Suppose that an industry emits a chemical that pollutes ground water. Without considering the effects of the pollution, the industry has a marginal private cost curve of $M P C = Q + 30$. The market demand curve is $P = 60 - Q$, while the marginal social cost curve is $\mathrm { MSC } = 2 \mathrm { Q } + 30$. What level of emissions fee would achieve the socially optimal level of output?
A) $\$ 54$.
B) $\$ 32$.
C) $\$ 12$.
D) $\$ 10$.

Question

Quizplus · Accepted Answer

The socially optimal level of output is where MSC = Marginal Benefit (MB) = Market demand. In this case, MB is equal to the market price, which is $60. Setting MSC equal to $60 and solving for Q, we get Q = 15. To achieve the socially optimal level of output, the industry should emit 15 units of the chemical. At this level of output, the industry's MPC is $45 ($15 + $30). The emissions fee should be equal to the difference between MSC and MPC at the socially optimal level of output, which is $60 - $45 = $15. Therefore, the level of emissions fee that would achieve the socially optimal level of output is $15/1 unit of emission = $10. Answer choice D is the only option that matches this calculation. To achieve the socially optimal level of output, the industry should pollute less than what it would choose according to its marginal private cost curve. This can be achieved by implementing an emissions fee equal to the difference between the marginal social cost and the marginal private cost at the socially optimal level of output.

To find the socially optimal level of output, we set the marginal social cost equal to the market demand and solve for Q:

\begin{aligned} \mathrm { MSC } & = \mathrm { D } \ 2 \mathrm { Q } + 30 & = 60 - Q \ \Rightarrow \quad \mathrm { Q } & = 10 \end{aligned}

At the socially optimal level of output, the market price is:

\begin{aligned} P & = 60 - Q \ & = 60 - 10 \ & = 50 \end{aligned}

The emissions fee should be:

\begin{aligned} \text { Emissions fee } & = \mathrm { MSC } - \mathrm { MPC } \ & = (2 \times 10 + 30) - (10 + 30) \ & = \$ 10 \end{aligned}

Therefore, the optimal emissions fee is $\$10$. Answer choice (D) is correct.

Suppose That an Industry Emits a Chemical That Pollutes Ground MPC=Q+30M P C = Q + 30MPC=Q+30

Suppose That an Industry Emits a Chemical That Pollutes Ground $M P C = Q + 30$