中级微观经济学课件辉英语第二章VIP

1、Chapter TwoBudgetary and Other Constraints on ChoiceContentsuDescribe budget constraintAlgebraGraphuDescribe changes in budget constraintuGovernment programs and budget constraintsuNon-linear budget linesConsumption Choice SetsuA consumption choice set is the collection of all consumption choices av

2、ailable to the consumer.uWhat constrains consumption choice?Budgetary, time and other resource limitations.Budget ConstraintsuA consumption bundle containing x1 units of commodity 1, x2 units of commodity 2 and so on up to xn units of commodity n is denoted by the vector (x1, x2, , xn).uCommodity pr

3、ices are p1, p2, , pn.Budget ConstraintsuQ: When is a consumption bundle (x1, , xn) affordable at given prices p1, , pn?Budget ConstraintsuQ: When is a bundle (x1, , xn) affordable at prices p1, , pn?uA: When p1x1 + + pnxn mwhere m is the consumers (disposable) income.Budget ConstraintsuThe bundles

4、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 .Budget 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

5、 is the upper boundary of the budget set.Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m. m /p1m /p2Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m.m /p2m /p1Budget Set and Constraint for Two Commoditiesx2x1Budget constraint i

6、sp1x1 + p2x2 = m.m /p1Just affordablem /p2Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m.m /p1Just affordableNot affordablem /p2Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m.m /p1AffordableJust affordableNot affordablem /p2

7、Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m.m /p1BudgetSet the collection of all affordable bundles.m /p2Budget Set and Constraint for Two Commoditiesx2x1p1x1 + p2x2 = m is x2 = -(p1/p2)x1 + m/p2 so slope is -p1/p2.m /p1BudgetSetm /p2Budget ConstraintsuIf n =

8、 3 what do the budget constraint and the budget set look like?Budget Constraint for Three Commoditiesx2x1x3m /p2m /p1m /p3p1x1 + p2x2 + p3x3 = mBudget Set for Three Commoditiesx2x1x3m /p2m /p1m /p3 (x1,x2,x3) | x1 0, x2 0, x3 0 and p1x1 + p2x2 + p3x3 mBudget ConstraintsuFor n = 2 and x1 on the horiz

9、ontal axis, the constraints slope is -p1/p2. What does it mean?xppxmp21212= = Budget 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.xppxmp21212= = Budget Constraintsx2x1Slope is -p1/p2+1-p1/p2Budget

10、Constraintsx2x1+1-p1/p2Opp. cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2.Budget 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. -p

11、2/p1+1Budget Sets & Constraints; Income and Price ChangesuThe budget constraint and budget set depend upon prices and income. What happens as prices or income change?How do the budget set and budget constraint change as income m increases?Originalbudget setx2x1Higher income gives more choiceOrig

12、inalbudget setNew affordable consumptionchoicesx2x1Original andnew budgetconstraints areparallel (sameslope).How do the budget set and budget constraint change as income m decreases?Originalbudget setx2x1How do the budget set and budget constraint change as income m decreases?x2x1New, smallerbudget

13、setConsumption bundlesthat are no longeraffordable.Old and newconstraintsare parallel.Budget Constraints - Income ChangesuIncreases in income m shift the constraint outward in a parallel manner, thereby enlarging the budget set and improving choice.Budget Constraints - Income ChangesuIncreases in in

14、come m shift the constraint outward in a parallel manner, thereby enlarging the budget set and improving choice.uDecreases in income m shift the constraint inward in a parallel manner, thereby shrinking the budget set and reducing choice.Budget Constraints - Income ChangesuNo original choice is lost

15、 and new choices are added when income increases, so higher income cannot make a consumer worse off.uAn income decrease may (typically will) make the consumer worse off.Budget Constraints - Price ChangesuWhat happens if just one price decreases?uSuppose p1 decreases.How do the budget set and budget

16、constraint change as p1 decreases from p1 to p1”?Originalbudget setx2x1m/p2m/p1m/p1”-p1/p2How do the budget set and budget constraint change as p1 decreases from p1 to p1”?Originalbudget setx2x1m/p2m/p1m/p1”New affordable choices-p1/p2How do the budget set and budget constraint change as p1 decrease

17、s 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”/p2Budget Constraints - Price ChangesuReducing the price of one commodity pivots the constraint outward. No old choice is lost and new choices are added,

18、 so reducing one price cannot make the consumer worse off.Budget Constraints - Price ChangesuSimilarly, increasing one price pivots the constraint inwards, reduces choice and may (typically will) make the consumer worse off.Uniform Ad Valorem Sales TaxesuAn ad valorem sales tax levied at a rate of 5

19、% 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.Uniform Ad Valorem Sales TaxesuA uniform sales tax levied at rate t changes the constraint

20、 from p1x1 + p2x2 = mto (1+t)p1x1 + (1+t)p2x2 = mUniform 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).Uniform Ad Valorem Sales Taxesx2x1mp2mp1p1x1 + p2x2 = mp1x1 + p2x2 = m/(1+t)mt p()11

21、mt p()12 Uniform Ad Valorem Sales Taxesx2x1mt p()12 mp2mt p()11 mp1Equivalent income lossismmtttm = = 11Uniform Ad Valorem Sales Taxesx2x1mt p()12 mp2mt p()11 mp1A uniform ad valoremsales tax levied at rate tis equivalent to an incometax levied at ratett1 .The Food Stamp ProgramuFood stamps are coup

22、ons that can be legally exchanged only for food.uHow does a commodity-specific gift such as a food stamp alter a familys budget constraint?The Food Stamp ProgramuSuppose m = $100, pF = $1 and the price of “other goods” is pG = $1.uThe budget constraint is then F + G =100.The Food Stamp ProgramGF1001

23、00F + G = 100: before stamps.The Food Stamp ProgramF + G = 100: before stamps.Budget set after 40 foodstamps issued.GF10010014040F + G = 100+40 for F=40.The Food Stamp ProgramGF100100F + G = 100: before stamps.Budget set after 40 foodstamps issued.140The familys budgetset is enlarged.40The Food Stam

24、p ProgramuWhat if food stamps can be traded on a black market for $0.50 each?u0.5*(F-40)+G=100 for F=40The Food Stamp ProgramGF100100F + G = 100: before stamps.Budget constraint after 40 food stamps issued.140120Budget constraint with black market trading.40The Food Stamp ProgramGF100100F + G = 100:

25、 before stamps.Budget constraint after 40 food stamps issued.140120Black market trading makes the budget set larger again.40Budget 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 2

26、x1 + 3x2 = 12.Budget Constraints - Relative PricesuThe constraint is also 1.x1 + (3/2)x2 = 6,the constraint for p1=1, p2=3/2, m=6. uSetting p1=1 makes commodity 1 the numeraire and defines all prices relative to p1; ue.g. 3/2 is the price of commodity 2 relative to the price of commodity 1. Budget C

27、onstraints - Relative PricesuAny commodity can be chosen as the numeraire without changing the budget set or the budget constraint.uA relative price is the rates of exchange of commodities 2 for units of commodity 1.Shapes of Budget ConstraintsuQ: What makes a budget constraint a straight line?uA: A

28、 straight line has a constant slope and the constraint is p1x1 + + pnxn = mso if prices are constants then a constraint is a straight line.Shapes 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

29、 curved.Shapes of Budget Constraints - Quantity DiscountsuSuppose p2 is constant at $1 but that p1=$2 for 0 x1 20 and p1=$1 for x120.Shapes 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 isu2x1+x2=m for 0 x1 20u(x1-20)+2*20+2x