# PS_CH12 - ECON2296- 1 A monopolistically competitive firm...

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ECON 2296  -  Practice Questions Chapter 12 1. A monopolistically competitive firm is in long run equilibrium. Its long run total costs are given by: TC = Q 3 /2 - 10Q 2 + 100Q and the demand for its product is given by: Q = 17.5 - P/5. a) What is this firm's output and price in long run equilibrium? b) Show that the firm is operating with excess capacity in long run equilibrium 2. Two output setting firms that produce identical products are Cournot competitors. The total market demand for the products is Q T = 20 - P/5. The total cost of each firm is TC i = 10Q i . Note: Q T = Q 1 + Q 2 . a) What is firm 1's profit function? Hint: it is a function of Q 1 and Q 2 . b) What is firm 2's profit function? c) What is each firm's reaction function? d) According to each firm's reaction function, if one firm increased its output, what would the other firm do? Explain. e) How much output would each firm produce at the Cournot equilibrium? f) What is the market price at the Cournot equilibrium? g) What is each firm's profit at the Cournot equilibrium? 3. Suppose the two firms in Question 2. act as perfectly competitive firms. a) How much output would each firm produce? b) How does the industry output compare with that in the Cournot equilibrium? c) What is the market price? d) How does the market price compare with that in the Cournot equilibrium? e) What is each firm's profit? f) How does the joint profit of the two firms compare with that in the Cournot equilibrium? 4. Suppose the two firms in Question 2. formed a cartel and shared the cartel's profit equally. a) What is the joint profit function of the two firms? b) How much output would the cartel produce? c) How does the industry output compare with that in the Cournot equilibrium? d) What is the market price? e) How does the market price compare with that in the Cournot equilibrium? f) What is the cartel's profit? g) How does the cartel's profit compare with the joint profit of the two firms in the Cournot equilibrium? 5. Assume the two firms in Question 2. and firm 1 is a Stackelberg leader. a) What is firm 2's reaction function? b) What is firm 1's profit function? Hint: it is a function of only Q 1 . c) How much output would firm 1 produce at the Stackelberg equilibrium? Hint: optimize firm 1's profit function. d) How does firm 1's output compare with that in the Cournot equilibrium?

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e) How much output would firm 2 produce at the Stackelberg equilibrium? f) How does firm 2's output compare with that in the Cournot equilibrium?
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