AP Micro · Unit 6 · Market Failure and the Role of Government

Lake Cordis in Vintrala is an open-access fishery. Each fisher weighs only the private cost of sending out a boat, but every additional boat depletes the fish stock and raises costs for all other boats. Fishers harvest 800 tons of fish per year; the socially optimal harvest is 500 tons per year.

(a) Draw a correctly labeled graph of the market for fish harvested from Lake Cordis. On your graph, show each of the following.

• (i) The marginal private cost curve, labeled $MPC = S$, the marginal social cost curve $MSC$ lying above $MPC$ because of the depletion externality, and the marginal social benefit curve $MSB = MPB$, labeled $D$.
• (ii) The open-access market equilibrium quantity, labeled $Q_{mkt}$, where $MPC$ intersects $MPB$.
• (iii) The socially optimal quantity, labeled $Q_{opt}$, where $MSC$ intersects $MSB$, positioned to the left of $Q_{mkt}$.
• (iv) The market price, labeled $P_{mkt}$, corresponding to $Q_{mkt}$ on the demand curve.
• (v) The deadweight loss from overharvesting, shaded completely.
  (b) Suppose the government imposes a per-unit tax on fish harvested equal to the external cost at the socially optimal quantity. On your graph in part (a), show the marginal cost curve that fishers face after the tax, labeled $MPC + tax$, and label the new quantity harvested $Q_2$.
  (c)(i) Given the tax shown in part (b), will the marginal cost that each individual fisher considers when deciding whether to send out another boat increase, decrease, or remain the same? Explain.
  (c)(ii) Based on your answer to part (c)(i), will the total quantity of fish harvested in Lake Cordis increase, decrease, or remain the same relative to the original open-access quantity $Q_{mkt}$? Explain.
  (d) Suppose the government distributes all of the revenue from the tax as an equal lump-sum payment to every resident, whatever the resident's income. Will the Gini coefficient for Vintrala increase, decrease, or remain the same? Explain.