上财中级微观经济学Ch02Budget-PPT课件.pptx

2024/10/3 周四1Consumption Choice SetsuA consumption choice set is the collection of all consumption choices available to the consumer.uWhat constrains consumption choice?Budgetary,time and other resource limitations.2024/10/3 周四2Budget ConstraintsuA consumption bundle containing n commodities is denoted by the vector (x1,x2,xn).uCommodity prices are p1,p2,pn.2024/10/3 周四3Budget ConstraintsuThe bundles that are only just affordable form the consumers budget constraint.This is the set(x1,xn)|x1 0,xn 0 0 and p1x1+pnxn=m.2024/10/3 周四4Budget ConstraintsuThe consumers budget set is the set of all affordable bundles;B(p1,pn,m)=(x1,xn)|x1 0,xn 0 and p1x1+pnxn m uThe budget constraint is the upper boundary of the budget set.2024/10/3 周四5Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1+p2x2=m.m/p1m/p22024/10/3 周四6Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1+p2x2=m.m/p2m/p12024/10/3 周四7Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1+p2x2=m.m/p1Just affordablem/p22024/10/3 周四8Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1+p2x2=m.m/p1Just affordableNot affordablem/p22024/10/3 周四9Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1+p2x2=m.m/p1AffordableJust affordableNot affordablem/p22024/10/3 周四10Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1+p2x2=m.m/p1BudgetSet the collection of all affordable bundles.m/p22024/10/3 周四11Budget Set and Constraint for Two Commoditiesx2x1p1x1+p2x2=m is x2=-(p1/p2)x1+m/p2 so slope is-p1/p2.m/p1BudgetSetm/p22024/10/3 周四12Budget ConstraintsuIf n=3 what do the budget constraint and the budget set look like?2024/10/3 周四13Budget Constraint for Three Commoditiesx2x1x3m/p2m/p1m/p3p1x1+p2x2+p3x3=m2024/10/3 周四14Budget Set for Three Commoditiesx2x1x3m/p2m/p1m/p3(x1,x2,x3)|x1 0,x2 0,x3 0 and p1x1+p2x2+p3x3 m2024/10/3 周四15Budget ConstraintsuFor n=2 and x1 on the horizontal axis,the constraints slope is-p1/p2.What does it mean?2024/10/3 周四16Budget ConstraintsuFor n=2 and x1 on the horizontal axis,the constraints slope is-p1/p2.What does it mean?uIncreasing x1 by 1 must reduce x2 by p1/p2.2024/10/3 周四17Budget Constraintsx2x1Slope is-p1/p2+1-p1/p22024/10/3 周四18Budget Constraintsx2x1+1-p1/p2Opp.cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2.2024/10/3 周四19Budget Constraintsx2x1Opp.cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2.And the opp.cost of an extra unit of commodity 2 is p2/p1 units foregone of commodity 1.-p2/p1+12024/10/3 周四20How do the budget set and budget constraint change as income m increases?Originalbudget setx2x12024/10/3 周四21Higher income gives more choiceOriginalbudget setNew affordable consumptionchoicesx2x1Original andnew budgetconstraints areparallel(sameslope).2024/10/3 周四22How do the budget set and budget constraint change as income m decreases?Originalbudget setx2x12024/10/3 周四23How do the budget set and budget constraint change as income m decreases?x2x1New,smallerbudget setConsumption bundlesthat are no longeraffordable.Old and newconstraintsare parallel.2024/10/3 周四24Budget Constraints-Income ChangesuIncreases in income m shift the constraint outward in a parallel manner,thereby enlarging the budget set and improving choice.2024/10/3 周四25How do the budget set and budget constraint change as p1 decreases from p1 to p1”?Originalbudget setx2x1m/p2m/p1m/p1”-p1/p22024/10/3 周四26How do the budget set and budget constraint change as p1 decreases from p1 to p1”?Originalbudget setx2x1m/p2m/p1m/p1”New affordable choices-p1/p22024/10/3 周四27How do the budget set and budget constraint change as p1 decreases from p1 to p1”?Originalbudget setx2x1m/p2m/p1m/p1”New affordable choicesBudget constraint pivots;slope flattens from-p1/p2 to -p1”/p2-p1/p2-p1”/p22024/10/3 周四28Budget Constraints-Price ChangesuReducing the price of one commodity pivots the constraint outward.No old choice is lost and new choices are added,so reducing one price cannot make the consumer worse off.2024/10/3 周四29Budget Constraints-Price ChangesuSimilarly,increasing one price pivots the constraint inwards,reduces choice and may(typically will)make the consumer worse off.2024/10/3 周四30Uniform Ad Valorem Sales TaxesuAn ad valorem sales tax levied at a rate of 5%increases all prices by 5%,from p to(1+0.05)p=1.05p.uAn ad valorem sales tax levied at a rate of t increases all prices by tp from p to(1+t)p.uA uniform sales tax is applied uniformly to all commodities.2024/10/3 周四31Uniform Ad Valorem Sales TaxesuA uniform sales tax levied at rate t changes the constraint from p1x1+p2x2=mto (1+t)p1x1+(1+t)p2x2=m2024/10/3 周四32Uniform Ad Valorem Sales TaxesuA uniform sales tax levied at rate t changes the constraint from p1x1+p2x2=mto (1+t)p1x1+(1+t)p2x2=mi.e.p1x1+p2x2=m/(1+t).2024/10/3 周四33Uniform Ad Valorem Sales Taxesx2x1p1x1+p2x2=m2024/10/3 周四34Uniform Ad Valorem Sales Taxesx2x1p1x1+p2x2=mp1x1+p2x2=m/(1+t)2024/10/3 周四35Uniform Ad Valorem Sales Taxesx2x1Equivalent income