1. ## microeconomics externalities help!!!

Hi everyone,

I'm stuck on a problem for econ dealing with externalities. Okay, here's the scenario:

In a town with 1001 people one can drive cars and eat big macs. The externality is the congestion, noise, pollution, etc, created by traffic. A consumer's utility function is U(m,d,h) = m + 16d - d^2 - 6h/1000, where m = daily consumption of Big Macs, d = hours spent driving per day, h = total amount of driving (measured in person-hours per day) done by all the other residents of the town. The price of Big macs is $1 each, and every consumer has income of$40 per day. It does not cost anything to drive a car.

Question: What tax would be necessary in order to restrict the number of hours driven for each person to be 5 hrs? (p.s. you can substitute in 1000d for h in the utility function)

The hint for this question is to have the price equal a consumer's MRS between driving and big macs when he is driving the optimal amount. However, I don't know how to calculate MRS. The answer is \$6 but I don't know how to obtain it.

P.S. this comes from one of the workbook problems from "Workouts in Intermediate Microeconomics" on the chapter on externalities, ch 34.