Consider a two-period model. A consumer has preferences for current versus futur
ID: 1176918 • Letter: C
Question
Consider a two-period model. A consumer has preferences for current versus future consumption represented by:
U(C,C') = C1/4C'3/4
Current income y=100, future income y' = 10, current taxes t=20, future taxes t=10. Interest rate is r=0.10 (10%). (Hint: Solve for a relationship between C and C' before using the budget constraint)
a) Solve for the consumer's optimal consumption bundle.
b) Now assume the interest rate changes from r=0.10 to r=0.05 (10% to 5%). Resolve for the consumer's optimal bundle. Explain the effects at work resulting from this change in the interest rate, and how they impacted both future and current consumption.
c) Suppose the consumer is now no longer able to lend (interest rate is still 5%). Without changes to government taxes, what is his new consumption bundle and level of utility?
d) Continue to assume the consumer cannot lend, but now allow the government to change the timing of taxation (and that interest rate is 5%). Assuming the government wishes to maximize the consumer's level of utility, what change would it make? What would be the consumer's new consumption bundle given this change?
e) Explain why the Ricardian Equivalence Theorem does not hold in this case.