Location-then-Price Hotelling duopoly model

Consider the Location-then-Price Hotelling duopoly model studied in lectures with transportation cost incurred by the consumers represented by t = 4. Suppose the locations of the firms are initially fixed at x1 = x2 = 1, so that their profits in the second-stage Nash Equilibrium in prices are equal to _____________ . However, Firm One has the option to re-locate its store (so that x1 = 0), before the two firms simultaneously name prices. If it chooses to do so, the resulting Nash Equilibrium profit of Firm One will equal ______________ . But what if Firm Two unexpectedly fails to notice (or simply ignores) the fact that Firm One has changed location? That is to say, although Firm One will set the Nash Equilibrium price associated with x1 = 0 and x2 = 1, Firm Two sets its price as if x1 = x2 = 1 still. The profit of Firm One would then be equal to________________ , while that of Firm Two would equal ___________ . Finally, suppose the firms deliver the goods to the consumers, charging different prices depending on consumer location. Following the decision of Firm One to change location to x1 = 0, the second-stage equilibrium profits of Firm One would then equal _______________ Question 2 In the Vertical Product Differentiation model studied in lectures, suppose the quality of the product of Firm A is qA = 18, while that of Firm B has a quality qB = 0. If the usual price competition ensues, the profit of Firm A in the resulting Nash Equilibrium is ____________. However, suppose Firm A uni-laterally deviates from its equilibrium price, setting a price equal to the Nash Equilibrium price of Firm B plus 12. Assuming Firm B does not deviate from its equilibrium price, the profit of Firm A is then _____________ . Suppose now that, before competing in prices, the two firms take part in an auction to obtain exclusive patent right for a new production technology that would increase the quality of the winning firm to 27 without affecting the marginal production cost. Hence, if Firm A wins the auction, we have qA = 27 and qB = 0, so that the profit of Firm A in the ensuing Nash Equilibrium in prices equals _______________ minus whatever Firm A has paid for the patent right. In contrast, if Firm B wins, we have qA = 18 and qB = 27, so that the profit of Firm A in the ensuing Nash Equilibrium in prices equals ________________ . Consequently, the most that Firm A would be prepared to pay for the patent is ______________ , while, by an analogous argument, the most that Firm B would be prepared to pay is ____________ Question 3 A small number of companies operate bus services along A Road / B Road in X city. Most of their customers are students or other people with no access to alternative means of transport. In addition, a large proportion of commuters do not simply board the first bus that arrives. Instead, they wait for one operated by the company they prefer to use, e.g. because they bought a day, weekly or season pass from that company. They will readily switch companies if they find the one they presently use being more expensive or otherwise worse than its competitors. However, assume that, for the moment, consumers generally agree that there is little or no difference between the products offered by the competing firms. Taking this into account, consider the effect of the following three alternative actions by one of the competing bus companies:    

Sample Solution