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 )= y^22/2 (picture attached). 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 profit. 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 profit maximising problem. 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.
Suppose the inverse
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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