10. Consider a market with two firms, one incumbent and one potential entrant. They each produce an identical good. The entrant has a marginal cost of $5 per unit, while the incumbent has a marginal cost of $2. The demand curve for the market is given by

P= Q - 100

In order to enter the market, the potential entrant must build a factory at a cost of $F.

a) If the market is based on a Cournot equilibrium, for what values of F (if any) will the new firm enter the market?

b) If the market is based on a Bertrand equilibrium, for what values of F (if any) will the new firm enter the market?

c) How would your answers change if the incumbent had a marginal cost of $1 per unit?

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Question

Consider a market with 100 consumers. Each consumer would like to buy at most one unit and is willing to pay up to 10$. There is an incumbent firm that already operates in the market and a potential entrant firm that considers the possibility of entering the market. Both firms do not have any production costs but the entrant has a fixed entry costs of F = 280, that the entrant pays only if he enters the market. Out of the 100 consumers, 60 consumers are loyal to the incumbent and will not buy from any other firm. The remaining 40 consumers are non-loyal and will buy from the firm that charges the lowest price. At equal prices, non-loyal consumers will buy from the entrant. The timing is the following. In the first stage, the incumbent chooses a price, pI. In the second stage, the entrant observes pI and chooses whether to enter the market. If the entrant enters, the entrant pays F = 280 and then chooses a price, pE. If the entrant stays out, the entrant earns 0. Prices are continuous numbers. In the third stage, consumers decide from which firm to buy.

(a) What is the market outcome (entrantâs entry decision, prices and profits of the two firms)?

(b) Solve (a) for the case where F = 200 (instead of F = 280). Explain in words the differences between the two sections.

(c) Suppose again that F = 280. Suppose that the in first stage, the incumbent chooses a price, pI, and cannot change it later on. In the second stage, the entrant chooses whether to enter or not, and if the entrant enters, the entrant chooses a price, pE. However, the entrant cannot observe pI. The entrant knows that the incumbent charged a certain pI in the first stage and cannot change it, but the entrant cannot observe this pI. What are the prices and profits of the incumbent and the entrant? Explain your answer.

(d) Suppose now that there are two markets, A and B. Each market has 100 consumers, out of which 60 consumers are loyal. Consumers in market A are willing to pay up to 10$, while consumers in market B are willing to pay up to 15$. In each market there is an incumbent: incumbent A in market A and incumbent B in market B. There is one entrant that contemplates whether to enter into market A, market B, or non. The entrant does not have any entry costs (F = 0) and can enter only one of the markets. In the first stage, incumbent A chooses a price, pA. In the second stage, incumbent B observes the price of incumbent A and then chooses a price, pB. In the third stage, the entrant observes the two prices and chooses whether to enter one of the markets and if so, the entrant chooses a price. What is the market outcome (entrantâs entry decision, prices and profits of the three firms)?

Market Demand is p = 25 - 0.002Q. Firms have a constant marginal cost of c = 5 per unit produced with no fixed costs.

a. Suppose the government pays F to have a second firm enter the market to compete with the incumbent firm under Cournot competition.

i. what price will be charged? how much profit will each firm receive?

ii. how much surplus will consumers receive?

b. Ignore part a, suppose the government pays F to have second firm enter the market to compete with the incumbent firm under Bertrand competition

i. what price will be charged? how much profit will each firm receive?

ii. how much surplus will consumers receive?

R&D and entry. Consider a two-period model of a market with demand function Q=12-P. In period 1, an incumbent monopolist and a potential entrant compete to get the license of a new invention. Each can offer the R&D lab (which can't compete by itself) a sum of money for the invention. The lab sells the invention to the firm who gives the most (in case of a tie, assume that the lab sells the invention to the monopolist). Before buying the invention the monopolist has MC=4 and the potential entrant has MC=12. Whoever buys the invention will have MC=2. In case entry occurs, the two firms compete in quantity (Cournot). How many firms will exist next period and which firm will buy the invention and for how much?