Question 1 (20 points). Suppose a class of 1,000 students is comparing two caree

Question

Question 1 (20 points). Suppose a class of 1,000 students is comparing two careers – doctor or lawyer. Let n represent the number who choose to become doctors, so 1, 000 n is the number who choose to become lawyers. Each doctor’s income is a function of the number of others who choose to be doctors: p(n) = 250 n/6 (thousands of dollars). Each lawyer’s income is a constant s(n) = 150 (thousands of dollars).

(a) Write down the total income to the class as a function of n.

(b) Find the optimal n that maximizes the total income.

(c) How many students choose to become doctors in the Nash equilibrium?

Explanation / Answer

Total Income = n*Income of Docter + (1000-n)Lawyer

              = n*(250 - n/6) + (1000-n)*150       

                = 250n - n^2/6 + 150,000 - 150n

               TI     = -n^2/6 + 100n + 150,000

b. dTI/dn = -n/3 + 100

Putting dTI/dn = 0

               n = 300

c.

      For nash Equilibrium

       Income of Doctor = Income of Lawer

      250 - n/6 = 150

        n/6 = 100

         n = 600

So, 600 choose to become doctors in the Nash equilibrium

If you don't understand anything, then comment, I will revert back on the same.

And If you liked the answer then please do review the same. Thanks :)

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.