Question

Consider the market for toothbrushes. Inverse market demand for toothbrushes is described by the function: P = 8 − Q

Inverse market supply of toothbrushes is described by the function: P = Q

Suppose that fresh breath benefits everyone, as a result the market for toothbrushes generates a positive externality, where the external benefit is $2 per toothbrush.

1. Without government intervention this market will produce (A) 2 fewer (B) 1 more (C) 2 more (D) 1 fewer toothbrushes than is socially optimal.
2. Suppose the government intervenes in this market by imposing a tax of $2 on buyers of toothbrushes. Now the quantity of toothbrushes bought and sold is (A) Q = 2 units (B) Q = 5 units (C) Q = 4 units (D) Q = 3 units .

Answer 1

P = 8 − Q

P = Q

Marginal private benefit is represented by demand function

MPB= 8 − Q

Marginal social cost = 8 − Q , here we assume marginal social cost equals marginal private cost

Then equilibrium quantity produce =

8 − Q=Q

Q=4

When Q= 4

P= 4

For a socially optimum output, MSC= MSB

for that we should internalise external benefit. It can be done by adding external benefit to marginal private benefit equation

MSB= 8 − Q +2

=10-Q

Socially optimum output = MSB=MSC

10-Q=Q

Q=5

P= 5

Thus without government intervention, or without internalising external benefit, market produce one Less

ANSWER:D

2. When government impose tax on consumer marginal private curve shift downward. Tax on consumer impose additional burden on then.

MPB= 8-Q-2

=6-Q

MSC=Q

now equilibrium is

6-Q=Q

Q=3 units.

Answer D