a} ponsider a homogeneous goods industry where two rms operate and the linear demand is given by p(y1+ y2 } = a - b(y1 + y; ), where p is the market price, and 5:1 (3(2) is the output produced by rm 1 (2). There are no costs for firm 1 or rm 2. Derive the best responses (reaction curve} for firm 1 and rm 2. Explain the term best response (reaction curve}. Illustrate the best responses in a diagram. b} For the case in (a) determine the Cournot equilibrium (Nash equilibrium in quantities) when rm 1 and firm 2 compete simultaneoust in quantities. How large are firm 1's and rm 2's prots? What is the industry output? 0) Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 2 while firm 2 is the follower with a cost function c2(y2)=y?2. Firm 1 sets its price to maximise its profit. Firm 1 correctly forecasts that the follower takes the price leader's chosen price as given (price taker} and chooses output so as to maximise its own prot. Write down the profit function of the follower. Calculate the profit maximising quantity that the follower selects given the leader's chosen price p (i.e., calculate the follower's supply curve S(p)). Interpret the solution to the prot maximising problem. d} The leader is facing the residual demand curve R(p)=D{p)S{p) with Dfp) and 8(p) as dened in (0} above. Calculate the leader's residual demand curve using the result in (c). Solve for p as a function of the leader's output 31;, Le. the inverse demand function facing the leader. Write down the profit function of the leader and nd the prot-maximising level of output