- Regulating Q vs. regulating p
The process of tanning leather creates toxic byproducts that pollute the local water supply. Suppose that a city’s tanneries (i.e., producers) compete in a perfectly competitive market, facing demand given by p(Q) = 120−Q and a constant (private) marginal cost of 30. Leather production causes external damage equal to.
- Draw a clearly labeled graph representing this market. Your graph should include:
- The private marginal benefit curve (i.e., the demand curve)
- The private marginal cost curve (i.e., the supply curve)
- The marginal damage curve
- The social marginal cost curve
Include axis labels for all points where these curves intersect each other or the axes.
- On your graph from part a, mark the competitive quantity (Q_{c}) and price (p_{c}). Shade in the deadweight loss and compute its area. Then calculate the total surplus (by first computing the consumer surplus, producer surplus, and total external damage).
- Find the socially optimal quantity (Q_{s}). What is the marginal damage at Q_{s}? What is the social marginal cost? What is the willingness to pay of the marginal consumer?
- Suppose that the city sets a market-wide quota equal to Q_{s}. (For instance, if there are N firms, the city could allow each firm to sell up to ) Compute the total surplus. (Hint: the change in total surplus relative to part b should equal the original deadweight loss.) Would the tanneries support this policy? Why or why not?
- Now suppose that the city decides to switch from a quota to a Pigouvian tax. In class, we saw that the government can ensure that the socially optimal quantity is produced by imposing an appropriate corrective tax on producers. Suppose instead that the city imposes a specific tax t on consumers for each unit they purchase. Find the value t^{∗ }that results in the socially optimal amount Q_{s }being produced.
Copyright 2018 by Brendan M. Price. All rights reserved. 1
2 Types of goods
- Give an example of a public good that we haven’t discussed in class. Explain why you consider it a public good.
- Give an example of a common good that we haven’t discussed in class. Explain why you consider it a common good.
3 Neighborinos
Homer and Flanders can both contribute to mowing the grass between their properties. Let Q denote the total number of hours spent on mowing, where Q = q_{H}+ q_{F}is the sum of hours spent mowing by Homer and by Flanders, respectively.
Homer’s demand curve is | |||
p_{H}(Q) = | (
30 −Q |
for Q ≤ 30 | |
Flanders’ demand curve is | 0 | for Q >30 | |
p_{F}(Q) = | (
60 −Q |
for Q ≤ 60 | |
0 | for Q >60 |
(Note: we’ve been assuming all along that willingness to pay is zero rather than negative once a demand curve intersects the quantity axis: I’m just being explicit about this assumption here.) The marginal cost of mowing is the opportunity cost of time, which will change throughout the problem (sometimes the neighbors are busy, sometimes they aren’t).
- Calculate the social marginal benefit curve as a function of Q. (Hint: it’s a “kinked” or piecewise-linear curve, so you’ll need two equations to describe it: one for smaller values of Q and one for larger values of Q. You may find it helpful to draw a graph.)
- Suppose that the marginal cost of mowing is 70 for each neighbor. From the standpoint of Pareto efficiency, does it matter which neighbor does the mowing? If yes, who should do the mowing? What is the socially optimal total amount of mowing, Q_{s}?
- In reality, each neighbor chooses how much time to spend mowing, given his beliefs about what the other neighbor will do. Assuming again that the marginal cost is 70 for both players, find the Nash equilibrium quantitiesand.
- Now suppose that the marginal cost of mowing is 40 for each neighbor. What is the socially optimal total amount of mowing, Q_{s}? What are the Nash equilibrium quantities q_{H}^{∗ }and q_{F}^{∗ }?
- Suppose finally that the marginal cost is 20 for each neighbor. Find the socially optimal amount Q_{s }and the Nash quantities q_{H}^{∗ }and q_{F}^{∗ }.
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Last Updated on February 11, 2019 by EssayPro