Essay on Competition and Unit Cost
Week 16: beginning November 14th 2011
Price Competition and Bertrand Model
Discussion Questions
1. Suppose firm 1 and firm 2 each produce the same product and face a market demand curve described by:
Q = 5000  200P Firm 1 has a unit cost of production c1 equal to 6 whereas firm 2 has a higher unit cost of production c2 equal to 10. a. What is the BertrandNash equilibrium outcome? b. What are the profits for each firm? c. Is this outcome efficient?
Answer:
(a) At equilibrium, assuming that if both firms charge the same price, then the firms split the market evenly.
(b) The higher cost firm makes zero profit, whereas the lower cost firm’s profit is
(c) No, this …show more content…
(c) Yes, the outcome will change. The two lower cost firms will charge $10 and share the market equally.
(d) The answer may change depending on how much premium the consumers are willing to pay for the green balls endorsed by Tiger Woods.
3. Assume that 2 firms sell differentiated products, have the same constant unit costs of 2 and face the following demand curves: q1 = 15  p1 + 0.5p2 and q2 = 15  p2 + 0.5p1 a. Derive the reaction function for each firm b. What is the equilibrium set of prices in this market? What profits are earned at those prices?
Answer:
(a)
P1 = 6.5 + 0.25P2
P2 = 6.5 + 0.25P1
(b)
P1 = P2 = 8.67
Q1 = Q2 = 10.66
Profit1 = Profit2 = 71.10
4. Two internet cafes (A and B) face the following demand curves for their services:
QA = 100  2pA + pB and QB = 100  2pB + pA where QA, QB are demands (per period) for A and B; pA, pB are the prices charged (per period) in £s. a. Do these two cafes provide identical services? b. If both cafes face a constant marginal cost of £10 derive the reaction functions if they behave as Bertrand oligopolists.
c. Sketch the functions in (a) and show the path to equilibrium for the case in which the cafes previously colluded over prices and now have a price war. [Do not actually calculate the

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