Answer in Microeconomics for Adekunle #109774
April 21st, 2023
If the marginal cost of the follower, firm F, is equal to 3 with probability 0.25, and to 7 with probability 0.75, then the expected marginal cost is “MC = 3*0.25 + 7*0.75 = 6,” so the total cost TCF = 6yF.
First, we should find the follower’s reaction function.
The total profit equation of the follower is:
“TPF = TRF – TCF = (100 – 2yL – 2yF)*yF – 6yF = 94yF – 2yL*yF – 2yF^2,”
“TPF'(yF) = 0, so:”
“(94yF – 2yL*yF – 2yF^2)’ = 0,”
“94 – 2yL – 4yF = 0,”
“yF = 23.5 – 0.5yL.”
The total profit equation of the leader is:
“TPF = TRF – TCF = (100 – 2yL – 2yF)*yL – 0 = 100yL – 2yL^2 – 2yL*(23.5 – 0.5yL) = 53yL – yL^2,”
“TPF'(yL) = 0, so:”
“53 – 2yL = 0,”
“yL = 26.5” units,
“yF = 23.5 – 0.5*26.5 = 10.25” units.
“p = 100 – 2*26.5 – 2*10.25 = 26.5.”
