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Ch. 10 & 11 Worksheet — Answer Key

Econ 101 Discussion Section · Worksheet 8 · Chapters 10 & 11

Short Answer — Refrigerator Market with Negative Externality

Demand: P = 100 − Q   |   MPC: 10 + Q   |   External harm per unit: 0.5Q

Part (a) — Unregulated market equilibrium
Assume the negative externality is not being corrected. Find market output and price.
Q* = 45   |   P* = $55
Set Demand = MPC (firms ignore the externality) 100 − Q = 10 + Q 90 = 2Q Q = 45 P = 100 − 45 = $55 Check: MPC = 10 + 45 = 55 = P ✓ Explanation: In an unregulated market, producers only consider their private costs. They produce where the demand curve (marginal benefit to buyers) equals the marginal private cost, ignoring the pollution damage imposed on society.
Part (b) — Marginal Social Cost (MSC)
The MSC accounts for both private production costs and the external harm to society. What is the MSC equation?
MSC = 10 + 1.5Q
MSC = MPC + External Cost MSC = (10 + Q) + 0.5Q MSC = 10 + 1.5Q Explanation: The marginal social cost is the full cost to society of producing one more unit. It includes (1) the private cost borne by the firm (10 + Q) and (2) the external cost borne by third parties from CFC pollution (0.5Q). As production increases, both the private cost and the external harm grow, making the MSC steeper than the MPC.
Part (c) — Socially optimal output and price
How many refrigerators should be produced to achieve the social optimum? What would be the market price?
Qoptimal = 36   |   P = $64
Set Demand = MSC (social optimum where MB = MSC) 100 − Q = 10 + 1.5Q 90 = 2.5Q Q = 36 P = 100 − 36 = $64 Check: MSC = 10 + 1.5(36) = 10 + 54 = 64 = P ✓ Explanation: The socially optimal quantity is where the marginal benefit to consumers (demand) equals the marginal social cost (MSC). At Q = 36, the value of the last refrigerator to the buyer exactly equals the full cost to society of producing it. Compared to the unregulated Q = 45, the market overproduces by 9 units because firms don't bear the pollution cost. The price is higher ($64 vs. $55) because the true cost of production is reflected.
Part (d) — Corrective (Pigouvian) tax
What would be the size of the per-unit tax? What would be the new marginal cost of production after the tax?
Tax = $18 per unit   |   MC after tax = 28 + Q
Tax = External cost evaluated at socially optimal Q Tax = 0.5Q evaluated at Q = 36 Tax = 0.5(36) = $18 per unit New MC = MPC + Tax = (10 + Q) + 18 = 28 + Q Verify: Set Demand = New MC: 100 − Q = 28 + Q → 72 = 2Q → Q = 36 ✓ Explanation: A corrective (Pigouvian) tax forces producers to “internalize” the externality by making them pay for the pollution damage. The tax is set equal to the external cost at the socially optimal quantity ($18). With this tax, producers now face a higher marginal cost (28 + Q), so they voluntarily reduce production from 45 to 36 units — exactly the social optimum. The tax aligns private incentives with social welfare.
UnregulatedSocial Optimum
Quantity4536
Price$55$64
External Cost per Unit$22.50$18.00
Corrective Tax—$18.00
Multiple Choice — Table 10-2
QtyPrivate ValuePrivate CostSocial Value
1$51$45$57
2$48$48$54
3$45$51$51
4$42$54$48
5$39$57$45
6$36$60$42
Question 1 — Equilibrium quantity
What is the equilibrium quantity of output in this market?
B 2 units
Equilibrium: where Private Value = Private Cost (or where a rational buyer’s WTP meets the seller’s cost). At Q = 1: PV ($51) > PC ($45) → profitable, produce At Q = 2: PV ($48) = PC ($48) → equilibrium At Q = 3: PV ($45) < PC ($51) → not profitable, stop Explanation: In a private market without government intervention, firms produce as long as the buyer’s willingness to pay (Private Value) is at least as high as the cost of production (Private Cost). The last unit where this holds is Q = 2.
Question 2 — Socially optimal output
What is the socially optimal level of output in this market?
C 3 units
Social optimum: where Social Value = Private Cost. At Q = 1: SV ($57) > PC ($45) → net social benefit, produce At Q = 2: SV ($54) > PC ($48) → net social benefit, produce At Q = 3: SV ($51) = PC ($51) → social optimum At Q = 4: SV ($48) < PC ($54) → net social loss, stop Explanation: Social Value > Private Value at every quantity, meaning there is a positive externality (e.g., a benefit to society beyond what the buyer captures). The market under-produces at Q = 2 because buyers only consider their private value. A social planner would produce up to Q = 3 where the full social benefit equals the cost.
Question 3 — Subsidy size
How large would a subsidy need to be to move the market from equilibrium to the socially optimal level?
C $6
Key insight: The subsidy must make the 3rd unit privately profitable for the buyer. At Q = 3 (the target): Private Value = $45, Private Cost = $51 Gap = $51 − $45 = $6 Alternatively: External benefit per unit = Social Value − Private Value = $51 − $45 = $6 Explanation: A subsidy of $6 per unit effectively raises the buyer’s willingness to pay by $6 (or equivalently, lowers the seller’s cost by $6). With a $6 subsidy, the buyer’s effective value for the 3rd unit becomes $45 + $6 = $51, which exactly equals the cost. This “internalizes” the positive externality by rewarding market participants for the social benefit they create.
Multiple Choice — Figure 10-5

Graph shows Supply, Demand, and Social Value curves. Key points: Q = 40, 70  |  P = 15, 24, 36, 42, 63. Social Value curve lies above Demand.

