Question

Suppose the demand functions facing wireless telephone monopolists are:

Q£ =40-100F for each low-demand consumer and QÅ=140-100F for each high-demand consumer, where P is the per-minute price in dollars. The marginal cost is $0.20 per minute. Suppose the monopolist offers only a single two-part tariff. Instructions: Round your answers to 2 decimal places as needed. a. What will be the monopolist's profit from each type of consumer if it charges a per-minute price of $0.20 and a fixed fee that causes both types of consumers to make a purchase? Profitjow = $ Profithigh = $ b. What if it charges a per-minute price of $0.30? Profitlow = $ Proflthigh = $ c. If there are 100 high-demand consumers, how many low-demand consumers can there be for the monopolist to find the $0.30 price more attractive than the $0.20 price? low-demand consumers.

Here is the equation again in case it is hard to read:

Q Low = 400 - 100 P

Q High = 140 - 100 P

Answer 1

Monopolist maximises profit at the point where MR = MC

MR = dTR/dQ and TR = PxQ

TR for low demand

Q = 40 - 100P and P = 0.40 - 0.01Q

TR = 0.40Q - 0.01Q²

MR = 0.40 - 0.02Q?

At equilibrium, 0.40 - 0.02Q? = 0.20

Q = 10

TR = 0.20 x 10 = 2

TC = MC x Q = 0.20 x 10 = 2

Profit = TR - TC = 2-2 = 0

For high demand, Q = 140 - 100 P

P = 1.40 - 0.01Q

TR =  1.40 Q - 0.01Q²

MR =  1.40 - 0.02Q

At equilibrium, 1.40 - 0.02Q = 0.20

Q = 60

TR = 60 x 0.20 = 12

TC = 60 x 0.20 = 12

Profit = 12 - 12 = 0

TR for low demand

Q = 40 - 100P and P = 0.40 - 0.01Q

TR = 0.40Q - 0.01Q²

MR = 0.40 - 0.02Q?

At equilibrium, 0.40 - 0.02Q? = 0.20

Q = 10

TR = 0.30 x 10 = 3

TC = MC x Q = 0.20 x 10 = 2

Profit = TR - TC = 3-2 = 1

For high demand, Q = 140 - 100 P

P = 1.40 - 0.01Q

TR =  1.40 Q - 0.01Q²

MR =  1.40 - 0.02Q

At equilibrium, 1.40 - 0.02Q = 0.20

Q = 60

TR = 60 x 0.30 = 18

TC = 60 x 0.20 = 12

Profit = 18 - 12 = 6