Problem 5 (Watson 10.2 a-c). Consider a more general Bertrand model than the one presented in this chapter. Suppose there are n firms that simultaneously and inde- pendently select their prices, P1, P2, ..., Pn in a market. These prices are greater than or equal to zero. The lowest price offered in the market is defined as p = min{P1, P2, ,Pn}. Consumers observe these prices and purchase only from the firm (or firms) charging p, according to the demand curve Q: =a- - p. That is, the firm with lowest price gets all of the sales. If the lowest prices is offered by more than one firm, then these firms equally share the quantity demanded. Assume that firms must supply the quantities demanded of them and that production takes at a cost of c per unit. That is, a firm producing di units pays a cost cqi. Assume a > c> 0. (a) Represent this game in the normal form by describing the strategy spaces and payoff (profit) functions.

Problem 5 (Watson 10.2 a-c). Consider a more general Bertrand model than the one presented in this chapter. Suppose there are n firms that simultaneously and inde- pendently select their prices, P1, P2, ..., Pn in a market. These prices are greater than or equal to zero. The lowest price offered in the market is defined as p = min{P1, P2, ,Pn}. Consumers observe these prices and purchase only from the firm (or firms) charging p, according to the demand curve Q: =a- - p. That is, the firm with lowest price gets all of the sales. If the lowest prices is offered by more than one firm, then these firms equally share the quantity demanded. Assume that firms must supply the quantities demanded of them and that production takes at a cost of c per unit. That is, a firm producing di units pays a cost cqi. Assume a > c> 0. (a) Represent this game in the normal form by describing the strategy spaces and payoff (profit) functions.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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What membership fee would maximize profit for the club? Compared to the profit of a similar but single-price monopoly golf club, how much more profit does Northlands Golf Club make?
Consider a Bertrand (price choice) model where firms have identical costs. The equilibrium price is the same whether there are two or three firms in the market. (a) True. (b) False.
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Suppose Bang Bang is the only local swimming pool. She believes that there are 10 potential customers. Each of them has an identical demand function of QI = 250 – 0.02P, with QI as the unit of services of each customer. She operates with a constant variable cost of $500 per unit of service. In reality, demand from different customers may not be identical. Discuss how this might create problems to Bang Bang in conducting a two-part tariff.
Joe has just moved to a small town with only one golf course, the Northlands Golf Club. His inverse demand function is p=140-2q, where q is the number of rounds of golf that he plays per year. The manager of the Northlands Club negotiates separately with each person who joins the club and can therefore charge individual prices. This manager has a good idea of what Joe's demand curve is and offers Joe a special deal, where Joe pays an annual membership fee and can play as many rounds as he wants at $20, which is the marginal cost his round imposes on the Club. Joe marries Susan, who is also an enthusiastic golfer. Susan wants to join the Northlands Club. The manager believes that Susan's inverse demand curve is p=120-2q. The manager has a policy of offering each member of a married couple the same two-part prices, so he offers them both a new deal. What two-part pricing deal maximizes the club's profit? Will this new pricing have a higher or lower access fee than in Joe's original deal?…