Consumption & Saving Over Two Periods

Consumption and Saving

Effects of Changes in Income

Effects of Interest Rates

• 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)

• 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

Simple Two Period Model of Consumption

• Two Periods (t = 1,2)

• Income yt is exogenous (NO firms).

• Individuals consume ct 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.

• 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.

Households

• Chooses consumption in each period {c1*,c2*} given {y1,y2} and r to

subject to

OR the inter-temporal (lifetime) budget constraint:

),(max 21 ccu

scay 101

22 )1( crsy

r

cca

r

yywe

112

102

1

• An optimal choice {c1*,c2*} given {yt} and r solves

• Example:

)1(*)*,(

*)*,(

21

212,1

2

1 rccu

ccuMRS

c

ccc

21012 )1*)((* yrcayc

2/12

2/1121 ),( ccccu

Changes in Income

• How does an exogenous change in y1 and y2 affect {c1*,c2*}?

• Results:

dct/dy1 and dct/dy2 > 0 for t = 1,2

dct/da0 > 0

(Pure Income Effects)

Changes in Interest Rate

• How does an exogenous change in r affect {c1*,c2*}?

• Income Effects

Lender: dc1/dr > 0 and dc2/dr > 0

(s > 0)

Borrower: dc1/dr < 0 and dc2/dr < 0

(s < 0)

• Substitution Effects

Lender: dc1/dr < 0 and dc2/dr > 0

(s > 0)

Borrower: dc1/dr < 0 and dc2/dr > 0

(s < 0)

Case I: y1 < c1 (borrower)

Case II: y1 > c1 (lender)

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

Case III: y1 = c1 (not borrower or lender)

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.