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=100-5q while the private costs are given by the function P=20+5q. Additionally, we know that each car imposes a $10 per-unit external cost on society. What is the socially optimal number of cars produced?

Question

Business

Owen Lin

16 December, 01:27

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=100-5q while the private costs are given by the function P=20+5q. Additionally, we know that each car imposes a $10 per-unit external cost on society. What is the socially optimal number of cars produced?

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Answers (1)

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Lacey Raymond · Answer 1

Answer: 11 cars

Explanation:

Socially optimal quantity is determined where,

Demand = Marginal Social Cost

We have the demand function, now we must calculate the MSC.

We can do that as,

MSC = Marginal Private Cost + Marginal External Cost

MSC = 20 + 5q + 10

MSC = 30 + 5q

Going back to our original formula we can now solve for the socially optimal quantity as,

Demand = MSC.

100 - 5q = 20 + 2q

80 = 7q

q = 11.42

q = 11

11 is the socially optimal number of cars produced.