Classwork 2

Fish Harvest with External Damage

Continue from Classwork 1

The same weekly fish market has

Q_D=120-4P

and

Q_S=-40+4P.

Quantity is measured in metric tons of fish per week. Price and cost are measured in hundreds of dollars per metric ton.

For this activity, the one-week stock constraint is not binding. We add a current external cost, which is different from the finite-stock issue in Classwork 1.

Task 1 · Recover the private market

1. Write inverse demand as marginal benefit, MB(Q).
2. Write inverse supply as private marginal cost, PMC(Q).
3. Verify the Classwork 1 competitive quantity and price.

Add external damage

Commercial fish harvest can damage habitat and reduce future catch opportunities valued by people outside the fish market. Use the illustrative external marginal cost

EMC(Q)=0.5Q.

Task 2 · Construct social marginal cost

1. Write SMC(Q)=PMC(Q)+EMC(Q).
2. At the private market quantity, calculate MB, PMC, EMC, and SMC.
3. Explain why the private market harvest is too large when the external cost is omitted.

Task 3 · Find efficient harvest

1. Solve MB(Q)=SMC(Q) for the efficient quantity, Q^*.
2. On one graph, draw and label MB, PMC, and SMC.
3. Mark the private market quantity, Q_M, and the efficient quantity, Q^*.
4. At Q^*, report MB, PMC, and EMC.

Task 4 · Read welfare from graphical areas

1. On a separate EMC graph, shade the area under EMC through Q_M, then through Q^*.
2. Use those areas to find total external damage at each quantity. Do not derive or use a total-damage equation.
3. On the MB–SMC graph, shade the deadweight-loss triangle between Q^* and Q_M.
4. Find the deadweight loss from the triangle’s labeled base and height.

All areas have units of hundreds of dollars per week.

Internalize the harm

Task 5 · Corrective tax and welfare

1. Find the efficient Pigouvian tax per metric ton of fish.
2. Write the tax-inclusive private marginal cost.
3. Find the buyer price and the amount sellers receive after the tax.
4. Complete the table using

W=CS+PS+\text{tax revenue}-\text{external damage}.

Outcome	Q	Buyer price	Seller receipt	CS	PS	Tax revenue	External damage	W
Unregulated market
Corrective tax

Task 6 · Return to the stock

The fishery again begins with 180 metric tons of harvestable biomass and has no biological growth or recruitment during this short planning horizon.

1. How many weeks can the stock support the private market harvest flow?
2. How many weeks can it support the efficient harvest flow?
3. In one sentence, distinguish the externality cost today from the stock-scarcity cost across weeks.

Exit sentence

Complete:

The fish market overharvests because ________; the corrective tax changes the decision by ________.