Question

Consider the market for airline tickets. For the purpose of answering this question, suppose the airlines are perfectly competitive. Demand for airline tickets is given by Qd=3600-1000P and supply is given by Qs=500P Draw a diagram of this market, where the horizontal axis is total miles flown in a year, and the vertical axis is price per mile. Show the effect on this market of providing a subsidy of $1 a mile on the producer. Label the diagram and identify the areas on the diagram that correspond to: total producer surplus before and after the subsidy; consumer surplus before and after the subsidy; cost of the subsidy; total dead weight loss caused by the subsidy.

Answer 1

Before subsidy, equating Qd = Qs,

3600 - 1000P = 500P

1500p = 3600

P = 2.4

Q = 500 x 2.4 = 1200

After subsidy, supply curve shifts rightward by $1. New supply function is

Qs1 = 500 x (P + 1) = 500P + 500

Equating Qd = QS1,

3600 - 1000P = 500P + 500

1500p = 3100

P = 2.07 (Price paid by buyers)

Price received by sellers = 2.07 + 1 = 3.07

Q = 500 x 2.07 + 500 = 1035 + 500 = 1535

In following Graph, D0 and S0 are demand and supply curves intersecting at point E with price P0 (= 2.4) and quantity Q0 (= 1200). Consumer surplus (CS) is area AEP0 and producer surplus (PS) is area BEP0. After subsidy, new equilibrium is point F where new supply curve S1 intersects D0 with price paid by buyers being P2 (= 2.07), price received by sellers being P1 (= 3.07) and higher quantity Q1 (= 1535). New CS is area AFP2, new PS is area BGP1 and cost of subsidy is area P1GFP2. Deadwight loss is area EFG.