Suppose that a firm’s marginal production costs are given by mc = 10 + 4q. the firm’s production process generates a toxic waste, which imposes an increasingly large cost on the residents of the town where it operates: the marginal external cost (i. e. marginal damage inflicted on the residents) associated with the qth unit of production is given by 2q. hint: the social marginal cost takes into account the private cost of the firm as well the marginal damage to the society of the firm’s production activities.

(a) what is the marginal private cost associated with the 10th unit produced?
(b) what is the total marginal cost to society associated with producing the 10th unit (the marginal social cost of the 10th unit)?

A) Marginal private cost= 50

B) Total Marginal social cost to society = 70

Explanation:

A) In order to find the marginal private cost we will use the firms production cost formula as it is the private cost that the firm is enduring and is only relevant to the firm's cost and not the society's cost.

In order to find the marginal unit cost of the 10th unit produced will will replace Q in the formula by 10 as it represents quantity.

MC= 10 + 4Q

MC= 10 + 4(10)

MC= 10 +40 = 50

B) In order to find the marginal cost to society we will add the marginal external cost of the 10th unit to its private cost. We already know the marginal private cost is 50 now we need to find the marginal external cost to it to find the total marginal cost.

Marginal external cost = 2Q

Q= 10

Marginal external cost = 2*10 =20

The total Marginal cost to society= 50 + 20= 70