Consider the following 2 person, 1 good economy with two possible states of nature. There are two states of nature j E {1,2} and two individuals, i E {A, B}. In state- of-nature j = 1 the individual 1' receives income y\" whereas in atate-ofnature j = 2, individual 1' receives income pig. Let Cid denote the amount of the consumption good enjoyed by individual i if the stateonature is j. Stateofnnaturej occurs with probability 11']: and I1 4- {IT-2 = 1. Prior to learning the stateofnature, individuals have the alzailityr to purchase {or sell) contracts that specify delivery of the consumption good in each state-of-nature Let om- denote the number of consumption goods that individual i contracts to deliver in the eth that state-ofnature j is realised. The relative price of contracts that specify deli-Fer],r of goods in state-ofnature 2 is denoted by 1:. Individuals cannot create wealth by making promises to deliver goods in the future so the total net expenditure on purchasing contracts must equal zero, that is, om + pail; = II}. The individual's problem is stiing \"mic\" + \"*"(Ci'in subject to the budget constraints Gin = yin + an ct: = yes + {lie and aid + Page = U- Let the utility function u(c) = ln(c) so that u'(c) = %. Solve for the equilibrium price and allocations