Question

You are the manager of a firm that manufactures front and rear windshields for the automobile industry. Due to economies of scale in the industry, entry by new firms is not profitable. Toyota has asked your company and your only rival to simultaneously submit a price quote for supplying 100,000 front and rear windshields for its newest version of the Highlander. If both you and your rival submit a low price, each firm supplies 50,000 front and rear windshields and earns a zero profit. If one firm quotes a low price and the other a high price, the low-price firm supplies 100,000 front and rear windshields and earns a profit of $11 million and the high-price firm supplies no windshields and loses $2 million. If both firms quote a high price, each firm supplies 50,000 front and rear windshields and earns a $6 million profit. Determine your optimal pricing strategy if you and your rival believe that the new Highlander is a "special edition" that will be sold only for one year. Would your answer differ if you and your rival were required to resubmit price quotes year after year and if, in any given year, there was a 60 percent chance that Toyota would discontinue the Highlander? Explain.

Answer 1

Answer:

a. The optimal pricing strategy will be one-shot Nash equilibrium in which “You” charge low price, “Your Rival” charge low price and then the payoff is ($0, $0)

b. Yes, the anwer will differ becuase it is not possible to sustain the collusive outcome as a Nash equilibrium because $\pi ^{Cheat}$ > $\pi ^{Cooperate}$.

Explanation:

a. Determine your optimal pricing strategy if you and your rival believe that the new Highlander is a "special edition" that will be sold only for one year.

Note: See the attached excel file for the Representation of one shot normal for of the game played between "You" and "Your Rival" together with the payoffs.

From the attached excel file, the dominant strategy is for “You” and “Your Rival” to charge “Low Price” each. If the dominant strategy is played by “You” and “Your Rival”, the optimal pricing strategy will be one-shot Nash equilibrium in which “You” charge low price, “Your Rival” charge low price and then the payoff is ($0, $0).

b. Would your answer differ if you and your rival were required to resubmit price quotes year after year and if, in any given year, there was a 60 percent chance that Toyota would discontinue the Highlander? Explain.

When we have a year-after-year competition between “You” and “Your Rival” but with a 60 percent chance that Toyota would discontinue the Highlander, the payoffs of the firm that continue to comply with the collusive strategy of charging “High Price” by each firm under the normal trigger strategy whereby “You” and “Your Rival” agree to charge high price as long as there is no past deviation by any of the firm, otherwise charge a low price is as follows:

$\pi ^{Cooperate}$ = $6 + $6(100% - 60%) + $6(100% - 60%)^2 + 6(100% - 60%)^2 …….

$\pi ^{Cooperate}$ = $6 / 6% = $10

Therefore, what the firm that cheats earn today is $11 million and it earns $0 forever. The implication of this is that $\pi ^{Cheat}$ = $11

Therefore, the anwer will differ becuase it is not possible to sustain the collusive outcome as a Nash equilibrium because $\pi ^{Cheat}$ > $\pi ^{Cooperate}$.

Download xlsx