[PDF] - Wh What Youll ll Learn arn Today ay Review lifetime budget PDF Document

SLIDE 1

1

Aa Aaron Stevens EC1 EC171 71, 4 4 October 2011

Revised Lifetime Budget Constraint, Borrowing, And Consumption Smoothing

Wh What You’ll ll Learn arn Today ay

Review lifetime budget constraint
What happens when interest rates

change?

What happens if you have income in both

periods?

How borrowing can improve (reduce) your

happiness.

Building an n-period consumption smoothing

model in Excel

SLIDE 2

Reca Recall: Li Lifetime Budget Co Constraint*

Let’s suppose r > 0. Recall: Cy + S = W Co = S + rS Co = S (1 + r) By algebraic magic: W = Cy + Co/(1+r) In words: lifetime earnings = lifetime consumption

* * No Taxes and/or Benefits

Wh When to Co Consume?

Wh Which point makes you the happiest?

Cy Cy + + Co/( Co/(1+r +r) = = W

W

W(1+r +r) C0 Cy A

C

E D B

Starve Today,

, Splurge Tomorrow? Consume The same When Young & Consume The same When Young & Old? Old? Splurge Today, , Starve Tomorrow?

SLIDE 3

Wh What if Rates Ch Change?

W W(1+r +r) C0 Cy

C

Higher r Higher r Lower r Lower r S

With higher r, the same amount of saving will get you more future consumption.

C

Li Lifeti etime e Budget Budget Cons Constr trai aint: nt: Cy Cy + + Co/( Co/(1+r +r) = = W

A A 2- 2-Pe Period

d Mod

Model With In Income in in B Both P Perio iods

Yo You re rece ceive inco come me in both h peri riods ds: Wy Wy an and Wo Wo. Yo You can can borro rrow w or r lend d at at rat rate r. Wh When young: Cy Cy = Wy Wy -

S

Wh When ol

ld:

Co Co = Wo Wo + + S(1+r) Lifetim Lifetime e Budget Budget Constraint:

nstraint:

Cy Cy + Co/(1+r) = Wy Wy + + Wo Wo/(1 (1+r)

SLIDE 4

A A 2- 2-Pe Period

d Mod

Model With In Income in in B Both P Perio iods

Yo You can can shi hift yo your r co consump mption over r time me by y borro rrowi wing or lend lending, ing, so long a so long as th the budget constraint is satisfi fied. Lifetim Lifetime e Budget Budget Constraint:

nstraint:

Cy Cy + Co/(1+r) = Wy Wy + + Wo Wo/(1 (1+r)

Exa Exampl ple: e: Co Consuming Future Income

Lifetim Lifetime e Budget Budget Constraint:

nstraint:

Cy Cy + Co/(1+r) = Wy Wy + + Wo Wo/(1 (1+r)

Exam Exampl ple: e: bo borro rrow agai against fu futu ture inc ncom

me to

to co consum ume e more re when en yo youn ung, g, so Cy y > Wy Wy (S (S is is ne negative). Rep Repay ay when hen old, d, so Co Co < Wo Wo.

SLIDE 5

Fa Fami milies es With h Debt ebt

Per Percen entag age e of fam amilies es ho holding debt, what kind of debt. So Source: Su Survey of Co Consumer Fi Finances Wh What is the evidence say about borrowing?

Rea Reasons sons for

r Bor
rrow
wing

ng

Reas Reason for bo borrowing So Source: Su Survey of Co Consumer Fi Finances

One subtle problem with the use of these data is that, even though money is borrowed for a particular purpose, it may be employed to offset some other use of funds. For example, a family may have sufficient funds to purchase a home without using a mortgage but may instead choose to finance the purchase to free existing funds for another purpose.

SLIDE 6

Wh What if Rates Ch Change?

Wy

Wy

Cy

Wo

Wo

Co Co Repay Repay

Bo Borrow Yo Your ur maximum um possible Co Co i increases bu but the he maxi aximum Cy Cy d decreases. Put Put di different ntly, y, borrow the same am amount in order to keep consu suming th the e in initia itial l Cy Cy bu but repayment gr grows! Wh When r r increases, , borrowers are worse

ff
ff and len

enders ers are re better etter off.

ff.

Ma Maximizing Your Happiness

Increase in interest rates makes future consumption cheaper, but current consumption more expensive. Borrowing can help us maximize utility by smoothing consumption.

SLIDE 7

Bu Building a Co Consump mption Smoot Smoothi hing ng Mode

del in

n Excel

We We can think of the N-period lifetime budget budget co constrai raint as as a a PV PV equal equality: y:

PV(co PV(consumpt sumptio ion) ) is is the he PV PV of f all all fu future consumption. PV(earn PV(earnin ings) gs) is is the he PV PV of f all all fut future ure ea earnings.

Let Let’s s build a rough sketch in Excel… Ig Ignor nore ta taxes, s, tr transfe nsfers, s, etc tc.

PV(consumption) = = PV(earnings)

Wh What is the Present Value

f
f your
ur Fut

Futur ure e Ea Earni nings? ngs?

Find the e pres esen ent value e of future e ea earnings…

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Wh What is the Present Value

f
f Li

Lifet etime me Consump

nsumption?
n?

Find the e pres esen ent-value e of f fu future e consump mption

Wh What does it mean when your li lifetime budget net-PV net-PV is negati negative? e? How How can an we we fix fix that?

How How Muc uch h Ca Can n You

u Sp

Spend nd Pe Per Year?

Consider er the e lifet fetime me budget et constraint: We e can solve e fo for annual consump mption:

PV( PV(cons nsum umption) n) = PV( PV(earni nings ngs) Annua Annual Co Cons nsum umption=

= PMT MT(r, , years, , PV

PV(earnings)

SLIDE 9

How How Muc uch h Ca Can n You

u Sp

Spend nd Pe Per Year?

Given en the e PV PV or ea earnings, solve e fo for annual consump mption (PM PMT fu function):

How

w t

to I

Include N

Net W Wor

rth in

in Lif ifetime ime B Budget C Con

nstrain

int?

Net et Worth (NW) is the e value e of f asset ets mi minus deb ebts. Since e NW is mea measured ed in PV PV, we e can add (subtract) NW in the e LBC equ equation: Let et “wea ealth” = = NW + PV PV(ea earnings)

PV( PV(cons nsum umption) n) = NW + PV( PV(earni nings ngs) Annua Annual Co Cons nsum umption =

= PMT MT(r, , years, , wealth)

SLIDE 10

Our D Decis ision ion R Rule

Annua Annual Co Cons nsum umption =

= PMT MT(wealth, , years)

An Annual alized zed Lifet etime e Bu Budget dget Co Constrai raint: Ma Maximize Your Standard of Living

Accept a choice if it increases your sustainable standard of living. Reject a choice if it decreases your sustainable standard of living. Your sustainable standard of living is the amount of annual consumption that can be sustained until your maximum age of life, given all of your economic resources.

Wh What You Learned Today

The e 2-per eriod lifet fetime me budget et constraint with income me in both per eriods. . Borrow/len end to hel elp ma maximi mize e your happines ess (utility) An An n-per eriod lifet fetime me budget et constraint can be written en as PV PV(consump mption) = PV PV(ea earnings), and solved ed fo for an annualized ed lev evel el of f consump mption (sustainable e standard of f living). Dec ecision rule: e: ma maximi mize e your sustainable standard of f living, given en your total economi mic res esources es.