(Adapted from Catherine et al. 2020 and Sabelhaus and Volz 2020) Suppose that you are earning the salary of a median household in Manhattan ($51,000) and you just turned the age of 22. You intend to work until 67 and expect your salary to increase by inflation (2%). Assume that you're paid at the end of every age year (end of 22 to end of 66). At retirement, you are paid a Social Security payment equal to the 60% of your last wage and grows with a 1% price adjustment. You know for certain that you'll live until age 100 and want to compute the current present value of your human capital and transfer income.

a. Computing human capital. Suppose that your labor income is equally risky to the stock market, which has a required rate of return of 10%. What is the present value of your labor income at age 22 given that it grows by inflation?

b. Riskless Social Security. You receive your first Social Security payment at 67. Suppose that Social Security is discounted at a risk-free rate of 3%. What is the value of the Social Security wealth now (at age 22)?

c. Risky Social Security. Another group of economists tell you that Social Security is risky and should be discounted at the risky rate (10%): repeat the analysis under this assumption.

d. Comparison. Comment on the total wealth (Social Security + Human Capital) under both cases: which is larger? Why? What is the economic significance here?