Assume that there are two types of consumers who differ only in their endowments. Label these two types as Type A and Type B consumers. For Type A consumers, y = 120 and y′ = 65, where y is the current-period endowment and y′ is the future-period endowment. For Type B consumers, y = 65 and y′ = 120. Thus, Type A consumers have a larger endowment in the current period, while Type B consumers have a larger endowment in the future period. Assume that there are 10 Type A consumers and 10 Type B consumers. In addition, assume that current and future lump-sum taxes are equal to 10 (i.e., t = t′ = 10) and that the real interest rate is 10% (i.e., r = 0.10). And finally, assume that the preferences for Type A and Type B consumers are given by:
u(c, c′) = min{c, c′}

(a) Determine the lifetime wealth, we, of Type A and Type B consumers.

(b) For Type A and Type B consumers, determine the optimal current-period consumption, c, future- period consumption, c′, and savings, s. Are Type A consumers lenders or borrowers? Are Type B consumers lenders or borrowers?

(c) Determine aggregate private savings, Sp, and government savings, Sg. Is the government running a surplus, a deficit, or a balanced budget?

(d) Now assume that the government reduces current period taxes to t = 5, but does not change G and G′. What would future taxes, t′, have to be to satisfy the government's lifetime budget constraint?

(e) Given the new taxes in part (d), repeat parts (a), (b), (c). Does Ricardian equivalence hold in this model?