3. Consider an exchange environment with two consumers, Consumer 1 and Consumer 2, and two goods, a and b. Consumer 1 is initially endowed with e;, = 0 of good a and e;, = 10 of good b, while Consumer 2 is initially endowed with ez, = 10 of good a and ez = 0 of good b. The utility of Consumer 1 from consuming z1, R4 of good a and 1, R is U1 (21,4, 21) = VZT1,a T Z1b; while the utility of Consumer 2 from consuming z2 , R4 of good a and z2 R is (a) (b) U (22,0, T2p) = +/T2,q + Top- Consider general equilibrium in the context of this environment in which the price of good b is normalized to 1. Compute the equilibrium price p of good a and find the corresponding equilibrium quantities consumed by the various consumers. Consider the game in which, simultaneously, Consumer 1 submits a \"demand curve\" and Consumer 2 submits a \"supply curve\" to a market mediator. In particular, the strategy space of Consumer 1 is [0,10], and the strategy d of Consumer 1 corresponds to the demand curve D; in which D1 (pa) = d pq is the amount of good a being demanded at price p, of good a. Similarly, the strategy space of Consumer 2 is [0,10]], and the strategy s of Consumer 2 corresponds to the supply curve S5 in which S3(p,) = s + p, is the amount of good a being supplied at price p, of good a. If Consumer 1 chooses a strategy d and Consumer 2 chooses a strategy s such that d s, then trade occurs, the market mediator chooses the price p* at which Dy (p) = d p% = s+ p = S2(p%), Consumer 1 consumes D1 (p}) of good a and 10 p; D1 (p};) of good b, and Consumer 2 consumes 10 Sa2(p;) of good a and p;S2(p;) of good b. Find a pure-strategy Nash equilibrium of this game in which trade occurs, and give the resulting equilibrium price p} of good a as well as the corresponding quantities of the goods consumed by the consumers