Suppose a pay-as-you-go social security system where social security is funded by a proportional tax on the consumption of the young. That is, the tax collected by the government is sc,

where s is the tax rate and c is consumption of the young. Retirement benefits are given out as a fixed amount b to each old consumer. Can social security work to improve welfare for everyone under these conditions? Use diagrams to answer this question.

The lifetime budget constraint of an individual consumer in this scenario is

(CONSTRAINT 1) -> c(1+s) + c/(1+r) = y + (y+b)/(1+r)

Equality must exist between taxes collected on consumption of the young consumers and benefits given to old consumers. Therefore, by substituting for b, the constraint imposed on consumers by the social security system can be found that accounts for the relationship between population growth rate and real interest rate. This constraint (2) is given by

(CHOOSE BETWEEN A , B , C , OR D)

A. c * (1 + s/(1+n)(1+r)) + c/(1+r) = y + y/(1+r).

B. c * (1+s)(rn) + c/(1+r) = y + y/(1+r).

C. c * (1 + (1+n)s/(1+r)) + c/(1+r) = y + y/(1+r).

D. c * (1 + (rn)s/(1+r)) + c/(1+r) = y + y/(1+r).