Question

Count von Count likes to (loudly) count passing cars next to Oscar’s home. This creates a negative externality via noise pollution that irritates Oscar. The marginal private cost of counting is 40, and marginal damage is given by 2Q, so:

MPC = 40

MD = 2Q

a) Explain why the existence of externalities can be considered a market failure.

b) Ignoring the externality, find the privately optimal quantity (Q₀) of counting if the marginal benefit is given by: MB = 60 – 2Q. Assume Q is in terms of hours a week.

c) What is the equation for marginal social cost (MSC)?

d) Find the socially optimal quantity of hours of car counting (Q*).

e) Graph this scenario. Include MPC, MD, MSC and MB. Label all curves and intercepts.

f) How much does Oscar gain from reducing the hours of counting from Q₀ to Q*?

g) How much does Count lose due to reducing the hours of counting from Q₀ to Q*?

h) Explain the reciprocal nature of externalities in this specific scenario.

Answer 1

a)

The market failure occurs when the market fails to generate an equilibrium that reflects the actual cost and benefit of the economic transaction. The externality is the byproduct of economic activity whose value or benefit accrues to those who are not involved in the transaction. When the economic activity imposes a cost to the society, it is called a negative externality. The economic agents do not consider this cost of an externality in their value. Thus the social cost of a negative externality is higher than private cost. Thus, the market outcome which takes into account only the individual cost fails to generate an equilibrium that reflects the actual cost of the transaction. Hence, the market "fails" in the presence of an externality.

b)

At the private equilibrium: MB=MPC

$\therefore 60-2Q=40\\\\ \; or,\ 2Q=20$

$\therefore Q_0=10$

c)

The marginal cost takes into account the external cost of the noise. That is the MD of sound. then the marginal social cost is

$MSC=MPC+MD=40+2Q$

d)

At the social optimum, MSC=MB

$\therefore 60-2Q=40+2Q$

$or,\ 4Q=60-40=20$

$\therefore Q^*=5$

e)

The figure below gives the MPC, MD, MSC, and MB

f)

By reducing the value of the output from Q0 to Q8 decreases damage by the area A of the damaging party. Then the gain is area A.

$A=\frac{1}{2}\times 20\times 10-\frac{1}{2}\times 10\times 5=75$

g)

By reducing the counting, von Count reduces the benefit by the area B in the figure above.

$B=\frac{1}{2}\times \left (50-40 \right )\times (10-5)=25$

h)

According to Coase the nature of the externality is a reciprocal one. That is the gain due to externality causes loss to another party. To correct externality, the taken measure also decreases the gain of another party while reducing the loss of the society. Here decreasing output from Q0 to Q* increasing the gain of Oscar by 75 and the represents loss in the benefit for Count of the amount 25.