Linus Straight's utility function is U (a, b) = 2a+b, where a is his consumption of apples and b is his consumption of bananas. Lucy Kink's utility function is U (a, b) = min {2a, 19}. Lucy initially has no apples and 12 bananas. Linus initially has no bananas and 12 apples. In the Edgeworth box, goods for Lucy are measured from the upper right corner of the box and goods for Linus are measured from the lower left corner. Label the initial endowment point on the graph with the letter E. Draw two of Lucy's indifference curves in red ink and two of Linus's indifference curves in blue ink. Use black ink to draw a line through all of the Pareto optimal allocations.1 1. [4 marks] In this economy, in competitive equilibrium, determine the ratio of the price of apples to the price of bananas. 2. [4 marks] Let as be Linus's consumption of apples and let ()3 be his consumption of bananas. At competititive equilibrium, what is Linus's budget constraint? This gives us one equation in two unknowns. To nd a second equation, consider Lucy's consumption. In competitive equilibrium, total consumption of apples equals the total supply of apples and total consumption of bananas equals the total supply of bananas. Determine the Lucy's consumption of apples and bananas as a function of as and b3, respectively. 3. [8 marks] Determine each consumer's apple and banana consumption in the equilibrium. Show the contract curve and equilibrium point on the Edgeworth box. 4. [4 marks] At the equilibrium, determine whether each consumer is better off / worse off / indifferent by trading. Explain. Is this equilibrium Pareto efcient? Why / Why not