Using the two-period consumer choice model, explain a person's saving for each period (a) if there is no Social Security program and (b) if there is a pay-as-you-go Social Security program. What is the impact of this pay-as-you-go system (1) on the person's savings and (2) on national savings when everyone is similar to this individual?
has a diminishing marginal utility of consumption.
has an income of $40,000 in period 1 and an income of $20,000 in period 2.
has an interest rate for borrowing or lending at 5 percent per period.
intends to consume all income over their lifetime.
a. If there is no Social Security program, optimal consumption in each period leads the person to save $8000 in period 1.
b. If there is a pay-as-you-go Social Security program taking $4,000 from the individual in the first period and paying this amount with a 5 percent return in the second period.
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A two-period economic model assumes a lifetime of today and tomorrow with income expressed as y: y today and y' tomorrow. Savings may be made only in period 1, or today, and must be carried over to period 2 as part of income: y'+s.
Under a "no Social Security program" system, optimal consumption with the assumption of diminishing marginal utility (utility will be fulfilled at some point and begin to diminish thereafter; consumption will not be open-ended but contained within budget and utility constraints) leads to a savings of $8000 in period 1. This results in c+$8000-y-taxes for period 1 and c'-(5%)$8000+y'-t for period 2.
Under the "pay-as-you-go Social Security program," $4000 are automatically deducted from savings in period 1. The assumption is that income is consumed over the lifetime, which is period 1 plus period 2 (today and tomorrow). This savings is $4000 less than optimal consumption leads to in "no Social Security program" savings. This results in c+$4000-y-t for period 1 and c'-(5%)$4000+y'-t for period 2.
What is the impact of this pay-as-you-go system (1) on the person's savings and (2) on national savings when everyone is similar to this individual?
On the person's savings
The impact on the person's savings is to reduce it in period 1 and to carry over less in period 2. Since the assumption is that consumption equals all income in a given period c+s-y-t, it is probable the person will consider the $4000 unsaved income ($8000 optimal - $4000 pay-as-you-go = $4000) as consumable income and never commit it to savings: their consumption will increase and their savings remain at $4000. The end result of this consumption pattern would be less wealth in period 2 because of lower savings and greater consumption in period 1.
On national savings
A negative impact in personal savings results in a correlated negative impact in national savings. A theoretical case has just been made using the limits of the two-period economic model for a "no Social Security program" system when it is true that individuals receive income sufficient to allow $8000 disposable income at the end of period 1. Note though that not everyone has an income that allows for optimal consumption with the assumption of diminishing marginal utility and a surplus of $8000 "today."
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