Wh What Youll ll Learn arn Today ay Review lifetime budget - PDF document

Revised Lifetime Budget Constraint, Borrowing, And Consumption Smoothing Aa Aaron Stevens EC1 EC171 71, 4 4 October 2011 1 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

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? , Splurge Tomorrow? Cy Cy + + Co/( Co/(1+r +r) = = W Starve Today, C 0 Consume The same When Young & Consume The same When Young & A • W(1+r +r) B • , Starve Tomorrow? Old? Old? C • Splurge Today, D • E • C y W

Wh What if Rates Ch Change? Li Lifeti etime e Budget Budget Cons Constr trai aint: nt: Cy + Cy + Co/( Co/(1+r +r) = = W C 0 With higher r, the Higher r Higher r same amount of saving W(1+r +r) will get you more future consumption. • C Lower r Lower r • C • W C y S A 2- A 2-Pe Period od 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 old: Co Co = Wo Wo + + S(1+r) Lifetim Lifetime e Budget Budget Constraint: onstraint: Cy Cy + Co/(1+r) = Wy Wy + + Wo Wo/(1 (1+r)

A A 2- 2-Pe Period od 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: onstraint: 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: onstraint: 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 ome 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.

Fami Fa milies es With h Debt ebt Wh What is the evidence say about borrowing? 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 Rea Reasons sons for or Bor orrow owing ng 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. Reas Reason for bo borrowing So Source: Su Survey of Co Consumer Fi Finances

Wh What if Rates Ch Change? Yo Your ur maximum um possible Co Co i increases but the bu he maxi aximum Cy Cy d decreases. Co Co Put Put di different ntly, y, borrow the same amount in order to keep consu am suming the th e in initia itial l Cy Cy bu but repayment gr grows! When r Wh r increases, , borrowers are worse off and len off enders ers are re better etter off. off. • Repay Repay Wo Wo • Wy Wy C y Borrow Bo 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.

Bu Building a Co Consump mption Smoot Smoothi hing ng Mode odel 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(consumption) = = PV(earnings) PV(consumpt PV(co 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. Wh What is the Present Value of of your our Fut Futur ure e Ea Earni nings? ngs? Find the e pres esen ent value e of future e ea earnings…

Wh What is the Present Value of of Li Lifet etime me Consump onsumption? on? 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 ou Sp Spend nd Pe Per Year? Consider er the e lifet fetime me budget et constraint: PV( PV(cons nsum umption) n) = PV( PV(earni nings ngs) We e can solve e fo for annual consump mption: Annua Annual MT ( r, PV(earnings ) umption = = PMT , years, , PV Co Cons nsum

How How Muc uch h Ca Can n You ou 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 ow t to I o Include N Net W Wor orth in in Lif ifetime ime B Budget C Con onstrain 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: PV( PV(cons nsum umption) n) = NW + PV( PV(earni nings ngs) Let et “wea ealth” = = NW + PV PV(ea earnings) Annua Annual MT ( r, , wealth ) umption = = PMT , years, Co Cons nsum

Our D Decis ision ion R Rule An Annual alized zed Lifet etime e Bu Budget dget Co Constrai raint: MT ( wealth, , years ) Annual Annua umption = = PMT Cons Co nsum 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. Maximize Your Standard of Living Ma Accept a choice if it increases your sustainable standard of living. Reject a choice if it decreases your sustainable standard of living. 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.

Announc Announceme ment nts and nd To o Do Do Readings: • FE, ch 4 (today) Before next Thursday’s class: Go to http://www.choosetosave.org/ballpark/ • read the introduction • do the interactive ballpark estimate • bring a print-out to class to discuss QUIZ 2 on Tuesday 10/11 Homework 3 (TVM problems) due Today