1Regulating *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

- On your graph from part a, mark the competitive quantity (
*Q*) and price (_{c}*p*). 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)._{c} - Find the socially optimal quantity (
*Q*). What is the marginal damage at_{s}*Q*? What is the social marginal cost? What is the willingness to pay of the marginal consumer?_{s} - Suppose that the city sets a market-wide quota equal to
*Q*. (For instance, if there are_{s}*N*firms, the city could allow each firm to sell up to units.) 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*being produced._{s }

Include axis labels for all points where these curves intersect each other or the axes.

=