1. Suppose there are only two firms in the market, firm A and firm B. They produ
ID: 1124642 • Letter: 1
Question
1. Suppose there are only two firms in the market, firm A and firm B. They produce identical products. Firm A and firm B have the same constant marginal cost, MCA MCB 10.The market demand function is given by Q600 30P a. If the two firms behave under the Bertrand model, what will be the Nash equilibrium market price and output level? b. Now assume that these two firms behave under the Cournot model. Write the best response functions for firm A and firm B.. What is the Cournot output level for each firm? What is the market output level? What is the market price?. c. d. Calculate the profit for each firm in the Cournot model e. Graph the best response functions for firm A and B, and label the CournotNash f. If the firms behave under the Stackelberg model and firm A moves first, what are g. Calculate the profits for each firm in the Stackelberg model. Explain why firm A has equilibrium in the graph. the output levels for firm A and firm B? a first moveradvantage by comparing your answers for part d and g.Explanation / Answer
a) Products are identical and marginal cost is same for both firms. Hence, Nash equilibrium has P = MC = 10. At this level there is no profit and quantities are 600 - 300 = 300 units for market and 150 units for each firm
b) Cournot firms have BRF when marginal revenue = marginal cost. Demand is P = 20 - (1/30)(q1 + q2)
MR1 = MC and MR2 = MC
20 - (2/30)q1 - (1/30)q2 = 10 and 20 - (2/30)q2 - (1/30)q1 = 10
The BRFs are
q1* = 15 - (1/20)q2 and q2* = 15 - (1/20)q1
c) Solve BRFs to get q1 = q2 = 100 units and market quantity = 200 units. price = 20 - (1/30)*200 = 13.33
d) Profits are (13.33 - 10)*100 = $330
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