1. The US Social Security system provides workers with the option of retiring at age 62 and having a lower monthly social security benefit or waiting until age 67 and receiving their full benefits. This year, somebody retiring at age 62 would receive $2,364 per month whereas somebody who turns 67 this year would receive $3,345 per month. Each year, the benefit levels increase with inflation. In other words, if somebody is currently age 62 and starts taking benefits now, next years monthly income will be $2,364 increased by one year of inflation. If the 62-year-old waits until age 67 to retire, their first-year benefits would be higher than $3,345 by five years of inflation.

a. You are advising a family friend who is about to turn 62 on whether they should start receiving benefits now or wait until age 67. Assume that the appropriate discount rate is 4.5%, inflation is expected to be 2.5% per year for the foreseeable future, and that the person you are advising expects to live until age 85 (assume they die right before their 85^th birthday, meaning they would receive 23 or 18 years of payments). Assuming no changes to the program, would it be more valuable to wait until age 67 or start receiving benefits now? Evaluate on an annual basis (ignore within year compounding). (25)

b. Policymakers are concerned about the long-term viability of Social Security and are considering dramatic changes to the program. The Social Security system is projected to raise $1.088 trillion this year in income and to pay $1.145 trillion this year in benefits. It therefore will run a deficit this year, which it covers out of its $2.852 trillion trust fund at the beginning of this year. With the ongoing retirement of the Baby Boom generation, benefits levels are expected to increase at the rate of 3.8% per year (2.5% inflation plus 1.3% annual increase in the number of beneficiaries) whereas income (FICA taxes) is expected to grow only 2.5% per year (inflation) as the workforce is not forecast to grow. Continue to assume that the appropriate discount rate is 4.5%. Using a 75-year forecast time period (as used by policymakers), estimate the solvency of the Social Security system as of the beginning of this year. In other words, what is the value of its expected payments relative to its expected tax revenues plus the value of the trust fund? For simplicity, assume that the income and payments are made at the end of the year. (30)

c. To bring the system to solvency, by how much would they have to modify aggregate benefits this year, i.e. the new baseline level of benefits (that will still grow with inflation plus the growth rate in the number of beneficiaries assumed above)? (15)