Question 5. (20 marks) Consider an exchange economy with two consumers and two goods. Let Iin denote the consumption of good l by consumer n. Suppose that Consumer l's preferences are given by the utility func- tion u1 (911, 121) = 111 + 121 and Consumer 2's preferences are given by the utility function U2 (112, 022) = x 12.722 Suppose that the endowment vectors are wi = (8,3) and W2 = (2,7). Normalise the price vector so that P2 = 1. (1) Find an expression for Consumer l's demand for good 1 in terms of p. Also find Consumer 2's demand for good 1 in terms of pi. (5 marks) (2) Find the equilibrium price vector and the equilibrium allocation. (5 marks) (3) Represent this economy in an Edgeworth Box diagram. Clearly mark and label: the initial endowment; the equilibrium allocation; the equilibrium price; the equilibrium budget constraint; the con- sumers' indifference curves through the equilibrium allocation and the initial allocation, and the contract curve. (10 marks)