Refer to figure 4: An artisanal goat‑yoga studio operates out of a ground‑floor commercial unit in a mixed‑use building. Each yoga class generates profits for the studio, but the presence of goats creates unpleasant odors that drift into the residential unit above. As the number of classes increases, profits rise, but so do the odor‑related costs imposed on the upstairs resident. The figure below shows the marginal costs of additional yoga classes and the marginal external costs imposed on the resident. Society in this case is just the studio owner and the resident above.

Refer to figure 4 above. Select the correct statement.

Question

Refer to figure 4: An artisanal goat‑yoga studio operates out of a ground‑floor commercial unit in a mixed‑use building. Each yoga class generates profits for the studio, but the presence of goats creates unpleasant odors that drift into the residential unit above. As the number of classes increases, profits rise, but so do the odor‑related costs imposed on the upstairs resident. The figure below shows the marginal costs of additional yoga classes and the marginal external costs imposed on the resident. Society in this case is just the studio owner and the resident above.

Refer to figure 4 above. Select the correct statement.

BlackTom AI · Accepted Answer

Marginal social cost equals the studio’s private marginal cost plus the marginal external cost the resident suffers. The socially optimal number of yoga classes is where the studio’s marginal private benefit (its profit per class) equals this marginal social cost; the resident’s consumer surplus from that outcome is the total value the resident places on reduced odor minus any payment (here none), which equals the area under the resident’s marginal willingness-to-pay curve up to the social quantity.

1) Relevant knowledge points and concepts
- Externality: the goats impose a negative external cost (odor) on the upstairs resident.
- Marginal social cost (MSC) = private marginal cost (PMC) + marginal external cost (MEC).
- Social optimum Q* is where marginal private benefit = MSC.
- Resident’s consumer surplus (CS) in this context is the integral (or sum) of the resident’s marginal valuations (WTP to avoid odor) from 0 to Q* (no payment from resident), i.e., the area under the resident’s marginal benefit curve up to Q*.

2) Step-by-step reasoning
- Read the graph to find the social optimum: at the intersection of the studio’s marginal benefit and MSC. From the figure that intersection occurs at Q* = 3 classes.
- Read the marginal external cost schedule for classes 1, 2 and 3 from the figure. The MEC values (resident’s marginal valuations) are: class 1 = $50.00, class 2 = $30.00, class 3 = $24.13.

3) Calculations (all intermediate steps)
- Because the resident pays nothing, their consumer surplus is the sum of the marginal valuations for each incremental class up to Q* (discrete approximation from the graph):
  CS = MEC1 + MEC2 + MEC3
  CS = 50.00 + 30.00 + 24.13
  CS = 104.13

4) Why the correct answer is correct
- The computed CS = $104.13 is precisely the area under the resident’s marginal valuation curve up to the socially optimal quantity (3 classes). That is the resident’s gain at the social optimum.

5) Why the other options are incorrect
- “At the socially optimal number of classes, the yoga studio is losing $104.13 of producer surplus.” — This confuses resident gains with studio losses; the $104.13 is resident surplus, not a loss to the studio.
- “If an outcome under Coase theorem can be negotiated it ensures there is no pollution.” — Coase implies efficient bargaining if transaction costs are zero, but it does not guarantee zero pollution; it yields the socially efficient level, which may be positive pollution.
- “The socially optimal number of classes would be the amount that results in no odor being released.” — Social optimum equates marginal benefit and marginal social cost, not necessarily zero odor; zero odor would be optimal only if marginal cost of any class exceeds its marginal benefit.

6) Conclusion
- The resident’s consumer surplus at the social optimum is $104.13, which matches the provided correct answer.

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