Smith and Jones are stranded on a desert island. Each has in his possession some slices of ham (H) and cheese (C). Smith is a very choosy eater and will eat ham and cheese only in the fixed proportions of 2 slices of cheese to 1 slice of ham. His utility function is given by Us= min(H,C/2). Jones is more flexible in his dietary tastes and has a utility function given by Uj= 4H + 3C.
Total endowments are 100 slices of ham and 200 slices of cheese.
a. Draw the Edgeworth box diagram that represents the possibilities for exchange in this situation. What is the only exchange ratio that can prevail in any equilibrium?
b. Suppose Smith initially had 40 H and 80 C. What would be the equilibrium position be?
c. Suppose Smith initially had 60 H and 80 C. What would be the equilibrium position be?
d. Suppose Smith (much the stronger of the two) decides not to play by the rules of the game. Then what could the final equilibrium position be