Two firms compete by choosing price. Their demand functions areQ1= 140-P1+P2 andQ2=140+P1-P2,
where P1 and P2 are the prices charged by each firm respectively and Q1 and Q2 are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they want, and earn infinite profits. Marginal costs are zero.
a. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.). Each firm will charge PRICE $___. Each firm will produce _____ units of output. In turn, each firm will earn profit of $____
b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be? Firm 1 will charge a price of _____. Firm 2 will charge a price of _____. Firm 1 will sell ___units and Firm 2 will _____ units. Firm 1 will earn profit of $_____ and firm 2 will earn profit of ______
c. Suppose you are one of these firms, and there are three ways you could play the game: (i) Both firms set price at the same time. (ii) You set price first. (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why.
You would choose:
a- to set price first to earn profit of $30,625.00.
b- to set price simultaneously with the other firm to earn profit of $30,625.00
c-to set price first to earn profit of $22,050.00
d- to se price to earn profit of $ 30,625.00
e- to set price simultaneously with the other firm to earn profit of $19,600.00