Question

Two people in the world. First person (Person A) has a demand curve of streetlights Qa= 200 – 2 P. For person B, the demand curve for street light is Qb= 200 – P. Streetlights is a public good (everyone can use it and its non excludable)...

What is the efficient level of this activity if it could be produced at a constant marginal cost of $75 per unit?

What is the consumer surplus from the efficient level of street lights (Assume consumers pay for the efficient level themselves.)

My Answers:

I got 400-3Q as the equation people are willing to pay and the efficent level to be 108.3333333333333 (but it seems to be very high and my numbers could be wrong)

I also got Consumer surplus to be 9, 375 for QA and Consumer Surplus 7,812 for Qb...However, my numbers seem to be very high

Answer 1

Find market demand function as sum of inverse demand functions

Pa = 200/2 - Qa/2 or Pa = 100 - 0.5Qa

Pb = 200 - Qb.

P = Pa + Pb = 300 - 1.5Q

Thus the demand function for streetlights is P = 300 - 1.5Q. Marginal cost is $75. Find the efficient

quantity at P = MC

300 - 1.5Q = 75

Q = 150 units.

A pays, 100 - 150*0.5 = $25 and B pays = 200 - 150 = $50.

Consumer surplus = 0.5*(maximum willingness - price faced)*quantity

CS for A = 0.5*(100 - 25)*150 = $5625

CS for B = 0.5*(200 - 50)*150 = $11250.