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 e₁,a = 0 of good a and e1,6 = 10 of good b, while Consumer 2 is initially endowed with e2,a = 10 of good a and e2,6 = 0 of good b. The utility of Consumer 1 from consuming 1,a ER+ of good a and x1,6 € R is u1(x1,a,1,b) = √1,a+1,b, while the utility of Consumer 2 from consuming 2,a ER+ of good a and x2,b ER is u2(x2,a, x2,b) = √x2,a + x2,b. (a) Consider general equilibrium in the context of this environment in which the price of good b is normalized to 1. Compute the equilibrium price pt of good a and find the corresponding equilibrium quantities consumed by the various consumers. = (b) 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 D₁ in which D1(pa) dpa is the amount of good a being demanded at price pa 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 S2 in which S2(Pa) =-s+pa is the amount of good a being supplied at price pa of good a. If Consumer 1 chooses a strategy d and Consumer 2 chooses a strategy s such that ds, then no trade occurs and each consumer consumes their initial endowments. If Consumer 1 chooses strategy d and Consumer 2 chooses a strategy s such that d>s, then trade occurs, the market mediator chooses the price po at which D₁(p+) = d − p t = −s+p+ = S2 (pt), Consumer 1 consumes D₁(p) of good a and 10 – på D₁(p) of good b, and Consumer 2 consumes 10 - S₂(pt) of good a and på S2 (pa) of good b. Find a pure-strategy Nash equilibrium of this game in which trade occurs, and give the resulting equilibrium price på of good a as well as the corresponding quantities of the goods consumed by the consumers.