Question 4 — Type of externality
The graph represents a market in which…
B there is a positive externality
Explanation: The graph shows a “Social Value” curve that lies above the Demand curve (private value). When the social value exceeds the private value, it means that consuming/producing the good generates benefits for third parties beyond the buyer — this is a positive externality. Examples include education, vaccinations, or historic building restoration. The market under-produces because buyers only consider their own benefit, not the spillover to society.
Question 5 — Socially optimal quantity
The socially optimal quantity of output is…
D 70 units, since the value to society of the 70th unit is equal to the cost incurred by the seller of the 70th unit
Market equilibrium: Demand = Supply at Q = 40 (private value = cost = $24). Social optimum: Social Value = Supply at Q = 70 (social value = cost ≈ $42). Explanation: A social planner maximizes total surplus by producing where the social value of the last unit equals its cost. At Q = 40, the social value ($42) still exceeds the cost ($24), so society benefits from more production. At Q = 70, the social value curve intersects the supply curve, meaning the benefit to society of the 70th unit exactly equals its production cost. Answer (a) is wrong because it references the buyer’s value, not society’s value. Answer (c) is wrong for the same reason.
Question 6 — Benevolent social planner
A benevolent social planner would prefer…
B 70 units to any other quantity of output
Why not (a)? $24 is the market equilibrium price at Q = 40, which is under-production. The planner wants Q = 70. Why (b)? Q = 70 maximizes total social surplus (Social Value = Supply cost). This is the socially optimal quantity. Why not (c)? At Q = 70, the gap between Demand ($15) and Supply ($42) is $27. A $30 subsidy would overshoot, pushing output beyond 70. The planner wants exactly $27. Why not (d)? A tax would reduce output below 40, moving further from the optimum. With a positive externality, you need a subsidy, not a tax.
More Multiple Choice
Question 7 — Corrective taxes
Which of the following is not an advantage of corrective taxes?
C They subsidize the production of goods with positive externalities
Explanation: Corrective taxes (Pigouvian taxes) are designed to address negative externalities by making producers/consumers pay for the harm they cause. They do NOT subsidize goods with positive externalities — that would require a subsidy, which is the opposite policy tool. The other options are all genuine advantages: corrective taxes raise government revenue (a), enhance efficiency by correcting market failures (b), and move resource allocation toward the social optimum (d).
True / False
Question 8
Buyers and sellers neglect the external effects of their actions when deciding how much to demand or supply.
A True
Explanation: This is the fundamental definition of an externality. When making decisions, buyers consider only their private value and sellers consider only their private cost. Neither party accounts for the costs or benefits imposed on third parties (external effects). This is precisely why externalities cause market failure — the market equilibrium diverges from the social optimum because the full costs/benefits to society are not reflected in the price.
Question 9
When firms internalize a negative externality, the market supply curve shifts to the left.
A True
Explanation: “Internalizing” a negative externality means the firm now bears the external cost (e.g., through a Pigouvian tax or regulation). This increases the firm’s marginal cost of production. When costs rise, the supply curve shifts to the left (upward), meaning firms supply less at every price. This reduces quantity toward the socially optimal level. In our refrigerator example, the $18 tax shifted the supply curve from MPC = 10 + Q to MC = 28 + Q, reducing output from 45 to 36.
Scenario 10-2 — Historic Buildings

50th restored historic building: Private Cost = $800,000  |  Private Value = $650,000  |  Social Value = $800,000

