endowment. Now what mutually beneficial trades might occur and what utility levels would be experienced by Smith and Jones?
d) Suppose that Jones objects to the transfer of ham proposed in part c and states, ‘‘I’d rather throw the ham away than give it to Smith.’’ If Jones carries through on her threat, what mutually beneficial trades are now possible and what utility levels will be experienced by Smith and Jones?
e) Suppose that Smith expects the ham transfer from Jones and, through carelessness, allows 20 slices of her initial ham endowment to spoil. Assuming the transfer from Jones actually happens, now what mutually beneficial trades are possible, and what are the potential utility levels for Smith and Jones?
f) Suppose now that both of the adverse incentive effects mentioned in parts d and e occur simultaneously. What mutually beneficial trading opportunities remain, and what are the potential utility levels for Smith and Jones?