1. Two 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
2. Instead, the firms compete by setting quantities rather than prices. Rewriting the demand equations P1=[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