Question

Tell me why its the correct answer and show work

Greater air pollution from car production leads to increased rates of asthma and infant mortality, imposing costs on the rest of society. The inverse demand for cars is given by the function P = 55−3q while the private costs are given by the function P = 10 + 2q. Additionally, we know that each car imposes a $5 per-unit external cost on society. What is the socially optimal number of cars produced? (a) 6 (b) 7 (c) 8 (d) 9 (e) 10

Answer 1

Answer

The correct answer is (c) 8.

Social optimum quantity is that quantity where MSB = MSC

MSB = Marginal Social Benefit and MSC = Marginal Social cost.

Inverse Demand is given by : P = 55 - 3q and note that there is not external benefit so MSB = MPB(Marginal private Benefit).

As inverse demand curve shows the price consumers are willing to pay for different level of quantity and this is decided by their Maximum willingness to pay and as consumers pay maximum that amount at which they get maximum worth of benefit.

Thus Inverse demand curve is similar to Marginal private benefit(MPB) curve.

Thus, MSB = MPB = 55 - 3q.

MSC = MPC + External cost and here external cost = 5 and Marginal private cost = 10 + 2q

Hence MSC = 10 + 2q + 5 = 15 + 2q

Thus, MSB = MSC => 55 - 3q = 15 - 2q

=> 40 = 5q

=> q = 8

Thus,, socially optimal number of cars produced = 8 units.

Hence, the correct answer is (c) 8.