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(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?

(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?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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(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?
Transcribed Image Text:(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?
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Please answer part C and D -  As answered earlier the first two parts with ery clear solutions with clear steps and explainantion. Please do not answer if you are not confident.

(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 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? 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(y₁1)=cy₁ while firm 2 is the follower with a cost function c₂(y2 )=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.
Transcribed Image Text:(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 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? 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(y₁1)=cy₁ while firm 2 is the follower with a cost function c₂(y2 )=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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