Problem
We used the example of Carlo to help us better understand the social security system from the individual perspective and we made the following simplifying assumptions
1. He was paid the same each year
2. The interest rate and inflation rate are zero
3. We know how long he will work and live
4. We assumed perfectly smooth consumption
From our analysis we showed that under these assumptions the social security system did not seem to affect the consumption and savings decision of the consumer.
If we were to relax some of the assumptions, specifically, the second assumption that the real interest rate is zero and allow for a positive rate. Under this scenario I want you to answer the following two questions
i. What happens to Carlo's lifetime income and consumption when we introduce a real interest rate of 5%.
ii. How do changes in social security affect consumption and savings when the real interest rate is 0% and 5%