1、Chapter 2Consumer Behavior and Demand TheoryChapter 2 includes:n 2.1 Preference and Utilityn 2.2 Utilityization and Choicen 2.3 Income and Substitution Effectsn 2.4 Market Demand and Elasticity2Overview of Last Classn Assumptions of Consumers Preferencen Defining Utilityn How to Get Indifference Cur

2、ven Characteristic of Indifference Curven Diminishing MRS（邊際替代率遞減法則）32.2 Utilityization and Choicen 2.2.1 Budget Constraint(預算約束)n 2.2.2 Application of Budget Constraintn 2.2.3 Utility Optimal Choice)ization (Consumersn 2.2.4Types of Optimal Solution42.2 Utilityization and Choicen 2.2.1 Budget Const

3、raint(預算約束)n 2.2.2 Application of Budget Constraintn 2.2.3 Utility Optimal Choice)ization (Consumersn 2.2.4Types of Optimal Solution51.Budget Constraint Set（預算約束集）n An individuals budget constraint Set (Consumption Choice set) is the set that income places on the combinations ofgoods and services th

4、at acan buy.n 預算約束集是指消費者利用其收入所能購買到的商品和勞務的一系列消費組合的集合。6Budget Sets and Constraintsn Consumption bundle: (x1, x2, , xn)n Commodity prices: p1, p2, , pnn Budget set defined by income constraint:+ + pnxn £ Ip1x1x1 ³ 0, , xn ³ 0n I = consumers (disposable) income（可支配收入）n Budget constraint l

5、ine assumes all income is spentn p1x1 + + pnxn = In Is thus upper boundary of budget set（預算約束集的上邊界）7Budget Set, Constraint for Two GoodsBudget constraint is p1x1 + p2x2 = IIntercepts（截距） are I/p1and I/p2x2I /p2x1I /p18Budget Set, Constraint for Two Goodsx2I /p2Budget constraint isp1x1+ p2x2= Ix1I /p

6、19Budget Set, Constraint for Two Goodsx2Budget constraint isI /p2p1x1+ p2x2 = I.Just affordablex1I /p110Budget Set, Constraint for Two Goodsx2I /pBudget constraint is2p1x1+ p2x2 = I.Not affordable Just affordablex1I /p111Budget Set, Constraint for Two Goodsx2I /pBudget constraint is2p1x1+ p2x2 = I.N

7、ot affordable Just affordableAffordable with cash leftx1I /p112Budget Set, Constraint for Two Goodsx2I /p2Budget constraint isp1x1+ p2x2 = ICollection of all affordable bundlesBudget Setx1I /p113Budget Set, Constraint for Two Goodsx2I /p2Budget Setx1I /p114Budget Constraint (2 Goods)x2Slope is - p1/

8、p2-p1/p2+1x1152. Changes in Budget Constraint Setn (1)Effects of changes in income I;n (2) Effects of changes in price(P1,P2).16(1)Effects of increase in income INew affordable consumptionx2choices budget set expandsOriginal and new budget constraints are parallel (same slope).Original budget setx11

9、7(1)Effects of decrease in income mx2Consumption bundles that are no longer affordable.Old and new constraints are parallel.x1New, smaller budget set18(2)Effects of p1Decrease from p1 to p1”x2I/p2-p1/p2Original budget setI/p1”I/p1x119(2)Effects of p1 decrease from p1 to p1”x2I/p2New affordable choic

10、esBudget constraint pivots; slope flattensfrom -p1/p2 to-p1”/p2-p1”/p2-p1/p2Original budget setI/p1I/p1”x120(2)Effects of p1 increase from p1 to p1”x2I/p2New affordable choicesBudget constraintpivots; slope is steeper from -p1/p2 to-p /p-p1”/p212New, smaller budget set-p1”/p2I/p1”I/p1x1212.2 Utility

11、ization and Choicen 2.2.1 Budget Constraint(預算約束)n 2.2.2 Application of Budget Constraintn 2.2.3 Utility Optimal Choice)ization (Consumersn 2.2.4Types of Optimal Solution221. Sales Taxes and budget constraintn Proportional or ad valorem sales tax（從價稅）n Levied at proportional rate tn Increases price

12、from p to (1+t)pn Changes budget constraint to(1+t)p1x1 + (1+t)p2x2p1x1 + p2x2 = I/(1+t).= I23Uniform AdValorem Sales Taxesx2p1x1+ p2x2= IIp 2 I p1x124Uniform AdValorem Sales Taxesx2 I p 2p1x1 + p2x2 = Ip1x1+ p2x2= I/(1+t)I(1 + t) p2x1 I(1+ t) p1 I p125Uniform AdValorem Sales Taxesx2IEquivalent inco

