Suppose that all workers live for two periods (young and old). All workers earn income of $300 when young and $0 when old. Suppose there is an unfunded Social Security system. In every period, the government taxes each young worker $50 and immediately pays each old worker an even share of the total tax revenue. The population grows at a constant rate of 2%, so each new cohort is 2% larger than the last. Calculate the rate of return for the first generation (young before and old after social security begins), the last generation (young before and old after social security ends), and each generation in between.