Question

The private marginal benefit associated with a product’s consumption is PMB = 540 − 6Q and the private marginal cost associated with its production is PMC = 8Q. Furthermore, the marginal (external) damage associated with this good’s production is MD = 4Q. To correct the externality, the government decides to impose a tax of T per unit sold. What tax T should it set to achieve the social optimum?

Answer 1

Tax = 120 per unit

Step-by-step explanation:

First lets calculate Socially optimum Marginal Profit,

This can be computed by factoring in the marginal external benefit in the costs.

thus,

PMB = (PMC + MD)

This gives us the socially profit maximizing level of Product Q in quantity produced terms. we solve for Q the above equation. As generally profit is maximized at Marginal cost = Marginal Revenue

540 - 6Q = 8Q + 4Q

540 = 18Q

Q = 30 units

Since the tax amount should equal the value of marginal external damage so the amount of tax at socially optimum level thus is,

MD = T,

that gives T = 4 * 30 = 120 per unit

This shall then give the revised Marginal cost function of

Revised marginal cost = 8Q + 120. This corrects the externality by making production more expensive.

Hope that helps.