Classwork 1

Market Diagnostic: Fish Harvest from a Finite Stock

Author

Byeong-Hak Choe

Published

September 2, 2026

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.

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.

Task 3 · Binding harvest quota

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. Is the quota binding? Explain using 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.

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?

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.

Exit sentence

Complete:

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

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