Q. 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 Edge worth box diagram which represents the possibilities for exchange in this situation. Illustrate what is the only exchange ratio which can prevail in any equilibrium?
b. Assume Smith initially had 40 H and 80 C. Illustrate what would be the equilibrium position be?
c. Assume Smith initially had 60 H and 80 C. Illustrate what would be the equilibrium position be?
d. Assume Smith (much the stronger of the two) decides not to play by the rules of the game. Then illustrate what could the final equilibrium position be?