Homework #8 Due date: Tuesday, May 3. Problem 1 Consider an exchange economy with two consumers, named Lisa (L) and Bart (B), and two goods, apples (a) and bananas (b). Denote by (al, b4) Lisa's and by (aB, bB) Bart's consumption bundle. Consumers' utility functions and initial endowments are given by: u" (at, bl) = min{at; b'}, ( W2 , wb ) = ( 10 , 6 ) . UB (a B, bB ) = aB. 6B ( wa , w! ) = ( 0 , 4 ) . Let Pa be the price for apples and po the price for bananas which is normalized, i.e., Po = 1. 1. Draw the Edgeworth box for this economy and depict the initial allocation. (Measure Lisa's consumption from from the lower left corner and Bart's from the upper right. ) 2. For each consumer, draw the indifference curve that passes through his/her initial endowment in the Edgeworth box. Shade the area of all feasible allocations that make both consumers better off than the initial endowment allocation. 3. Determine the equation for the contract curve and draw it in the Edgeworth box. 4. Determine Lisa's and Bart's income m and mB. 5. Derive Lisa's demand function for apples a (Pa, Pb, m ) and bananas b" (Pa, Pb, m!) as a function of prices, Pa and Po, and her income m. 6. Derive Bart's demand function for apples a (Pa, Pb, m) and bananas be (Pa, Pb, mB) as a function of prices, Pa and Pb, and her income m 7. Determine the Walrasian market equilibrium for this economy (i.e., equilibrium prices and equilibrium allocation). Illustrate the equilibrium situation in the Edgeworth box. 8. Consider the Pareto-efficient allocation x = ((al, b ) = (2, 2), (aB, bB) = (8, 8)). De- termine the prices Pa and po and the distribution of transfers TL and to for which the Walrasian (competitive) market equilibrium at (Pa, Pb) generates this allocation