3. Consider a duopoly with a demand curve given by P = a-bQ, where a and b are positive constants and Q is the total production by the two firms. Firms sell identical goods and have an identical constant marginal cost of production c. Fixed costs are equal to zero. We assume firms choose quantities simultaneously (Cournot competition). a. Obtain the first order condition of profit maximization for each firm. Use graphical analysis and economic intuition to explain what they represent. b. Obtain the profit maximizing quantity for each firm. Explain what they represent using game theory concepts c. Demonstrate using relevant graphical analysis and economic intuition that the results obtained in b are not a Pareto Optimum for the firms involved. d. How would the graphical analysis in part a change if Firm A had a fixed cost of production

3. Consider a duopoly with a demand curve given by P = a-bQ, where a and b are positive constants and Q is the total production by the two firms. Firms sell identical goods and have an identical constant marginal cost of production c. Fixed costs are equal to zero. We assume firms choose quantities simultaneously (Cournot competition). a. Obtain the first order condition of profit maximization for each firm. Use graphical analysis and economic intuition to explain what they represent. b. Obtain the profit maximizing quantity for each firm. Explain what they represent using game theory concepts c. Demonstrate using relevant graphical analysis and economic intuition that the results obtained in b are not a Pareto Optimum for the firms involved. d. How would the graphical analysis in part a change if Firm A had a fixed cost of production

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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12. Consider a duopoly market. Two firms are selling identical products and all costs are assumed to be zero for simplicity. Market demand schedule is given in the following table. Note that firms always choose an integer value for the quantity of production. Quantity Price Total Profit 3 $12 4 11 5 8 6 6. 7 4 8 2 1 10 a. Fill in the column of total profit.
17) Suppose the demand for Pepsi-Cola is qp = 50 - 2pp + 1pc. The firm faces a constant marginal cost of m, and pc denotes the price of Coca-Cola. Assuming Bertrand behavior, derive Pepsi-Cola's best-response function and explain how the firm changes price in response to changes in its own marginal cost and changes in Coca-Cola's price. 18) In a Bertrand duopoly with product differentiation, explain how a change in one firm's marginal cost can have an effect on the price charged by the other firm.
5. Suppose there are two firms in a Cournot type setting (choosing quantity simultaneously). How would an increase in the marginal cost of firm 1 change the equilibrium output of firm 1 and firm 2? Depict your answer graphically.
Explain in few lines Three firms are competing through prices (Bertrand competition). They are all selling the same products. The only difference is that the first two firms have a constant marginal cost equal to 2 while the third firm has a constant marginal cost equal to 5. In equilibrium the two firms with lower marginal cost will set their price just slightly below 5
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1. Suppose we live in a world where the widgets market is a monopolistically competitive market with homogenous firms (i.e. no productivity differences among firms). There are two countries: A and B. In each country, consumer demand for widgets can be written as Q = S x- x (P – P), 30 where n is the number of widget firms, P the price of widget charged by the firm, and P the average price of widget by other firms in the market. Moreover, widget firms in both countries have the same total cost function, which is C = 750 + (5 × Q). It is also given that marginal revenue of each 30Q firm can be written as MR = P – Total demand for widget in country A is SA = 900 and Sg = 1600 in country В. a) Derive the average cost function from the total cost function. What is the marginal cost? b) Calculate the number of firms and the prices of widget in each country when trade is not allowed (that is, calculate na, ng, Pa, PBÌ- c) Calculate the number of firms and the price of widget in the unified…
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