Classwork 1

Market Diagnostic: Fish Harvest from a Finite Stock

Author

Byeong-Hak Choe

Published

September 2, 2026

Purpose

This is an ungraded diagnostic. Work independently first, compare with a partner, then revise in another color. The goal is to identify which microeconomics tools need review—not to produce a score.

Scenario

The weekly market for fish from a single fishery has:

Q_D=120-4P

Q_S=-40+4P

Quantities are measured in metric tons of fish per week, and price in hundreds of dollars per metric ton.

Task 1 · Equilibrium

  1. Solve for the competitive equilibrium price and quantity.
  2. Draw labeled demand and supply curves.
  3. Show the equilibrium on the graph.
Demand runs from a price intercept of 30 to a quantity intercept of 120; supply crosses the price axis at 10. The curves intersect at Q equals 40 metric tons per week and P equals 20 hundreds of dollars per metric ton. Each positive intercept and equilibrium coordinate is labeled on its axis.
Figure 1: The original equilibrium in the weekly fish market.

Set 120-4P=-40+4P. The equilibrium is P^*=20 ($2,000 per metric ton) and Q^*=40 metric tons per week.

Task 2 · Surplus

  1. Find the demand choke price.
  2. Find the supply intercept price.
  3. Calculate consumer surplus and producer surplus.
  4. Using your graph, identify:
    • total benefit (TB) as the area under MB from Q=0 to the equilibrium quantity; and
    • total cost (TC) as the area under MC over the same quantities.
  5. Calculate TB and TC. Verify that TB-TC=CS+PS.
Demand crosses the axes at P equals 30 and Q equals 120; supply crosses the price axis at 10. At Q equals 40 and P equals 20, the dark-blue consumer-surplus triangle lies below demand and the light-blue producer-surplus triangle lies above supply. Each area equals 200 hundreds of dollars per week. The intercepts and equilibrium values appear on the axes.
Figure 2: Consumer surplus and producer surplus are each 200 hundreds of dollars per week.

Inverse demand is P=30-0.25Q; inverse supply is P=10+0.25Q.

CS=\tfrac12(30-20)(40)=200

PS=\tfrac12(20-10)(40)=200

Each surplus is 200 in hundreds of dollars per week, or $20,000 per week.

Graphically, TB is the entire area under MB through Q^*=40, while TC is the entire area under MC over those same 40 metric tons:

TB=\tfrac12(30+20)(40)=1{,}000

TC=\tfrac12(10+20)(40)=600.

Therefore,

TB-TC=1{,}000-600=400=CS+PS.

These areas are measured in hundreds of dollars per week, so TB=\$100{,}000, TC=\$60{,}000, and total surplus is \$40{,}000 per week.

Two panels show full marginal curves and shade their areas from zero through the equilibrium Q equals 40. Marginal benefit crosses P equals 30 and Q equals 120, and marginal cost crosses P equals 10. The shaded total benefit and total cost are 1,000 and 600 hundreds of dollars per week.
Figure 3: Total benefit is the area under marginal benefit, and total cost is the area under marginal cost, through the equilibrium quantity.

Task 3 · A harvest quota that limits quantity

Suppose the government limits total fish harvest to 30 metric tons per week. Assume the sellers who supply this restricted quantity receive the quota-created price difference.

  1. Does the quota actually limit harvest? Explain by comparing it with the competitive quantity.
  2. On your graph, keep the original MC curve visible. Draw the effective market supply following MC through 30 metric tons and then becoming vertical at the quota.
  3. At Q=30, use demand to find the market price and use MC to find the marginal harvesting cost.
  4. Shade and calculate the quota rent and the deadweight loss.
  5. Calculate CS, PS including quota rent, and total surplus under the quota.

Yes. The quota limits harvest because 30 metric tons is below the competitive quantity of 40.

At Q=30,

P_D=30-0.25(30)=22.5,

while

MC=10+0.25(30)=17.5.

