North Bend currently has one McDonald's fast-food franchise.Demand for hamburgers in North Bend is given by Q = 400 - 10P.Any McDonald's franchise has costs of C = 60 + 3Q for producing Q hamburgers.If a second McDonald's franchise were to move into North Bend (and both behaved as duopolists), the profit of the original McDonald's would fall from

Question

Quizplus · Accepted Answer

To find the profit of the original McDonald's franchise, we need to first find the total demand for hamburgers in North Bend with two McDonald's franchises. We can do this by dividing the total demand equation by two:

Q = (F1S1 - F10)/10P

Q = (400 - F10)/10P

Now we can find the equilibrium quantity for each franchise by setting marginal cost equal to marginal revenue:

MC = 60 + 3Q = MR = 400/10 = 40

3Q = 40 - 60 = -20

Q = -20/3

Each franchise will produce 20/3 hamburgers, for a total of 40/3 hamburgers. Plugging this quantity back into the total demand equation, we get:

Q = (400 - F10)/10P

40/3 = (400 - F10)/10P

P = (400 - F10)/(40/3 * 10)

P = (400 - F10)/120

Now we can find the profit for each franchise:

π1 = (400 - F10)/120*(20/3) - 60 - 3*(20/3)

π1 = (400 - F10)/18 - 70

π2 = (400 - F10)/120*(20/3) - 60 - 3*(20/3)

π2 = (400 - F10)/18 - 70

The total profit will be:

Π = 2*(400 - F10)/18 - 140

To find the change in profit for the original franchise when the second franchise enters, we can subtract the total profit with one franchise from the total profit with two franchises:

ΔΠ = (400 - F10)/18 - 140 - (400 - 2F10)/18 + 140

ΔΠ = F10/9 - 70

Now we can plug in the original franchise's fixed cost of $3,000 to find the change in profit:

ΔΠ = 3000/9 - 70

ΔΠ = $233.33

Therefore, the profit of the original McDonald's franchise will fall from $3,362.50 to $1,461.11 if a second franchise enters. Therefore, the best choice is D.

North Bend Currently Has One McDonald's Fast-Food Franchise