Question

Question 9

firms:

Q1=75-P1+.5P2

P1=75+.5P2-Q1

75+.5P2-2Q1=30

Q2=75-P2+.5P1

AC=MC=30

a) Confirm firm 1's optimal price depends on P2 according to P1=52.5+.25P2 (Set up profit expression of profit firm 1=(p1-30)Q1 =(P1-30)(75-P1+.5P2) and set marginal profit = 0 to solve for P1 in terms of P2. Alternatively, set MR1=MC and solve for Q1 and then P1 in terms of P2.

Question 10

Instead, the firms compete by setting quantities rather than prices. Rewriting the demand equationsP1=[150-(2/3)Q2]-(4/3)Q1
and P2=[150-(2/3)Q1]-(4/3)Q2. Increases in the competitor's output lowers the intercept of the firm's demand curve

a) MR1=MC to confirm that firm 1's optimal quantity depends on Q2, according to Q1=45-.25Q2

b) Equilibrium Q1=Q2