## Question

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

Two firms compete by choosing price. Their demand functions are; Q_{1}=80−P_{1+}P_{2} and Q_{2}=80+P_{1+}P_{2.}

where P_{1} and P_{2} are the prices charged by each firm, respectively, and Q_{1} and Q_{2} 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