Oligopoly Answer quide

a. set P = 90 - 0.25 Q = 0 = MC (in this example)

0.25 Q = 90

Q = 360

b. set MR = 90 - 0.5 Q = 0

Q = 180

P = 45

c. draw the diagram

d and e . P = 90 - .25(Q1 + Q2)

R1 = 90 Q1 - 0.25 Q1² - 0.25 Q1Q2

set MR1 = 90 - 0.5 Q1 - 0.25 Q2 = 0 = MC

solve for

Q1 = 180 - 0.5 Q2 likewise Q2 = 180 - 0.5 Q1

Q1 = 180 - 0.5 (180 - 0.5 Q1)

3/4 Q1 = 90

Q1 = Q2 = 120

P = 90 - 0.24(120+120) = 30

f. 90 Q1 - 0.25 Q1² - 0.25 Q1 ( 180 - 0.5 Q1)

90 Q1 - 0.25 Q1² - 45 Q1 + .125 Q1²

45 Q1 - 0.125 Q1²

45 - 0.25 Q1 = 0

Q1 = 180

Q2 = 90

g. just like the bonus problem

h. see part (a)