1. Consumption & Saving Over Two Periods Consumption and Saving Effects of Changes in Income Effects of Interest Rates

2. One Period Macro Model: Very Clean! Microeconomic foundations of decisions. Endogenous – GDP, consumption, labor, real wages. Competitive Equilibrium vs. Pareto Optimality Effects of productivity shocks, fiscal policy (taxes & government spending)

3. Problem – Lacks time dimension (e.g. dynamics). Cannot discuss other macroeconomic variables defined by time: Savings vs consumption Interest Rates Money supply growth & Inflation Taxes & Budget Deficits Economic Growth

4. Simple Two Period Model of Consumption Two Periods (t = 1,2) Income y t is exogenous (NO firms). Individuals consume c t in each period and can borrow or lend amount s at interest rate r: s > 0  lender s < 0  borrower Interest rate r is exogenous.

5. Present discounted value (PDV) is a way of measuring future value in terms of current values: The PDV of $(1+r) tomorrow is $1 today. The PDV of $1 tomorrow is $1/(1+r) today.

6. Households Chooses consumption in each period {c 1 *,c 2 *} given {y 1,y 2 } and r to subject to OR the inter-temporal (lifetime) budget constraint:

7. An optimal choice {c 1 *,c 2 *} given {y t } and r solves Example:

8. Changes in Income How does an exogenous change in y 1 and y 2 affect {c 1 *,c 2 *}? Results: dc t /dy 1 and dc t /dy 2 > 0 for t = 1,2 dc t /da 0 > 0 (Pure Income Effects)

9. Changes in Interest Rate How does an exogenous change in r affect {c 1 *,c 2 *}? Income Effects Lender: dc 1 /dr > 0 and dc 2 /dr > 0 (s > 0) Borrower: dc 1 /dr < 0 and dc 2 /dr < 0 (s < 0)

10. Substitution Effects Lender: dc 1 /dr 0 (s > 0) Borrower: dc 1 /dr 0 (s < 0)

11. Case I: y 1 < c 1 (borrower)

12. Case II: y 1 > c 1 (lender)

13. In the aggregate economy (without investment) s = 0  substitution effects dominate.

14. Case III: y 1 = c 1 (not borrower or lender)

15. Remarks Consumption between two individuals with different incomes vs consumption for an individual over time! The interest rate will ultimately be determined endogenously by closing the model with competitive equilibrium.