Question 10 — Identifying the externality
Is there an externality associated with this market? If yes, is it positive or negative?
Yes — Positive externality
Social Value ($800,000) > Private Value ($650,000) Explanation: Since the social value exceeds the private value, the restoration of historic buildings generates benefits for people beyond just the buyer. These external benefits could include neighborhood beautification, increased tourism, preservation of cultural heritage, and higher property values for nearby residents. Because society values these restorations more than individual buyers do, this is a positive externality, and the market will tend to under-produce restored buildings.
Question 11 — Size of external benefit
Is there an external cost or external benefit associated with the 50th building? What is its amount?
External benefit = $150,000
External benefit = Social Value − Private Value = $800,000 − $650,000 = $150,000 Explanation: The external benefit is the difference between what society values the good at and what the private buyer values it at. The buyer is willing to pay $650,000 for the restoration, but society as a whole values it at $800,000. The $150,000 difference represents the spillover benefit to third parties (neighbors, tourists, the community). Note: there is no external cost here since no Social Cost information is given that differs from Private Cost.
Chapter 11 — Types of Goods
Question 12 — Excludability
A good is excludable if…
D people can be prevented from using it
Explanation: Excludability means it is possible to prevent someone who hasn’t paid from using the good. For example, a movie theater can exclude non-paying customers. Option (a) describes rivalry, not excludability. Option (b) is about government regulation, which is unrelated. Option (c) about normal goods refers to income effects and is a different concept entirely. The four types of goods based on excludability and rivalry: • Private goods: excludable + rival (food, clothing) • Public goods: non-excludable + non-rival (national defense) • Common resources: non-excludable + rival (fish in the ocean) • Club goods: excludable + non-rival (cable TV, uncrowded toll road)
Question 13 — Private goods
Private goods are both…
C excludable and rival in consumption
Explanation: Private goods have two key properties: (1) Excludable — the seller can prevent non-paying customers from consuming the good (e.g., a store can refuse to give you a sandwich if you don’t pay). (2) Rival — one person’s consumption reduces the amount available for others (if you eat the sandwich, no one else can eat it). Most everyday goods (food, clothing, electronics) are private goods. These are the goods for which competitive markets work most efficiently.
Table 11-1 — Springfield Park (Public Good)
AcresSophiaAmberCedricTotal WTPCostNet Surplus
1$10$24$6$40$24+$16
2$8$18$5$31$24+$7
3$6$14$4$24$24$0
4$3$8$3$14$24−$10
5$1$6$2$9$24−$15
Question 14 — Optimal park size
If the cost is $24 per acre, how many acres should the park be to maximize total surplus?
C 3 acres
For a public good, add up everyone’s willingness to pay for each additional acre: Acre 1: $10 + $24 + $6 = $40 ≥ $24 cost → build (surplus +$16) Acre 2: $8 + $18 + $5 = $31 ≥ $24 cost → build (surplus +$7) Acre 3: $6 + $14 + $4 = $24 = $24 cost → build (surplus $0) Acre 4: $3 + $8 + $3 = $14 < $24 cost → don’t build (loss −$10) Explanation: For a public good (non-rival), everyone can enjoy each acre simultaneously, so the social value of each acre is the sum of all residents’ willingness to pay. Build additional acres as long as total WTP ≥ cost. The 3rd acre just breaks even (total WTP = cost), and the 4th acre would destroy value. Total surplus from 3 acres = $16 + $7 + $0 = $23.
Question 15 — Majority voting outcome
If residents split costs equally ($8/acre each) and vote on park size to maximize their own surplus, what is the largest size the majority votes “yes”?
C 2 acres
Cost per person per acre: $24 ÷ 3 = $8 Each resident votes “yes” on an additional acre if their WTP ≥ $8: Acre 1: Sophia $10 ≥ $8 (yes), Amber $24 ≥ $8 (yes), Cedric $6 < $8 (no) → 2–1 passes Acre 2: Sophia $8 ≥ $8 (yes), Amber $18 ≥ $8 (yes), Cedric $5 < $8 (no) → 2–1 passes Acre 3: Sophia $6 < $8 (no), Amber $14 ≥ $8 (yes), Cedric $4 < $8 (no) → 1–2 fails Explanation: Under majority voting with equal cost-sharing, each person votes based on whether their personal benefit exceeds their $8 share. The 3rd acre fails even though its total social value ($24) equals its cost — only Amber wants it. This illustrates the free-rider problem: Cedric and Sophia benefit from the first 2 acres but won’t vote for the 3rd even though it’s socially efficient. Majority voting under-provides the public good compared to the social optimum (2 acres instead of 3).
True / False — Chapter 11
Question 16
The free-rider problem arises when the number of beneficiaries is large and exclusion of any of them is impossible.
A True
Explanation: The free-rider problem occurs with non-excludable goods (people cannot be prevented from using them). When you can’t exclude non-payers and the number of beneficiaries is large, individuals have an incentive to “free ride” — enjoy the good without paying, hoping others will foot the bill. This leads to under-provision of public goods because no one has a private incentive to pay. Classic example: national defense benefits everyone, but no individual would voluntarily pay for it. This is why governments typically provide public goods financed through taxation.
Question 17
One solution to the “Tragedy of the Commons” is to turn the common resource into a private good.
A True
Explanation: The Tragedy of the Commons occurs when a shared resource (non-excludable but rival) is overused because no individual bears the full cost of their consumption. Examples: overfishing, overgrazing, traffic congestion. One solution is privatization — assigning property rights so that a single owner controls access. The private owner has a direct incentive to manage the resource sustainably because they bear the full cost of depletion. Other solutions include government regulation (quotas, limits) and corrective taxes. This connects to the Coase Theorem: when property rights are well-defined and transaction costs are low, private bargaining can achieve efficient outcomes.