Question

A microeconomics question with policy application. Thank you!

The daily supply of taxi rides in Podunk is given by Q = 18 + 2P, and the demand for taxi rides (daily) is given by P = 60 – .25Q. The usual competitive equilibrium is established, and all is well in Podunk. Then the city council, coming under some surreptitious “lobbying” from the taxi industry, elects to limit the number of daily taxi rides allowed in Podunk to 60. This quota is perfectly enforced. Daily, what is the most that the taxi industry was willing to spend to have this quota introduced and wow much would consumers be willing to pay (daily) to have the quota lifted? What is the (daily) deadweight loss of the quota program? Best if you are able to provide a graph, indicating the pre- and post-quota situations, along with the deadweight loss arising from the quota. Thank you!

Answer 1

Demand: P = 60 - 0.25Q

Supply: Q = 18 + 2P, or P = (Q - 18) / 2 = 0.5Q - 9

From demand function, when Q = 0, P = $60 (Vertical intercept of demand curve)

From supply function, when P = 0, Q = 18 (Horizontal intercept of supply curve)

In equilibrium, quantity demanded equals quantity supplied.

60 - 0.25Q = 0.5Q - 9

0.75Q = 69

Q = 92

P = (0.5 x 92) - 9 = 46 - 9 = $37

When a quota is imposed at Q = 60,

Demand price (From demand function) = 60 - (0.25 x 60) = 60 - 15 = $45

This is the price consumers will be willing to pay.

Supply price (From supply function) = (0.5 x 60) - 9 = 30 - 9 = $21

This is the price taxi industry will be willing to spend (per ride).

Deadweight loss = (1/2) x $(45 - 21) x (92 - 60) = (1/2) x $24 x 32 = $384

In following graph, AB & CD are demand & supply curves with intercepts derived above, intersecting at point E with equilibrium price P0 (= $37) and quantity Q0 (= 92). When a quota is imposed at Q1 (= 60), Demand price is P1 (= $45) and supply price is P2 (= $21) and deadweight loss is area EFG.