Classwork 7

Quiz 1

Section 1. Multiple Choice and Filling-in-the-Blanks

Question 1.

The Coase Theorem states that if property rights are well defined and transaction costs are negligible, then private bargaining will lead to:

1. A more equitable distribution of wealth.
2. The lowest possible transaction costs.
3. Efficient allocation of resources, even with externalities.
4. Government intervention to correct market failures.

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c. Efficient allocation of resources, even with externalities.

Why? With zero transaction costs and well-defined rights, parties can bargain to internalize externalities and reach the efficient outcome regardless of the initial allocation of rights.

Question 2.

For a (pure) public good, individual willingness to pay (WTP) typically ____(a)____ the true Marginal Benefit (MB), resulting in ____(b)____ when provided through the market.

1. (a) understates; (b) underprovision
2. (a) overstates; (b) overprovision
3. (a) understates; (b) overprovision
4. (a) overstates; (b) underprovision

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a. (a) understates; (b) underprovision.

Why? People have an incentive to free‑ride, so their stated WTP is below their true MB. Summing private demand understates the social MB, yielding too little provision in markets.

Question 3.

The two primary characteristics used to classify goods and resources in the table are _________________________ (Does one user’s harvest reduce what’s left for others?) and _________________________ (Can users who haven’t paid be kept out?).

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Rivalry and Excludability.

Section 2. Analytical Models

Consider a perfectly competitive market for a good whose production generates pollution as a byproduct. The marginal cost (\(MC\)) of producing the good is given by

\[ MC(Q) = 10 + 2Q, \]

where \(Q\) is the quantity produced. The external marginal cost (\(EMC\)) of pollution is given by

\[ EMC(Q) = 2Q. \]

The market demand is

\[ MB(Q) = 70 - 2Q. \]

Question 4

Draw the \(MB\), \(MC\), and \(EMC\) curves, and label both the market equilibrium (\(Q_M\) and \(P_M\)) and the socially optimal equilibrium (\(Q^*\) and \(P^*\)).

Question 5

Graphically indicate the deadweight loss (DWL) caused by the negative externality on the graph.

Question 6

Calculate the optimal Pigouvian tax per unit that would lead producers to produce the socially optimal quantity.

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Algebra.

Market equilibrium (ignoring externality): set \(MB(Q)=MC(Q)\):
\(70 - 2Q = 10 + 2Q \Rightarrow 60 = 4Q \Rightarrow \boxed{Q_M = 15}\).
Price: \(\boxed{P_M = MB(15) = MC(15) = 40}\).

Socially optimal equilibrium: set \(MB(Q)=SMC(Q)\):
\(70 - 2Q = 10 + 4Q \Rightarrow 60 = 6Q \Rightarrow \boxed{Q^* = 10}\).
Consumer price at the social optimum (what demand is willing to pay): \(\boxed{P^* = MB(10) = 50}\).

Pigouvian tax: set \(t^{*} = EMC(Q^{*})\):
\(t^{*} = EMC(Q^{*}) = 2Q^{*}. \Rightarrow t^{*} = 2Q^{*} \Rightarrow \boxed{t^{*} = 20}\).