Problem 4. Suppose two OSU freshmen Kyle (k) and Brock (b) went on a spring break and ended up on a desert island. After roaming the island for 3 hours, Kyle found 3 quinces (q) and 2 watermelons (w). Brock roamed the island for 7 hours and found 1 quince (q) and 6 watermelons (w). Kyle and Brock have identical tastes. Kyle's utility function is UAWmm) : qku'k, and Brock's utility function is Ub(qb,u'b) : qbwb, where q,- is the number of quinces for Kyle (2' : k) and Brook (1' : b), and w,- is the number of watermelons for Kyle (1' = k) and Brook (2' = b). (a) Draw and Edgeworth box. Put 5} on the horizontal axis and w on the vertical axis. Measure Kyle's fruits from the lower left corner and Brook's fruits from the upper right corner (make sure that the length of the box is equal to the total supply of q and the height of the box is equal to the total supply of \\1'). Label sides of the box, locate the initial allocation, and label it A. (b) Draw an indifference curve for Kyle when his utility is 6. Draw an indifference curve for Brock when his utility is 6. (c) At any Pareto optimal allocation, where both guys consume quinces and watermelons , Kyle's marginal rate of substitution (MRS) is equal to that of Brock. State this condition in terms of consumption of each kind of food by each person. (d) Use condition in (c) to draw the locus of Pareto optimal allocations on your graph (Hint: use the condition in (c) and the total endowment of two kinds of food to find the slope of the line, which goes through all PO points (contract curve)). (e) What is the slope of Kyle's indifference curve at a Pareto optimal (PO) allocation? P9 P11' (f) What is the price ratio at the competitive equilibrium? (9) What is Kyle's consumption bundle in the competitive equilibrium? (h) What is Brook's consumption bundle in competitive equilibrium? (i) Draw the competitive equilibrium allocation and Kyle's competitive budget line in your Edgeworth box