Question

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 = 75 − 3q while the private costs are given by the function P = 10 + 2q. Additionally, we know that each car imposes a $10/unit external cost on society. How many more cars will be produced in the market equilibrium versus the social optimum?

a) 2
b) 4
c) 5
d) 1
e) 3

Answer 1

2 more cars will be produced in the market equilibrium versus the social optimum. The right answer is a.

Step-by-step explanation:

According to the given data we have the following:

demand for cars is given by the function P = 75 − 3q

private costs are given by the function P = 10 + 2q

75 − 3q= 10 + 2q

Therefore, 65=5q

q=13

P=36

Therefore, socially optimal number of cars is 13.

To calculate How many more cars will be produced in the market equilibrium versus the social optimum, we have to calculate the following:

social cost=10+2q+10

=20+2q

75 − 3q=20+2q

55=5q

q=11

P=20+2(11)=42

Therefore, Qm-Qs=13-11

Qm-Qs=2

2 more cars will be produced in the market equilibrium versus the social optimum