# Suppose a class of 100 students is comparing two careers—lawyer or engineer. An engineer gets…

Suppose a class of 100 students is comparing two
careers—lawyer or engineer. An engineer gets take-home pay of \$100,000 per
year, irrespective of the numbers who choose this career. Lawyers make work for
each other, so as the total number of lawyers increases, the income of each
lawyer increases—up to a point. Ultimately, the competition between them drives
down the income of each. Specifically, if there are N lawyers, each will get
100N 2 N 2 thousand dollars a year. The annual cost of running a legal practice
so forth) is \$800,000. Therefore, each lawyer takes home 100N 2 N 2 2 800
thousand dollars a year when there are N of them.

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(a) Draw a graph showing the take-home income of each
lawyer on the vertical axis and the number of lawyers on the horizontal axis.
(Plot a few points—say, for 0, 10, 20, . . . , 90, 100 lawyers. Fit a curve to
the points, or use a computer graphics program if you have access to one.)

(b) When career choices are made in an uncoordinated way,
what are the possible equilibrium outcomes?

(c) Now suppose the whole class decides how many should
become lawyers, aiming to maximize the total take-home income of the whole
class. What will be the number of lawyers? (If you can, use calculus, regarding
N as a continuous variable. Otherwise, you can use graphical methods or a