lossis2024/10/3 周四36Uniform Ad Valorem Sales Taxesx2x1A uniform ad valoremsales tax levied at rate tis equivalent to an incometax levied at rate2024/10/3 周四37The Food Stamp ProgramuFood stamps are coupons that can be legally exchanged only for food.uHow does a commodity-specific gift such as a food stamp alter a familys budget constraint?2024/10/3 周四38The Food Stamp ProgramuSuppose m=$100,pF=$1 and the price of“other goods”is pG=$1.uThe budget constraint is then F+G=100.2024/10/3 周四39The Food Stamp ProgramGF100100F+G=100;before stamps.2024/10/3 周四40The Food Stamp ProgramGF100100F+G=100:before stamps.2024/10/3 周四41The Food Stamp ProgramGF100100F+G=100:before stamps.Budget set after 40 foodstamps issued.140402024/10/3 周四42The Food Stamp ProgramGF100100F+G=100:before stamps.Budget set after 40 foodstamps issued.140The familys budgetset is enlarged.402024/10/3 周四43The Food Stamp ProgramuWhat if food stamps can be traded on a black market for$0.50 each?2024/10/3 周四44The Food Stamp ProgramGF100100F+G=100:before stamps.Budget constraint after 40 food stamps issued.140120Budget constraint with black market trading.402024/10/3 周四45The Food Stamp ProgramGF100100F+G=100:before stamps.Budget constraint after 40 food stamps issued.140120Black market trading makes the budget set larger again.402024/10/3 周四46Budget Constraints-Relative Pricesu“Numeraire”means“unit of account”.uSuppose prices and income are measured in dollars.Say p1=$2,p2=$3,m=$12.Then the constraint is 2x1+3x2=12.2024/10/3 周四47Budget Constraints-Relative PricesuIf prices and income are measured in cents,then p1=200,p2=300,m=1200 and the constraint is 200 x1+300 x2=1200,the same as 2x1+3x2=12.uChanging the numeraire changes neither the budget constraint nor the budget set.2024/10/3 周四48Budget Constraints-Relative PricesuThe constraint for p1=2,p2=3,m=12 2x1+3x2 =12 is also 1.x1+(3/2)x2=6,the constraint for p1=1,p2=3/2,m=6.Setting p1=1 makes commodity 1 the numeraire and defines all prices relative to p1;e.g.3/2 is the price of commodity 2 relative to the price of commodity 1.2024/10/3 周四49Budget Constraints-Relative PricesuAny commodity can be chosen as the numeraire without changing the budget set or the budget constraint.2024/10/3 周四50Budget Constraints-Relative Pricesup1=2,p2=3 and p3=6 uprice of commodity 2 relative to commodity 1 is 3/2,uprice of commodity 3 relative to commodity 1 is 3.uRelative prices are the rates of exchange of commodities 2 and 3 for units of commodity 1.2024/10/3 周四51Shapes of Budget ConstraintsuQ:What makes a budget constraint a straight line?uA:A straight line has a constant slope and the constraint is p1x1+pnxn=mso if prices are constants then a constraint is a straight line.2024/10/3 周四52Shapes of Budget ConstraintsuBut what if prices are not constants?uE.g.bulk buying discounts,or price penalties for buying“too much”.uThen constraints will be curved.2024/10/3 周四53Shapes of Budget Constraints-Quantity DiscountsuSuppose p2 is constant at$1 but that p1=$2 for 0 x1 20 and p1=$1 for x120.2024/10/3 周四54Shapes of Budget Constraints-Quantity DiscountsuSuppose p2 is constant at$1 but that p1=$2 for 0 x1 20 and p1=$1 for x120.Then the constraints slope is -2,for 0 x1 20-p1/p2=-1,for x1 20and the constraint is2024/10/3 周四55Shapes of Budget Constraints with a Quantity Discountm=$1005010020Slope=-2/1=-2 (p1=2,p2=1)Slope=-1/1=-1 (p1=1,p2=1)80 x2x12024/10/3 周四56Shapes of Budget Constraints with a Quantity Discountm=$1005010020Slope=-2/1=-2 (p1=2,p2=1)Slope=-1/1=-1 (p1=1,p2=1)80 x2x12024/10/3 周四57Shapes of Budget Constraints with a Quantity Discountm=$100501002080 x2x1Budget SetBudget Constraint2024/10/3 周四58Shapes of Budget Constraints with a Quantity Penaltyx2x1Budget SetBudget Constraint2024/10/3 周四59Shapes of Budget Constraints-One Price NegativeuCommodity 1 is stinky garbage.You are paid$2 per unit to accept it;i.e.p1=-$2.p2=$1.Income,other than from accepting commodity 1,is m=$10.uThen the constraint is -2x1+x2=10 or x2=2x1+10.2024/10/3 周四60Shapes of Budget Constraints-One Price Negative10Budget constraints slope is-p1/p2=-(-2)/1=+2x2x1x2=2x1+102024/10/3 周四61Shapes of Budget Constraints-One Price Negative10 x2x1 Budget set is all bundles for which x1 0,x2 0 andx2 2x1+10.2024/10/3 周四62More General Choice SetsuChoices are usually constrained by more than a budget;e.g.time constraints and other resources constraints.uA bundle is available only if it meets every constraint.2024/10/3 周四63More General Choice SetsFoodOther Stuff10At least 10 units of foodmust be eaten to survive2024/10/3 周四64More General Choice SetsFoodOther Stuff10Choice is further restricted by a time constraint.2024/10/3 周四65More General Choice SetsSo what is the choice set?2024/10/3 周四66More General Choice SetsFoodOther Stuff102024/10/3 周四67More General Choice SetsFoodOther Stuff102024/10/3 周四68More General Choice SetsFoodOther Stuff10The choice set is theintersection of all ofthe constraint sets.