Consider two firms, Goodyear and Pirelli, which supply the market for automobile tires. The tires provided...

 

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Consider two firms, Goodyear and Pirelli, which supply the market for automobile tires. The tires provided by each company are perfect substitutes. Let's assume that these companies must make simultaneous decisions about production levels. The industry (inverse) demand curve is given by: P = 700 - 3Q where Q = q1+q2 is in thousands of tires. To simplify notation, let's denote Goodyear as firm 1 and Pirelli as firm 2. In addition to producing identical products, both firms have a constant marginal cost: MC₁=MC₂=100. a. Solve for each firm's (inverse) demand curve, taking the other firm's output as given. [Hint: If they are the same equation, how does the interpretation of the variables differ?] (4 points) b. Solve for each firm's total revenue and marginal revenue as a function of their own production level, given some production level of the other firm. (4 points) c. Solve for each firm's reaction curve (also called "best response function"). From the reaction curves, what do we know about how the firms respond to each other, i.e., if one firm were to choose a higher level of production, how would the other firm optimally adjust its production decision? [Hint: For a firm to be optimally responding, i.e., maximizing profits, marginal revenue must equal marginal cost.] (8 points) Consider two firms, Goodyear and Pirelli, which supply the market for automobile tires. The tires provided by each company are perfect substitutes. Let's assume that these companies must make simultaneous decisions about production levels. The industry (inverse) demand curve is given by: P = 700 - 3Q where Q = q1+q2 is in thousands of tires. To simplify notation, let's denote Goodyear as firm 1 and Pirelli as firm 2. In addition to producing identical products, both firms have a constant marginal cost: MC₁=MC₂=100. a. Solve for each firm's (inverse) demand curve, taking the other firm's output as given. [Hint: If they are the same equation, how does the interpretation of the variables differ?] (4 points) b. Solve for each firm's total revenue and marginal revenue as a function of their own production level, given some production level of the other firm. (4 points) c. Solve for each firm's reaction curve (also called "best response function"). From the reaction curves, what do we know about how the firms respond to each other, i.e., if one firm were to choose a higher level of production, how would the other firm optimally adjust its production decision? [Hint: For a firm to be optimally responding, i.e., maximizing profits, marginal revenue must equal marginal cost.] (8 points)

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Solving for Perfect Substitute Tire Firms Goodyear and Pirelli a Individual Demand Curves Given the ... View the full answer