Social security in the Diamond model. Consider a Diamond economy where g is zero, production is Cobb-Douglas, and utility is logarithmic.
(a) Pay-as-you-go social security. Suppose the government taxes each young individual an amount T and uses the proceeds to pay benefits to old individuals; thus each old person receives (1 + n)T.
(i) How, if at all, does this change affect equation (2.60) giving kt +1 as a function of kt?
(ii) How, if at all, does this change affect the balanced-growth-path value of k?
(iii) If the economy is initially on a balanced growth path that is dynamically efficient, how does a marginal increase in T affect the welfare of current and future generations? What happens if the initial balanced growth path is dynamically inefficient?