Quantitative Question 3 of 3:

Davis and Sacramento are located ten miles apart, with a population ofcustomers evenly distributed between the two cities.

In each city, a set of perfectly competitive firms produce a good.

A customer's utility depends on the price of the good and how far they have to travel to buy the good.Specifically, the utility a customer gets from purchasing the good in a city is given by: U = 40 - p - 2*d, where p is the price of the good in the city and d is the distance the person needs to travel to reach the city.

The firms in Sacramento have MC =12.

The firms in Davis have MC = 16.

(a) (4 points) Which customers will purchase in Davis?

(b) (4 points) Suppose the production of the good also creates pollution.The marginal benefit of abatement is given by MBA = 20 - 2A and the marginal cost of abatement is given by MCA = 2 + A, where A is the amount of abatement.If a government wanted to set a Pigouvian tax on emissions, what would it be?

(c) (4 points) Suppose Davis decides to implement the Pigouvian tax, but Sacramento does not, and that the Pigouvian tax raised the marginal cost for firms in Davis to 16 + t, where t is the Pigouvian tax from part (b).What impact would the policy have on sales in the two cities?

(d) (5 points) Based on your answers above, briefly explain why it might be better for California to implement the Pigouvian taxstate-widethan to let each city decide whether to implement the Pigouvian tax.