Chapter 3 1 Your airplane crashes in the Pacific Ocean. You land on a desert island with one other passenger. A box containing 100 little bags of peanuts also washes up on the island. The peanuts are the only thing to eat. In this economy with two people, one commodity, and no production, represent the possible allocations in a diagram, and explain why every allocation is Pareto efficient. Is every allocation fair? 2. Suppose that Tang and Wilson must split a fixed 400 pounds of food between them. Tang's utility function is Up = squt (F1 ) and Wilson's utility function is Uw = /2 squt (F2). where F, and F2 are pounds of food to Tang and Wilson, respectively. a. How much utility will Tang and Wilson receive if the food is distributed evenly between them? b. If the social welfare function is UT + Uw, then what distribution of food between Tang and Wilson maximizes social welfare?c. If social welfare is maximized when they each obtain the same level of utility, then what is the distribution of food between Tang and Wilson that maximizes social welfare?3. Suppose that Hannah's utility function is Up = 37 + 4C and that Jose's utility function is Uj = 47 + 3C, where Tis pounds of tea per year and C is pounds of coffee per year. Suppose there are fixed amounts of 28 pounds of coffee per year and 21 pounds of tea per year. Suppose also that the initial allocation is 15 pounds of coffee to Hannah (leaving 13 pounds to Jose) and 10 pounds of tea to Hannah (leaving 11 pounds of tea to Jose). a. What do the utility functions say about the marginal rates of substitution of coffee for tea? b. Draw the Edgeworth Box showing indifference curves and the initial allocation.c. Draw the contract curve on the Edgeworth Box. Explain why it looks different from the contract curves depicted in the text. d. Is the initial allocation of coffee and tea Pareto efficient?4. Imagine a simple economy with two people: a. Let the social welfare function be W = UL + UA where UL and UA are the utilities of Livia and Augustus, respectively. Graph the social indifference curves. How would you describe the relative importance assigned to their respective well-being? b. Repeat part a when W = UL +2UAc. Assume that the utility possibilities curve is as follows: Graphically show how the optimal solution differs between the welfare functions given in parts a and b