Suppose that consumption takes place this period and next period, and consumption is always a normal good. Suppose further that income now is positive and income next period is zero.
A: Explain why the following either cannot happen or, if you think it can happen, how:
(a) Savings behavior is immune to changes in the interest rate, but taxing interest income causes a dead weight loss.
(b) Savings behavior is immune to changes in the interest rate, and taxing interest income causes no dead weight loss.
(c) Savings decreases with increases in the interest rate and there is a deadweight loss from taxation of interest.
(d) Savings increases with increases in the interest rate and there is a deadweight loss from taxation of interest.
(e) Savings decreases with an increase in the interest rate and there is no deadweight loss.
(f) Savings increases with an increase in the interest rate and there is no deadweight loss.
B: Now suppose that tastes can be summarized by the CES utility function u (c1, c2) = (0.5c1−ρ + 0.5c2−ρ) −1/ρ, where c1 is consumption in the first period and c2 is consumption in the second period.
(a) Are there values for ρ that would result in the scenario in A (a) and A (b)?
(b) Are there values for ρ that would result in the scenario in A (c)?
(c) Are there values for ρ that would result in the scenario in A (d)?
(d) Are there values for ρ that would result in the scenario in A (e) or A (f)?