Ch 10 Worksheet — Externalities

Question a

What is the market equilibrium price and quantity (ignoring the externality)?

Market Price ($)

Market Quantity

Hint Set private supply equal to demand: 6 + 2Q = 30 − 2Q. Solve for Q, then plug back in to find P.

Explanation Set demand = private supply: 30 − 2Q = 6 + 2Q → 24 = 4Q → Q_mkt = 6. Plug back in: P = 30 − 2(6) = $18. The market ignores the $8/unit external cost imposed on bystanders.

Question b

What is the socially optimal quantity and price? Use the social cost curve P = 14 + 2Q.

Optimal Quantity (Q*)

Optimal Price ($)

Hint Set social cost = demand: 14 + 2Q = 30 − 2Q. Solve for Q*, then find P from either curve.

Explanation Set social cost = demand: 14 + 2Q = 30 − 2Q → 4Q = 16 → Q* = 4. Plug in: P = 30 − 2(4) = $22. The social optimum has less steel (4 vs. 6 units) at a higher price — because the full cost of production (including pollution harm) is accounted for.

Question c

What Pigovian tax per unit should the government impose to achieve the social optimum?

Tax per unit ($)

Hint The Pigovian tax should equal the external cost per unit — the gap between the social cost curve and the private supply curve.

Explanation The Pigovian tax = external cost = Social Cost − Private Cost = (14 + 2Q) − (6 + 2Q) = $8 per unit. This tax shifts the supply curve up by $8 (from P = 6 + 2Q to P = 14 + 2Q), making the new market equilibrium coincide with the social optimum at Q* = 4.

Question d

What is the deadweight loss from the negative externality (with no government intervention)?

Deadweight Loss ($)

Hint The DWL is the triangle between the social cost curve and the demand curve, from Q* = 4 to Q_mkt = 6. Use ½ × base × height.

Explanation The DWL triangle has:
Base = Q_mkt − Q* = 6 − 4 = 2 units.
Height = gap between social cost and demand at Q* = 0 (they meet), and at Q_mkt: Social Cost = 14+12 = $26, Demand = 30−12 = $18. Height at Q_mkt = $26 − $18 = $8.
DWL = ½ × 2 × 8 = $8. These are units produced where social cost exceeds social value — pure economic waste.

Question e

What is the market equilibrium quantity and price (ignoring the external benefit)?

Market Quantity

Market Price ($)

Hint Same as always — set demand equal to supply: 30 − 2Q = 6 + 2Q. Ignore the external benefit for now.

Explanation 30 − 2Q = 6 + 2Q → 4Q = 24 → Q_mkt = 6, P = $18. This is the private market outcome — students decide based on their own benefit, ignoring the benefit they generate for employers and society.

Question f

What is the socially optimal quantity and price? Use the social value curve P = 38 − 2Q.

Optimal Quantity (Q*)

Optimal Price ($)

Hint Set social value = supply: 38 − 2Q = 6 + 2Q. Solve for Q*, then find P.

Explanation 38 − 2Q = 6 + 2Q → 4Q = 32 → Q* = 8. P = 6 + 2(8) = $22. Society wants more education (8 vs 6 units) because it accounts for the external benefit to bystanders that the private market ignores.

Question g

What Pigovian subsidy per unit should the government provide to achieve the social optimum?

Subsidy per unit ($)

Hint The subsidy should equal the external benefit — the gap between the social value curve and the private demand curve.

Explanation The Pigovian subsidy = external benefit = Social Value − Private Value = (38 − 2Q) − (30 − 2Q) = $8 per unit. This subsidy shifts the effective demand (or reduces effective supply costs) upward by $8, so the private market now produces Q* = 8, the social optimum.

Question 1

A beekeeper sets up hives near an apple orchard. The bees pollinate the orchard's trees, improving the apple harvest. This is an example of a

negative externality for the beekeeper positive externality from the beekeeper to the orchard negative externality from the orchard to the beekeeper market internalization of costs

Hint Who is the bystander being affected? Is the effect a benefit or a harm?

Explanation The beekeeper produces honey and, as a side effect, pollinates the orchard — a benefit to the orchard owner who didn't pay for it. This is a positive externality from the beekeeper's activity to the orchard. Famously, Coase used exactly this example to show how property rights can help resolve externalities through private bargaining.

Question 2

When a negative externality exists, the market equilibrium quantity is

equal to the socially optimal quantity less than the socially optimal quantity greater than the socially optimal quantity indeterminate without more information

Hint With a negative externality, the supply curve only reflects private cost. The social cost curve lies above it. Where does demand intersect each?

Explanation The private supply curve (= private cost) lies below the social cost curve. Demand intersects private supply at a higher quantity than it intersects social cost. So the market produces more than the social optimum — overproduction. Each extra unit between Q* and Q_mkt costs society more than it is worth.

Question 3

A well-designed Pigovian tax on a negative externality causes the supply curve to

shift rightward (down) by the amount of the external cost shift leftward (up) by the amount of the external cost remain unchanged — only the demand curve shifts become perfectly inelastic at the optimal quantity

Hint A tax increases the cost sellers face. In P-Q space, an upward shift means sellers need a higher price to supply any given quantity.

Explanation A Pigovian tax adds to sellers' costs. This shifts the supply curve leftward (upward) — sellers now need a higher price to produce any given quantity. When the tax equals the external cost, the shifted supply curve coincides with the social cost curve, and the market equilibrium moves to the social optimum.

