In El Carburetor, California, population 1,001 , there is not much to do except to drive your car around town. Everybody in town is just like everybody else. While everybody likes to drive, everybody complains about the congestion, noise, and pollution caused by traffic. A typical resident's utility function is given by U(m,d,h) = m + 16d − d² − 6h/1000.
where m is the resident's daily consumption of Big Macs, d is the number of hours per day that he, himself, drives, and h is the total amount of driving (measured in person-hours per day) done by all other residents of El Carburetor. The price of Big Macs is $1 each. Every person in El Carburetor has an income of $40 per day. To keep calculations simple, suppose it costs nothing to drive a car. (a) What is the marginal benefit of driving for an individual (measured in utility units)? (b) What is the marginal private cost of driving? (c) If an individual believes that the amount of driving he does won't affect the amount that others drive, how many hours per day will he choose to drive (you can find it based on (a) and (b))? (d) If everyone does the same as you found in (c), what will be the utility of each resident? (e) Given that each individual's driving negatively affects the others' utility, what is the marginal cost of driving (the true marginal cost at the society level)? (f) What is the socially optimal amount of driving?