A little exchange economy has just two consumers, named Ken and Barbie, and two commodities, quiche and wine. Ken’s initial endowment is 3 units of quiche and 2 units of wine. Barbie’s initial endowment is 1 unit of quiche and 6 units of wine. Ken and Barbie have identical utility functions. We write Ken’s utility function as (XK, YK)=XKYK and Barbie’s utility function as (XB, YB)=XBYB, where XK and YK are amounts of quiche and wine for Ken and XB and YB are amounts of quiche and wine for Barbie. Ken’s marginal rate of substitution is |MRSXY|=YKXK and Barbie’s marginal rate of substitution is |MRSXY|=YBXB Required:
a. Draw an Edgeworth box below to illustrate this situation.
b. Use blue ink to draw an indifference curve for Ken that shows allocations in which his utility is 6. Use red ink to draw an indifference curve for Barbie that shows allocations in which her utility is 6.
c. At any Pareto optimal allocation where both consume some of each good, Ken's marginal rate of substitution between quiche and wine must equal Barbie's. Write an equation that states this condition in terms of the consumptions of each good by each person.
d. On your graph, show the locus of points that are Pareto efficient.
e. At any Pareto efficient allocation in which both persons consume both goods, Ken's indifference-curve slope will be . Therefore, since we know competitive equilibrium is Pareto efficient, we know that Pq /Pw = .
f. In competitive equilibrium, Ken's consumption bundle must be . How about Barbie's consumption bundle?