Question 4

Under a cap-and-trade system for pollution, the market price of pollution permits will be highest when

the cap is set very high (many permits issued) pollution abatement technology is cheap and available the cap is set low relative to firms' desired pollution all firms have identical abatement costs

Hint Think supply and demand in the permit market. What happens to permit prices when there are few permits but firms want to pollute a lot?

Explanation Permits are scarce goods. Their price rises when demand is high relative to supply. A low cap means few permits are issued, but firms have strong demand to pollute. This scarcity drives up the permit price. (Option A — high cap — means abundant permits, low price. Option B — cheap abatement — means firms need fewer permits, reducing demand and price.)

Question 5

According to the Coase theorem, private bargaining will achieve an efficient outcome provided that

the government assigns property rights to the polluter property rights are well-defined and transaction costs are low both parties prefer the same outcome government regulation sets a binding quantity limit

Hint Coase's insight was about what makes private bargaining possible. Two things need to be in place. Think: who has what right, and can they negotiate cheaply?

Explanation The Coase theorem states that private bargaining leads to efficiency when (1) property rights are clearly assigned (so parties know who owes compensation to whom) and (2) transaction costs are low (so bargaining is practical). Crucially, the theorem holds regardless of which party gets the property rights — the outcome is efficient either way, though distribution differs.

Question 6

A city imposes a congestion fee (toll) on driving into downtown during rush hour. This is best described as

a Pigovian subsidy for a positive externality command-and-control regulation a Pigovian tax on a negative externality an application of the Coase theorem

Hint Driving during rush hour imposes congestion and pollution costs on other drivers. The toll makes drivers internalize those costs. What type of policy is this?

Explanation Driving creates negative externalities: congestion (slows everyone else), air pollution, noise. A congestion fee is a Pigovian tax — it makes drivers pay for the external costs they impose, reducing driving to the social optimum. London, Stockholm, and Singapore all use congestion pricing based on this economic principle.

Question 7

Refer to the graph below. The deadweight loss from the negative externality equals the area of triangle

A — the triangle between the social cost curve, demand curve, and the vertical line at Q_mkt A represents producer surplus, not deadweight loss A represents the Pigovian tax revenue A represents consumer surplus at the market equilibrium

Hint DWL represents units produced where social cost exceeds social value. On the graph, for units between Q* and Q_mkt, the social cost curve is above the demand curve. The triangle capturing this gap is the DWL.

Explanation Area A is the DWL. For units between Q* and Q_mkt, the social cost (purple dashed curve) exceeds the social value (demand curve). Each of those units reduces total welfare. The triangle is formed by the social cost curve (top boundary), the demand curve (bottom boundary), and the vertical at Q_mkt (right boundary), with the apex at Q* where both curves meet.

Question 8

Which situation is MOST likely to be solved efficiently by private bargaining (Coase theorem) rather than government intervention?

Carbon dioxide emissions from thousands of power plants affecting millions of people A factory's noise affecting one neighboring office building Ocean plastic pollution from ships in international waters Air pollution over an entire metropolitan area from automobile exhaust

Hint Coase theorem requires low transaction costs. What determines whether bargaining is feasible? Think about how many parties are involved.

Explanation Option B — a factory and one neighboring office involves only two parties. Transaction costs are low (they can easily negotiate). All other options involve many dispersed parties (millions of people, international actors), making private bargaining impractical. The Coase theorem works best for small-number, local externality disputes.

Question 9

A positive externality means the market equilibrium quantity is less than the socially optimal quantity.

Hint With a positive externality, the social value curve lies above the demand curve. Where does supply intersect each?

Explanation True. With a positive externality, the social value curve lies above the private demand curve. Supply intersects social value at a higher quantity than it intersects private demand. So the market underproduces — Q_mkt < Q*. This is why governments subsidize education, vaccines, and R&D.

Question 10

According to the Coase theorem, efficiency requires that property rights be assigned to the victim of the externality (not the polluter).

Hint The Coase theorem says efficiency is achieved regardless of the initial assignment of rights. Which party holds the rights affects distribution, not efficiency.

Explanation False. The Coase theorem explicitly states that the efficient outcome is reached regardless of who receives the property rights, as long as rights are clear and transaction costs are low. If the polluter has the right to pollute, the victim pays to reduce it. If the victim has the right to clean air, the polluter pays compensation. Either way, the efficient level of pollution is the same.

Question 11

A Pigovian tax on pollution raises revenue for the government and simultaneously moves the market closer to the social optimum.

Hint What does a per-unit tax do to market supply? And what happens to tax revenue collected?

Explanation True. A Pigovian tax does double duty: (1) It raises the private cost of production, shifting supply left and reducing output toward the social optimum — improving efficiency. (2) It collects tax revenue (tax per unit × quantity sold) that can be used to reduce other distortionary taxes or fund public goods. Economists call this a "double dividend."

Question 12

In a cap-and-trade system, a firm that can reduce pollution cheaply has an incentive to reduce pollution more than its required amount so it can sell excess permits.

Hint If your abatement cost is $10/ton but permits sell for $30/ton, what's the profit from reducing pollution one more ton and selling that permit?

Explanation True. This is a key efficiency feature of cap-and-trade. If a firm's abatement cost is lower than the permit price, it profits by reducing pollution further (below its allocation) and selling those extra permits. This ensures that pollution reduction happens where it is cheapest — achieving the total reduction goal at minimum total cost. High-cost firms buy permits; low-cost firms sell them.

Practice Worksheet

Short Answer — Negative Externality: Steel Production

Short Answer — Positive Externality: Education

Multiple Choice

True or False