3. (Arrow-Debrou Economy) Consider a world in which there are only two and 1. At date 1 there are three possible states of nature: a good weather sta a fair weather state (FW), and a bad weather state (BW). Denote S, as the se states, i.c., s c S, = {GW, FW, BW). The state at date zero is known: Denote probability of the three states as a (.), * ($1) = (0.4, 0.3, 0.3). There is one non-storable consumption good - say apples. There are two c in this cconomy. Their preferences over apples are exactly the same and are giv following expected utility function " (so) + B ) * ($1) " (c ($1)) , where subscript i = 1, 2 denotes consumers. In period 0, both agents have utility while in period 1, the two consumers have the same CRRA instantanco function: u(c) = {, where the coefficient of RRA is y = 0.2. The consum discount factor, 8, is 0.98. The consumers differ in their endowments which are given in the table belo Consumers Endowments 1=0 1 =1 GW FW BW Consumer 1 0.4 3.2 1.8 0.9 Consumer 2 1.2 1.6 1.2 0.4 Consumer 3 2.0 1.2 0.6 0.2 i) Write down the consumers' budget constraints for all times and states. ii) Define a Sequential Market Equilibrium in this coonomy. Is there any trade Debreu securities possible in this coonomy? iii) Write down the Lagrangian for the consumers' optimisation problem and first order necessary conditions. iv) Characterise the equilibrium (i.c., find the allocations and prices defined in librium)