Suppose that Hannah’s utility function is U_H = 3T + 4C and that Jose’s utility function is U_J = 4T + 3C, where T is kilograms of tea and C is kilograms of coffee per year. Suppose there are fixed amounts of 28 kilograms of coffee per year and 21 kilograms of tea per year. Suppose also that the initial allocation is 15 kilograms of coffee to Hannah (leaving 13 kilograms to Jose) and 10 kilograms of tea to Hannah (leaving 11 kilograms of tea to Jose).
a. What do the utility functions say about the marginal rate of substitution of coffee for tea?
b. Draw the Edgeworth Box showing the indifference curves and the initial allocation.
c. Draw the contract curve on the Edgeworth Box. Explain why it looks different from the contract curve depicted in the text.
d. Is the initial allocation of coffee and tea Pareto efficient?