Please include step by step working and derivation of any methods used in the following questions: 1. a) Consider a homogeneous goods industry where two firms operate and the linear demand is given by p(y1 + y2) = a - b(y1 + y2 ), where p is the market price, and y1 (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 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 firm 1 and firm 2 compete simultaneously in quantities. How large are firm 1’s and firm 2’s profits? What is the industry output?
Please include step by step working and derivation of any methods used in the following questions:
1. a) Consider a homogeneous goods industry where two firms operate and the linear
p(y1 + y2) = a - b(y1 + y2 ), where p is the market price, and y1 (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 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
c) 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 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its price to maximise its profit. Firm 1 correctly
d) The leader is facing the residual demand curve R(p)=D(p)-S(p) with D(p) and S(p) as defined in (c) above.Calculate the leader’s residual demand curve using the result in (c). Solve for p as a function of the leader’s output y1, i.e. the inverse demand function facing the leader. Write down the profit function of the leader and find the profit-maximising level of output.
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