Consider a quantity-setting oligopoly (Cournot model) where demand is linear and each firm's marginal cost is a constant ; for each firm i. The demand function is P = a b(g; + g;), where the subindex i denotes firm 's own production while subindex denotes the combined production of all other firms in the market. In the simple case of a duopoly we have only ; and gs. (a) Suppose we're in a duopoly market. On a graph with g; on the x-axis and , on the y-axis, draw each firm's best-response function. Label the Nash equilibrium of the game played by the firms. Note: Remember that best response in a Cournot game specifies the production of the firm given the production of all other firms in the market in a duopoly, this would be a function of firm 1's production given how much firm 2 produces: ;(g2). Explain your answer by arguing what happens with this function. (b) Show on the graph how the equilibrium changes as Firm 2's marginal cost decreases. How are the equilibrium quantities for each firm affected? (c) Suppose two firms are Cournot competitors with T'C'(;) = 1000+ 320g; (where g; is a given firm's output) and demand curve p = 800 2Q), where Q = ; + is total industry output (summing all firm's quantities, as usual). i. Compute the Cournot equilibrium price, profits for each firm, and the overall consumer sur- plus. ii. Suppose a third firm enters (with the same cost function). Recalculate the equilibrium. Are total industry profits (summing across all firms) higher in (a) or (b)? What about consumer surplus in (a) vs. (b)