Question

The marginal and average cost curves of taxis in the town of Pleasantville are constant at $.25/mile. The demand curve for taxi trips in Pleasantville is given by p = 1 – 0.0000075q, where p is the fare, in dollars per mile, and q is measured in miles per year. If the industry is perfectly competitive and each cab can provide exactly 12,500 miles per year of service, how many cabs will there be in equilibrium and what will be the equilibrium fare?

Answer 1

Answer : Given, Marginal Cost (MC) = 0.25/mile and demand : P = 1 - 0.0000075q

At equilibrium in perfect competition , P = MC

=> 1 - 0.0000075q = 0.25

=> 1 - 0.25 = 0.0000075q

=> 0.75 / 0.0000075 = q

=> q = 100000

Form demand function, we have,

P = 1 - 0.0000075×100000

=> P = 1 - 0.75 = 0.25

As total capacity of each cab is 12500 miles ,

the number of cabs at equilibrium is ( 100000/12500 ) = 8 cabs and the equilibrium fare is $0.25 per mile.