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?

Tax = 120 per unit

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.

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