Question

Digicom is a wireless services company with a monthly demand for cell phone minutes for each client that can be expressed as follows:

P = $2 – 0.02Q

Where P is the price paid by the client per minute and Q is the number of minutes bought by the client each month. T

he marginal cost is $0.20 per minute. Assume that Digicom offers a single per minute price, which means that the price per minute is the same for all clients, regardless of the number of minutes they actually use each month.

What is the profit-maximizing quantity and price? (5 points) What is the profit per client? (5 points)

What is the consumer surplus? (5 points)

Assume now that Digicom offers a two-part tariff with a monthly fixed fee and a per minute charge.

What is the optimal two-part tariff? (5 points)

What is the profit per client? (5 points)

How many minutes are used per month for each client? (5 points)

Answer 1

(1) With single pricing, MR = MC.

TR = P x Q = 2Q - 0.02Q²

MR = dTR/dQ = 2 - 0.04Q

2 - 0.04Q = 0.2

0.04Q = 1.8

Q = 45

P = 2 - 0.02 x 45 = 2 - 0.9 = 1.1

(2) Profit = Q x (P - MC) = 45 x (1.1 - 0.2) = 45 x 0.9 = 40.5

(3) When Q = 0, P = 2

Consumer surplus (CS) = area between demand curve and price = (1/2) x (2 - 1.1) x 45 = 22.5 x 0.9 = 20.25

(4) With two part tariff, P = MC and Profit = CS

So, Optimal two part tariff = MC = 0.2

(5) When P = MC = 0.2,

0.2 = 2 - 0.02Q

0.02Q = 1.8

Q = 40

Profit = CS = (1/2) x (2 - 0.2) x 40 = 20 x 1.8 = 36

(6) When P = MC = 0.2, Q = 40