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(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 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. 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.
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(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 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. 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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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c and d
Transcribed Image Text: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(2)→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 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.
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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