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.
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- 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 (Qc) and price (pc). 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 (Qs). What is the marginal damage at Qs? 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 Qs. (For instance, if there are 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 Qs being produced.
Include axis labels for all points where these curves intersect each other or the axes.