The quota keeps sellers from expanding output even though the market price exceeds the marginal cost of the 30th metric ton. The resulting quota rent is

(22.5-17.5)(30)=150,

or $15,000 per week.

The consumer-surplus triangle is 112.5. Producer surplus excluding quota rent is also 112.5, so producer surplus including quota rent is 262.5. Total surplus is therefore 375, all in hundreds of dollars per week.

The deadweight-loss triangle between Q=30 and Q=40 is 25 hundreds of dollars per week, or $2,500 per week.

Demand crosses the axes at P equals 30 and Q equals 120, while marginal cost crosses the price axis at 10. Effective supply follows marginal cost through the quota Q equals 30 and then becomes vertical. At the quota, market price 22.5 and marginal cost 17.5 are labeled on the price axis. A purple rectangle shows quota rent of 150, and a red triangle from Q equals 30 to 40 shows deadweight loss of 25.
Figure 4: A quota that limits harvest to 30 metric tons makes effective supply vertical at the quota while leaving the marginal-cost curve unchanged.

Task 4 · Demand shock

A surge in restaurant demand increases demand to:

Q_D'=140-4P

  1. Find the new equilibrium.
  2. Calculate the percentage change in equilibrium price and quantity. Which changes more in percentage terms?

The new equilibrium is P'=22.5 and Q'=50.

Using the original equilibrium, P^*=20 and Q^*=40, as the baseline:

\begin{aligned} \%\Delta P &=\frac{P'-P^*}{P^*}\times 100\\ &=\frac{22.5-20}{20}\times 100\\ &=12.5\%. \end{aligned}

\begin{aligned} \%\Delta Q &=\frac{Q'-Q^*}{Q^*}\times 100\\ &=\frac{50-40}{40}\times 100\\ &=25\%. \end{aligned}

Therefore, quantity rises more than price in percentage terms.

Original demand runs from P equals 30 to Q equals 120; new demand runs from P equals 35 to Q equals 140. Supply crosses the price axis at 10. Equilibrium moves from Q equals 40 and P equals 20 to Q equals 50 and P equals 22.5. These intercepts and projected equilibrium values appear on the axes.
Figure 5: Demand shifts from the dashed curve D₀ to the solid curve D₁. Supply is unchanged.

Task 5 · Add the stock

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

  1. How many weeks can the original equilibrium harvest flow continue?
  2. Which information is missing if fishers choose harvest using only this week’s supply curve?
  3. Write one sentence distinguishing the stock from the flow.

For week t, use the stock accounting identity

S_{t+1}=S_t+G_t-H_t.

A timeline runs from the start of week t, when the fish stock S subscript t equals 180 metric tons, to the start of week t plus 1, when stock S subscript t plus 1 equals 140. During the week, net growth and recruitment G subscript t adds zero and harvest H subscript t subtracts 40 metric tons.
Figure 6: One week of stock accounting: next week’s stock equals this week’s stock plus net growth and recruitment minus harvest.

Because G_t=0 and harvest remains H_t=40 metric tons per week, the stock after n weeks is

S_n=S_0-nH=180-40n.

The stock is exhausted when S_n=0:

\begin{aligned} 0&=180-40n,\\ 40n&=180,\\ n&=\frac{180}{40}=4.5\text{ weeks}. \end{aligned}

Thus, the stock supports four complete weeks of 40 metric tons each, leaving 20 metric tons for one-half of the fifth week.

This exercise sets biological growth and recruitment to zero. The weekly supply curve omits the value of leaving fish available for future use and how today’s harvest affects future opportunities.

The stock is the fish biomass available in the water at a point in time; the flow is the fish harvested per week.

Exit sentence

Complete:

The ordinary market graph helps me see ________, but a natural-resource model must also track ________.

The ordinary market graph helps me see prices, quantities, and gains from trade today, but a natural-resource model must also track how today’s harvest changes the resource stock and future opportunities.

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