7. (50 points) Suppose the inverse demand for taxi drivers for one day is D(O) m

Question

7. (50 points) Suppose the inverse demand for taxi drivers for one day is D(O) marginal cost for taxi drivers is $100 per driver 500-40, The price and quantity under perfect competition and free entry? What is the equilibrium (5pts) a. Now suppose the government restricts the amount of drivers by law to g b. What are the total profits for the taxi drivers that are allowed to drive as a function of g? That is, what is (092 (10pts) What are the profits per-driver, as a function of Q'? (5pts) c. Now suppose the government sells the right to drive a taxi. That is, the government forces drivers to buy taxi medallions. d. At what O' does the government maximize the revenue it collects from medallions? (10 pts) e. What is the price that the government would charge for medallions? (5pts) f. What is the taxi drivers' total profit when they have to buy medallions at the revenue maximizing price and quantity? (5pts) Finally, assume a technological innovation (Uber/Lyft) shifts the inverse demand curve for regular taxi drivers to D(O) = 250-3 g. h. What is the new revenue for the government from taxi medallions? (5 pts) Explain how the technological innovation can "solve" the transitional gains trap. (5pts)

Explanation / Answer

a)D(Q) = 500-5/2Q = 100

400 = 5/2Q

Q = 400*2/5

Q = 160

P = 100

b) Profit((Q’))) = P*Q’ – 100Q’ = 0

At Q=Q’

P= 500-2.5Q’

Profit = (500-2.5Q’)Q’ – 100Q’

=400Q’ -2.5Q’^2

c) profit per driver = (Q’))/Q’

=(400Q’ -2.5Q’^2)/Q’

= 400-5Q’

d)

One that maximize profit maximize the government revenue:

d((Q’))/dQ’ = 0

=d(400Q’-2.5Q’^2)/dQ’

=400-5Q’ = 0

Q’ = 400/5 = 80

Q’ =80 maximize revenue

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