13、me lossp2ItI -=II1 + t1 + t(1 + t) p2x1 Ip 1 I(1+t)p1262. A Budget Set With Rationing（實物配給）+£p 1 x 1x 1£pxI22x 127x1Taxing Consumption Greater Than283.The Food Stamp Program（食品券）n Food stampsn Popular income support programn Coupons（優待券） given to poor (used to be sold)n Can be legally exch

14、anged only for foodn Popular with some donors (“in kink” transfers)n Popular with agricultural interests29The Food Stamp Programn What is effect on budget constraint?n Suppose I = $100n pF = $1n Price of “all other goods” is pG = $1n Budget constraint isF + G =100n Key factor: Income available for “

15、other goods” does not change with receipt of food stampsn Suppose receive food stamps good for 40 units of food30The Food Stamp ProgramGF + G = 100, before food stamps100F10031The Food Stamp Program（食品券計劃）GF + G = 100: before stamps100Budget set after 40 food stamps issuedF4010014032The Food Stamp P

16、rogramG100Welfare up since budget set is enlargedF4010014033The Food Stamp Programn If food stamp program is generous, families may be at “kink”（折彎處） of budget setn What if food stamps can be traded on a black market for $0.50 each?34The Food Stamp ProgramG120100Budget constraint with black market t

17、rading,$0.50 on dollarF4010014035The Food Stamp ProgramGBlack market trading expands budget set further120100F40100140364.Quantity-Based Prices（以數量為基礎的價格）n Price may be a function of quantityn Discounts for large buyers, or,n Penalties for buying “too much”n Budget constraints “kinked” where p chang

18、esn Suppose quantity discount:n p2 constant at $1 and I=100n p1=$2 for 0 £ x1 £ 20; -p1/p2 = -2n p1=$1 for x1>20; -p1/p2 = -137Budget Constraints / Quantity Discountx2100I = $10020 units p=2 60 units p=1Slope = - 2Slope = - 1x180205038Budget Constraints / Quantity Discountx2I = $100100B

19、udget ConstraintBudget Setx180205039Budget Constraints / Quantity Penaltyx2Budget ConstraintBudget Setx1402.2 Utilityization and Choicen 2.2.1 Budget Constraint(預算約束)n 2.2.2 Application of Budget Constraintn 2.2.3 Utility Optimal Choice)ization (Consumersn 2.2.4Types of Optimal Solution41Utilityizat

20、ion（效用最大化）n An individual can afford all bundles of X and Y that fall within the budget constraint represented by the shaded area in Figure 2.7.n Point A is affordable but not all of the consumers income would be spent.n Point B is affordable but is not on the highest indifference curve that can be

21、reached by the consumer.42FIGURE 2.7: Graphic Demonstration of Utility izationX2BDIncomeU3X2*CU2U1A0X1*X143Utilityizationn Point D is on a higher indifference curve than C, but is not affordable given the budget constraint.n Point C, where the consumer chooses X1*,X2*is the point that is affordable

22、that lies onthe highest indifference curve, so itrepresents utilityization.44UtilityizationOptimal Choicen At point C all income is spent.n At point C indifference curve U2 to the budget line so that theis tangentSlope of budget constraint = Slope of indifferen ce curveP1n or= MRS.P245Optimal choice

23、: Typically where slope of indifference curve equals slope budget line¶u( x1, x2 )¶x1MU1p1MRS=¶u( x1, x2 )¶x212MUp22Rewrite this condition as:MU1= MU 2p1p2The marginal utility of the last penny spent on each good is the same46An example with well behavedpreferencesu = x0.5 + x0.5

24、Max.12+ p2 x2 = Ip1x1S.T.= 0.5= 0.5MUMU1x0.52x0.512p2xpMRS = ( 2 )x1=p1 x1 =0.5 1p2 2 x2p1Use this in the budget constraint to solve for the demand function for x1,x2:pp=x1Ix2+I2+p pp1p pp21211247The Lagrangean approach is an alternative approach for Constrained optimization problemL( x1, x2 , l ) =

25、 u( x1 , x2 ) - l p1x1+ p2 x2- I The budget constraintTake first order necessary conditions forum¶¶u(x1, x2 ) - lpu(x , x)- lp = 0= 01212¶x¶x12p1x1 + p2 x2 - I = 048Utility is to beised2.2 Utilityization and Choicen 2.2.1 Budget Constraint(預算約束)n 2.2.2 Application of Budget Const

26、raintn 2.2.3 Utility Optimal Choice)ization (Consumersn 2.2.4Types of Optimal Solution491.Optimal choice with well behaved preferencesinterior solution50Optimal choice with well behaved preferences interior solution2.Optimal choice with not well-behaved preferencesCorner Solution(角解)The tangency condition will not hol