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Consider two types of investors and two possible states at t=1. with a Bernoulli utility function of the form: u(cj0)+[1u(cj1)+2u(cj2)] where 1 is the probability of state 1 and 2=11 is the probability of state 2 , and w0,w1, and w2 denote the aggregate endowments at t=0 and the two states at t=1, respectively. a) With the usual notations introduced in the optional lecture notes on Arrow-Debreu Economy and General Equilibrium, solve for the asset price qi in a competitive equilibrium. b) Now consider a social planner who divides the aggregate endowments up into amounts allocated to each of the two representative investors subject to the resource constraints w0c10+c20;w1c11+c21;w2c12+c22 in order to maximize a weighted sum of their expected utilities. Find expressions that relate marginal rates of substitution between t=0 and t=1 across the two agent types. c) How do your answers in Parts a) and b) say about the relationship between the competitive equilibrium and social planner problem? Briefly explain