Question

Two firms compete by choosing price. Their demand functions are; Q₁=80−P₁₊P₂ and Q₂=80+P₁₊P_2.

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​ wanted, and earn infinite profits. Marginal costs are zero.

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.)

A) Each firm will charge what price?

B) Each firm will produce how many units?

C) In turn, each firm will earn how much profit?

D) Suppose Firm 1 sets its prices first and then Firm 2 sets it price, what will they charge then?

E) Based off of the information from D, how many units will they sell?

F) How much profit will they earn?

G) Suppose you are one of these firms and there are three options present; both firms could set their prices at the same time, you set the price first, or they set the price first. If you could choose among these options, which would you choose?

a) to set the price second and earn a profit of X

b) to set the price first and earn a profit of X

c) to set the price simultaneously and earn a profit of 1/3X

d) to set the price first and earn a profit of 1/3X

e) to set the price simultaneously and earn a profit of X

Answer 1

then, T = P (80- Pit PBR) = P, (80- Pit 40+05P) TIE Pi ( 120.5 p.) ani/a Piz 120 - 05(2 P.) =0 so 120 = PT P2 = 40+ •5X120 = 100, E then q= 80-120 + 100 = 60, 92 = 80 +120 - 100 = 100 A ni= Pixq = 60X120 7200 Tg = 100X100= 10000 G thus higher profet , when price. Second, to earn 10,000. a.) option