To make the calculation of the present discounted value of a worker's human capital more realistic, suppose labor income starts at $50,000 initially, but then grows at a constant rate of 2% per year after that. Let wt be labor income in year t, so that

where 0 = $50,000 and = 0.02. The steps below will walk you through the problem.
(a) If the interest rate is R, what is the formula for the present discounted value today (in year 0) of labor income from a particular future year t?
(b) Now add up these terms from t = 0 to t = 45 to get a formula for the present discounted value of labor income. Your answer should look something like that in equation (7.12).
(c) Write your answer to part (b) so that it takes the form of the geometric series:
pdv = 0 (1 + a + a2 + a3 + . . . + a45).
What is the value of a that you find?
(d) Apply the geometric series formula to compute the present discounted value for the case of R = 0.04, R = 0.03, and R = 0.02. What weird thing happens (and why) when R = 0.02?
(e) Comment on your results.

Transcribed Image Text:

w, = w(1 + g, и.