Question

The Japanese airline company, Kamikadze, which is the only agent that offers flights to the Moon, has to set the price of full fare (demand function: QN = 800 – 2PN) and the price of reduced fare (demand function: QU = 400 – 2PU). The transport costs of one passenger amount to 10.
(a) What is the firm’s maximum profit if there is one price for all the passengers?
(b) What is the change in the profit level of this firm if the company begins price discriminating. What will
be the price of a full fare and the price of a reduced fare?

Answer 1

QN = 800 – 2PN

QU = 400 – 2PU

a)

If the firm charges one price, it will maximize profit subject to the aggregate demand curve.

Adding both the demand curves we get,

Q = 1200 - 4P

P = 300 - 0.25Q

Total Revenue = TR = P*Q = (300 - 0.25Q)Q

Marginal Revenue = dTR/dQ = 300 - 0.5Q

MC = 10

MR = MC

300 - 0.5Q = 10

0.5Q = 290

Q = 580

P = 300 - 0.25Q = 155

b)

When the firm charges different price it equates the marginal revenue of each demand function separately with the marginal cost.

QN = 800 – 2PN

PN = 400 - 0.5QN

Total Revenue = TR = PN*QN = (400 - 0.5QN)QN

Marginal Revenue MR1 = dTR/dQ = 400 - QN

MC = 10

400 - QN = 10

QN = 390

PN = 205

QU = 400 - 2PU

PU = 200 - 0.5QU

Total Revenue = TR = PU*QU = (200 - 0.5QU)QU

Marginal Revenue MR1 = dTR/dQU = 200 - QN

MC = 10

200 - QU = 10

QU = 190

PU = 105