Hank, who maximizes the lifetime present value of earnings, has just graduated from high school and is going to live 2 more periods. He has found a job that pays WHS = $25 thousand in each of his 2 remaining periods right out of high school. If Hank earns a college degree this period, he can earn WC = $80 thousand in his last remaining period. However, college costs C = $20 thousand in tuition, books, and fees, and R = $5 thousand in room and board expenses during the first period. (HINT: Why does one distinguish between tuition, books, and fees on the one hand, and room and board on the other?)
a. Derive an equation that expresses the critical discount rate, rCRIT, at which Hank will choose to attend college, as a function of WHS, WC, and C. At what values of r will Hank attend college, and at what values will he not? Be sure to show all of your computations clearly, formulas, and all.
b. Use your equation in (a) to explain whether rCRIT rises or falls (or remains unchanged) if (1) R rises; (2) C rises; (3) WHS rises; (4) WC falls. (By "use," I mean note whether a variable is in the numerator or denominator, and so on, and intuit what happens to the relative present values of the high school and college paths.)