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.
Please tell me if you have any questions about my wording. Please help me on this! I've solved all the other parts to the problem, so please help me on this last one!