Question

Light as Air is an airline flying a particular route that has seasonal demand. The firm’s total demand is given by: Q = 600 – 4P Where Q is the number of passengers per year, in thousands, and P is the fare (in $). In the peak (High) season the demand is given by: Q_H = 320 – 1.5P_H And in the off-season (Low) the demand is given by: Q_L = 280 – 2.5P_L Assume that fixed costs are $6 million per year and that marginal costs are constant at $60 per passenger. Thus the cost function is given by: C = 6000 + 60Q Where C is total costs (in $’000) a. Calculate the profit-maximizing price and output without price discrimination, and the size of the profit. b. Calculate the profit-maximizing price and output with price discrimination, and the size of the profit. c. Calculate the demand elasticities of the two segments at their profit-maximizing prices.

Answer 1

a) If the airline charges the same price in each market, then we get the profit maximization price and output by setting marginal revenue equal to marginal cost.
The inverse demand function for the market is P = (600-Q)/4
Total Revenue is = PQ = (600Q - Q2)/4. Therefore, MR = (600-2Q)/4

Total Cost is = 6000+60Q. Therefore, MC = 60.

Now, from MR = MC. => (600-2Q)/4 = 60 => Q* = 180 and P* = 105
Size of profit = (P-MC)*Q = (105 - 60)*180 = 8,100.

b)The inverse demand function for the towo markets is PH = (320 - QH)/1.5
and PL = (280 - QL)/2.5

MRH = (320 - 2QH)/1.5 = MC = 60 => QH* = 115 and PH* = 136.67

And, MRL = (280 - 2QL)/2.5 = 60 => QL* = 65 and PL* = 86

The size of the profit is = (PH - MC) * QH + (PL - MC) * QL
= (136.67 - 60)*115 + (86-60)*65 = 10,507.05

c) Demand elasticity for peak season:-

QH = 320-1.5PH Eu= Pad Q. 136.67 (-1.5) "CH d p - 15 l TENE - 1.78

Demand elasticity for off-season

Q = 280-2.5PL E = Pudde - 86 (-2.5) E = -3.311 di d PL 65 l