(Word Limit: 500 words) For this exercise t=1+the fourth digit of your student number. Consider a good consumed in two possible states of nature S= {a,b}. There are two types of contracts, each delivering one unit of the commodity in one state a or b, which can be traded in corresponding markets at prices p(a) and p(b). (i) Consider a consumer h with preferences and endowment • Un (xn(a), xh (b)) = 2log xn(a) + 3 log xn (b), (en(a), en (b)) = (3,4 × t) who wishes to trade in contingent markets. Setup the optimization problem of this consumer and compute the optimal consumption plan as a function of the prices of the contingent contracts. [10 marks] (ii) Consider another consumer k with preferences and endowment • Uk (xk(a), xk (b)) = 3 log x (a) + 2log xk (b), (ek(a), ek(b)) = (2,4 × t) who also wishes to trade in contingent markets. Setup the optimization problem of this consumer and compute the optimal consumption plan as a function of the prices of contingent contracts. [10 marks] (iii) Consider another consumer m with preferences and endowment • Um (xm(a), xm (b)) = xm(a) + log xm(b), (em(a), em(b)) = (0,2 × t) who also wishes to trade in contingent markets. Setup the optimization problem of this consumer and compute the optimal consumption plan as a function of the prices of the contingent contracts. [10 marks] (iv) Consider now an economy consisting of (in millions): 3 individuals of type h, 9 individuals of type k and 5 individuals of type m. Compute the equilibrium prices and allocation of contingent commodities of this economy. [15 marks] (v) Comment on the equilibrium risk allocation for type m individuals. Comment on the Pareto optimality of the equilibrium. [5 marks]