A little exchange economy has just two consumers, named Ken and Barbie, and two commodities, quiche and wine. Ken's initial endowment is O units of quiche and 20 units of wine. Barbie's initial endowment is 40 unit of quiche and 10 units of wine. Ken and Barbie have identical utility functions. We write Ken's utility function as, U(QK, Wx) = QxWx and Barbie's utility function as UQB,WB) = min{QB,WB), where Qx and We are the amounts of quiche and wine for Ken and QB and We are amounts of quiche and wine for Barbie. (a) Draw an Edgeworth box to illustrate this situation. Put quiche on the horizontal axis and wine on the vertical axis. Measure goods for Ken from the lower left corner of the box and goods for Barbie from the upper right corner of the box. (Be sure that you make the length of the box equal to the total supply of quiche and the height equal to the total supply of wine.) Locate the initial allocation in your box, and label it W. On the sides of the box, label the quantities of quiche and wine for each of the two consumers in the initial endowment. (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 2. (e) Set po = 1, price for quiche is 1. Find Ken and Barbie's demand functions for good 2 as function of pw price for wine. Show your work (d) Find the competitive equilibrium for Ken and Barbie. (Hint: Set total demand of one good equal to its total supply, solve for pw. Then find the quantity demanded for Ken and Barbie in the competitive equilibrium.) (e) On the Edgeworth box for Ken and Barbie, draw in the competitive equilibrium allocation and draw Ken's competitive budget line (with black ink)