EC4004 Lecture 20Consumption & Saving

Today

RecapConsumption Saving in 2 PeriodsSaving in n Periods

Stuff to Know

Static BCMulti Year Budget ConstraintEffects of changes in Investment

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Recall

Household budget constraint(Let π /P = 0)

– C + (1/P)·∆B+ ∆K = ( w/ P)·L + i·( B/ P + K)– consumption+ real saving = real income

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Consumption and Saving

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Consumption and Saving

Consumption Over Two YearsYear1

C1 + ( B1/ P + K1) − ( B0/ P + K0) = ( w/P)1 · L + i0 · ( B0/ P + K0)

consumption in year1 + real saving in year1 = real income in year1

Year2

C2 + ( B2/ P + K2) − ( B1/ P + K1) = ( w/ P) 2 · L + i1 · ( B1/ P + K1)

consumption in year 2 + real saving in year 2 = real income in year 2

So What?

Pensions.

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Consumption and SavingConsumption Over Two YearsCombine the budget constraints to describe a household’s choice between consuming this year, C1, and next year, C2.

– B1/P + K1 =

B0/P + K0 + i0·(B0/P + K0) + ( w/P)1·L− C1

– Real assets end year1 =

real assets end year0 + real income year1

− consumption year1

Chill.Be Like Fonzi.

I know.

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Consumption and Saving

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Consumption and Saving

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Consumption and Saving

Present valueIf the interest rate, i1, is greater than zero, €1 received or spent in year 1 is equivalent to more than €1 in year2.

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Consumption and Saving

Euros received or spent in year2 must be discounted to make them comparable to euros in year1.

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Consumption and Saving

The term 1+i1 is called a discount factor.

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Consumption and Saving

Choosing consumption: income effectsHousehold chooses the time path of consumption—in this case, C1 and C2—to maximize utility, subject to the budget constraint.

Consumption & Income Effects

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Consumption and Saving

Choosing consumption: income effects– C1 + C2/(1+i1) = (1+ i0)·(B0/P+K0) + (w/P)1 · L + (w/P)2·L/(1+i1) − ( B2/P+K2)/(1+i1)

– p.v. of consumption = value of initial assets + p.v. of wage incomes − p.v. of assets end year 2

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Consumption and Saving

Choosing consumption: income effects– V = ( 1 + i0)·(B0/P+K0) + (w/P)1·L + (w/P)2·L/

(1+i1)

– p.v. of sources of funds = value of initial assets + p.v. of wage incomes

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Consumption and Saving

Choosing consumption: income effects– C1 + C2/(1+i1) = V − (B2/P+K2)/(1+i1)

– p.v. of consumption = p.v. of sources of funds − p.v. of assets end year 2

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Consumption and Saving

Choosing consumption: income effects

Since households like to consume at similar levels in the two years, we predict that C1 and C2 will rise by similar amounts.

The responses of consumption to increases in initial assets or wage incomes are called income effects.

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Consumption and Saving

Choosing consumption: the intertemporal-substitution effect.– C1 + C2/(1+i1) = V − (B2/P+K2)/(1+i1)

– p.v. of consumption = p.v. of sources of funds − p.v. of assets end year 2

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A higher i1 provides a greater reward for deferring consumption.

Therefore, the household responds to an increase in i1 by lowering C1 and raising C2.

This response is called the intertemporal-substitution effect.

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Consumption and Saving

Choosing consumption: the intertemporal-substitution effect.– C1 + (B1/P + K1) − ( B0/P+K0) = (w/P)1·L +

i0·(B0/P +K0)

– Consumption in year1 + real saving in year1

= real income in year 1

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Consumption and Saving

Choosing consumption: the intertemporal-substitution effect.We know from the intertemporal-substitution effect that an increase in the interest rate, i1, motivates the household to postpone consumption, so that this year’s consumption, C1, falls on the left-hand side.

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Choosing consumption: the intertemporal-substitution effect.

Since year 1’s real income, (w/P)1 · L+ i0 · (B0/P + K0) on the right-hand side of equation (7.2), is given, the decline in C1 must be matched by a rise in year1’s s real saving, (B1/P + K1) − (B0/P + K0).

The intertemporal-substitution effect motivates the household to save more when the interest rate rises.

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Consumption and Saving

The income effect from a change in the interest rate– C2 + ( B2/ P + K2) − ( B1/ P + K1) =

( w/ P) 2 · L + i1 · ( B1/ P + K1)

The income effect from i1, [i1·(B1/P + K1)]

– i1(B1/P)

– i1K1

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Consumption and Saving

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Consumption and Saving

Consumption Over Many YearsTwo-year budget constraint

• C1 + C2/(1+i1) = (1+ i0)·(B0/P+K0) + (w/P)1 · L + (w/P)2·L/(1+i1) − ( B2/P+K2)/(1+i1)

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Consumption and Saving

Consumption Over Many YearsMultiyear budget constraint:

• C1 + C2/(1 + i1) + C3/[(1 + i1)·(1 + i2) ] + · · · =

(1+ i0)·(B0/P+K0) +

(w/P)1·L + (w/ P)2·L/(1+ i1) +

(w/P)2·L/[(1+i1)·(1+i2) ] + · · ·

Stuff to Know

Static BCMulti Year Budget ConstraintEffects of changes in Investment

Next Time

Business CyclesRecap on the Course

EC4004 Lecture 20Consumption & Saving