An environmental economic consulting firm is hired to measure the negative externalities associated with the pollution from an industry. The consultants calculate the marginal social cost of production to be $M S C = 2 Q + 30$ and the marginal private cost of production to be $M P C = Q$ $+ 30$. The market demand curve can be expressed as $P = 60 - Q$. The net social benefit at the market equilibrium (i.e. the equilibrium where production decisions do not take into account the externality) is:

Question

Quizplus · Accepted Answer

At market equilibrium, marginal private cost (MPC) is equal to market price (P). Therefore:
$$Q + 30 = 60 - Q$$
$$2Q = 30$$
$$Q = 15$$
Substituting Q into the demand equation yields:
$$P = 60 - 15 = 45$$
Therefore, at market equilibrium, the quantity produced is 15 and the price is 45. The marginal social benefit (MSB) can be derived from the demand curve:
$$MSB = P = 45$$
The marginal external cost (MEC) can be calculated by subtracting MPC from MSC:
$$MEC = MSC - MPC = (2Q + 30) - (Q + 30) = Q = 15$$
Therefore, the net social benefit (NSB) at market equilibrium can be calculated as:
$$NSB = MSB - MEC = 45 - 15 = 30$$
However, because the question asks for the "negative" externality, the NSB must be multiplied by negative one to represent the cost of the externality. Therefore, the answer is:
$$NSB_{negative} = -30$$
Which corresponds to answer choice B. First, we need to find the equilibrium quantity and price without taking into account the externality. This occurs where $M P C = P$. Substituting in $P = 60 - Q$, we get:

$$Q + 30 = 60 - Q$$

$$Q = 15$$

Therefore, $P = 60 - Q = 45$.

To find the net social benefit, we need to find the difference between the total social benefit and the total social cost. The total social benefit is the area under the demand curve up to the equilibrium quantity, which is:

$$T S B = \frac{(60 + 45)}{2} \cdot 15 = 112.5$$

The total social cost is the area under the marginal social cost curve up to the equilibrium quantity, which is:

$$T S C = \int_0^{15} (2Q + 30) dQ = \left[ Q^2 + 30Q \right]_0^{15} = 675$$

Therefore, the net social benefit is:

$$N S B = T S B - T S C = 112.5 - 675 = -562.5$$

This negative value indicates that there is a net social cost associated with production at the market equilibrium. However, we are asked for the net social benefit, which is the negative of the net social cost. Therefore, the answer is $B$ $\$112.5$.

An Environmental Economic Consulting Firm Is Hired to Measure the Negative