Budget ConstraintsEdward MoreyEdward Morey: draft Oct 24, 2012This lecture covers the topic of budget constraints.Economics is all about modeling behavior in a world of scarcity.(Note that a bunch of the material in this lecture is not covered in KW.)For the individual, scarcity represents itself in terms of constraint on herbehavior–the consumer’s consumption is constrained/limited by what she can,and cannot, a¤ord. Your budget constraint is is one of two factors that deter-mine what you purchase and do not purchase, and why demand curves slopedown. The other factor is your preference ordering (ranking of bundles).Imagine that you have only two options: spending quality time shoppingwith your boyfriend (all he wants to do is shop) or going snow- boarding atEldora ski area. (In this world, going to school is not an option; you are eithershopping or boarding.)Your boyfriend neither skis nor boards, so if you board you are on your own.The week has 168 hours and you are constrained to sleep at least 12 hours anight (you badly need your beauty sleep). So you have 168  12(7) = 84 hoursto shop and ski.Let pSbe the money cost of a shopping trip with the boyfriend (gas, cloths,co¤ee, etc.) and let pBbe the money cost of a trip to Eldora to board (gas, liftticket, lunch)Further assume it requires 4 hours for each shopping trip (boyfriend getsbogged down in the shoe department), tS= 4, and it takes 7 hours for a tripto Eldora, tB= 7. So tSis the time cost of a shopping trip and tBis the timecost of a boarding trip.1Given your kind, and rich parents, you have m dollars a week to spend onboarding without boyfriend, and shopping with boyfriend.What combinations of shopping and boarding trips can you a¤ord?2Let S b e your number of shopping trips with what’s-his-name and let B bethe number of trips to Eldora.1 Budget constraint in terms of moneyYour budget constraint, in terms of money, ispsS + pBB  mThe total amount of money you spend on shopping and boarding cannot bemore than you have.How many shopping trips can you a¤ord if all you do is shop?mpSHow many Eldora trips can you a¤ord if all you do is board?mpBIf you spend all of your money on shopping and boarding (likely, nothingelse to do)psS + pBB = mSolving this for S one getsS =mpSpBpsBThis says what? If you spend all of your money on shopping, you can buympStrips. But every time you take another trip to Eldora (B increases by one),the number of shopping trips you can a¤ord in terms of money declines bypBps,pBpsis the slope of the line.For example , if pS= $150 (it is expensive to shop with boyfriend) andpB= 60, every time you take another trip to Eldora you give uppBps=60150=0:4 shopping trips. Ignoring the time constraint, this is your opportunity costof boarding: how many shopping trips you give up every time you take anotherboarding trip.Said another way, the opportunity cost of a shopping trip ispSpB=15060= 2:5 boarding trips.3Let’s graph your budget constraint (budget set) assuming you have $2000 aweek to spend on boarding without him or shopping with him.S =200015060150B = 13: 333  0:4B. (Draw this as well on the ‡oor.)0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32024681012BSbudget constraint: m=2000, ps=150, pb=60In terms of money, you can a¤ort to board 30+ times a week.4If you are consuming a bundle to the left of the red line? If you consume abundle on the red line? To the right of the red line?What happens after the stock market crashes and your parents cut yourweekly allowance back to $500Red budget line is S =200015060150BOrange budget line is S =50015060150B0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32024681012BSred: m=2000, ps=150, pb=60, orang: m=500, ps=150, pb=605Recessions suck: your demand for both shopping trips and boarding tripsdeclines because of the drop in your "income."Alternatively what happens if your allowance stays at $2000 =week (yourfamily is recession proof) and Nordstrom’s slashes their prices because of therecession, causing pSto decrease from $150 to $90?Red budget line is S =200015060150BBlue budget line is S =2000906090B0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 3205101520BSred: m=2000, ps=150, pb=60, blue: m=2000, ps=90, pb=60Recessions have their silver linings. The recession makes you better o¤. Youcan now a¤or more bundles. Some of us, those on …xed salaries, are made bettero¤ if a recession causes prices to fall.62 Budget constraint in terms of timeBut wait a minute, or an hour - it takes time to board and shop.Don’t you also have a time constraint in addition to your money cons traint?We have just been looking at your money budget constraint: psS +pBB  mYou also have a time constrainttsS + tBB  84tBand tSare the time prices of boarding and shopping, in contrast to the moneyprices.Continue to assume that tS= 4 and tB= 7, so4S + 7B  84Solving this for S, assuming you have to spend all of your time shopping orboarding (there is nothing else to do)one gets S =84474B = 21:0  1: 75B7Graphing the time constraint:S =84474B0 1 2 3 4 5 6 7 8 9 10 11 1205101520BSTime constraint: 84hrs, tb=7, ts=4in terms of time, you can only a¤ort to board 10+ timesIf you spend all of your time boarding and skiing you will be? Not all ofyour time? Can you be to the right of the line?83 Budget constraint in terms of time and moneyYou are constrained to not violate your time constraint or your money con-straint.Continuing to assume m = 2000, pB= 60 and ps= 150Your money budget line is S =200015060150B; it is drawn in red.Your time budget line is S =84474B; it is drawn in black0 1 2 3 4 5 6 7 8 9 10 11 1205101520BSBlack is budget line wrt time, red wrt moneyYour life is complicated. You cannot violate either your time constraint oryour money constraint. What can you a¤ord?Are you likely to spend all of your time and all of your money boarding andshopping? Maybe, just maybe, but, in general, NO.What happens if you have time or money left over?If both shopping and b oarding are goods (more is always preferred to less)will you choose a point on your kinked budget line?YESWhat determines which point you will choose?9YOUR PREFERENCESWhat is your opportunity cost of taking another trip to Eldora?The answer depends on where you are on your budget constraint.10Your T.A.s are busily working making up multiple-choice problems with twomore more budget constraints.Let’s take a look at some of the money budget constraint stu¤ in KW (theychoose, for