Q.1 In the two-period consumption-savings model there is a current period and a future period, no investment, no government and no trade.
a) Derive the lifetime budget constraint for an individual consumer. What is the interpretation of this budget constraint?
b) Now assume that there is a role for government, derive the lifetime budget constraint for the government and interpret it.
c) Define a competitive equilibrium.
Q.2 Suppose that a consumer's future income increases and the real interest rate increases as well.
a) How does the relative price of the future consumption good in terms of the current consumption good, 1/(1+r) change? How does this effect the lifetime budget constraint the consumer faces?
b) Assuming the consumer is a lender, explain how the consumer's optimal choice of current consumption and future consumption changes from an initial equilibrium point to the new equilibrium and how savings changes. Discuss the income and substitution effects. Show your answer graphically as well.
c) Now assume the consumer is a borrower, explain how the consumer's optimal choice of current consumption and future consumption changes from an initial equilibrium point to the new equilibrium and how savings changes. Discuss the income and substitution effects. Show your answer graphically as well.