Presentation on theme: "Income and Substitution Effects"— Presentation transcript:
1 Income and Substitution Effects Chapter 5Income and Substitution Effects
2 Demand FunctionsThe optimal levels of x1,x2,…,xn can be expressed as functions of all prices and incomeThese can be expressed as n demand functions of the form:x1* = d1(p1,p2,…,pn,I)x2* = d2(p1,p2,…,pn,I)•xn* = dn(p1,p2,…,pn,I)If there are only two goods (x and y), we can simplify the notationx* = x(px,py,I)y* = y(px,py,I)Prices and income are exogenous
3 xi* = xi(p1,p2,…,pn,I) = xi(tp1,tp2,…,tpn,tI) HomogeneityIf all prices and income were doubled, the optimal quantities demanded will not changethe budget constraint is unchangedxi* = xi(p1,p2,…,pn,I) = xi(tp1,tp2,…,tpn,tI)Individual demand functions are homogeneous of degree zero in all prices and income
4 Changes in IncomeAn increase in income will cause the budget constraint to shift out in a parallel fashionSince px/py does not change, the MRS will stay constant as the individual moves to higher levels of satisfaction
5 Effects of a Rise in Income Income-consumption curve shows how consumption of both goods changes when income changes, while prices are held constant.Engel curve - the relationship between the quantity demanded of a single good and income, holding prices constant.
6 Effect of a Budget Increase on an Individual’s Demand Curve YL12.8eBudget Line, L1I126.7XIPXY =-XPYPYE1Price of X12Initial ValuesPX = price of X = $12PY = price of Y = $35I = Income = $419.D126.7X, BudgetIIncome goes up!Y1= $419E*126.7X
7 Effect of a Budget Increase on an Individual’s Demand Curve yL2YL14.8e22.8eBudget Line, L1I2I126.738.2XIPXY=-XPYPYEEPrice of X1212Initial ValuesPX = price of X = $12PY = price of Y = $35I = Income = $419.D2D126.738.2X, BudgetIIncome goes up!$628Y= $6282E*2Y= $4191E*126.738.2X
8 Effect of a Budget Increase on an Individual’s Demand Curve 2YL1Income-consumption curvee37.14.8e22.8eI3Budget Line, L1I2I126.738.249.1XIPXY =-XPYPYEEEPrice of X12123Initial ValuesPX = price of X = $12PY = price of Y = $35I = Income = $837.D3D2D126.738.249.1X, BudgetIEngel curve for XY= $837*3E3Income goes up again!Y= $6282E*2Y= $4191E*126.738.249.1X
9 Increase in IncomeIf both x and y increase as income rises, x and y are normal goodsAs income rises, the individual choosesto consume more x and yQuantity of yCU3BU2AU1Quantity of x
10 Normal and Inferior Goods • If the income consumption curve shows that the consumer purchases more of good x as her income rises, good x is a normal good.• Equivalently, if the slope of the Engel curve is positive, the good is a normal good.• If the income consumption curve shows that the consumer purchases less of good x as her income rises, good x is an inferior good.• Equivalently, if the slope of the Engel curve is negative, the good is an inferior good.
11 Increase in IncomeIf x decreases as income rises, x is an inferior goodAs income rises, the individual chooses to consume less x and more yQuantity of yCU3BU2AU1Quantity of x
12 Normal and Inferior Goods Example: Backward Bending ICC and Engel Curve – a good can be normal over some ranges and inferior over others
13 Income Consumption Curve: Normal and Inferior Goods
14 • • • Price Consumption Curves Is the set of optimal baskets for every possible price of good x, holding all other prices and income constant.Y (units)PY = $4I = $4010•Price Consumption Curve••PX = 1PX = 2PX = 4X (units)XA=2XB=10XC=1620
16 Individual Demand Curve: Properties 1) The level of utility that can be attained changes as we move along the curve.2) At every point on the demand curve, the consumer is maximizing utility by satisfying the condition thatMRS of X for Y = the ratio of the prices of X and Y.
17 Changes in a Good’s Price A change in the price of a good alters the slope of the budget constraintIt changes the MRS at the consumer’s utility-maximizing choicesWhen the price changes, two effects come into playsubstitution effectincome effect
18 The Substitution Effect As the price of x falls, all else constant, good x becomes cheaper relative to good y and vice versa.This change in relative prices alone causes the consumer to adjust his/ her consumption basket.This effect is called the substitution effect.The substitution effect always is negative.
19 Income EffectAs the price of x falls, all else constant, purchasing power rises and vice versa.This is called the income effect of a change in price.The income effect may be positive (normal good) or negative (inferior good).
20 Changes in a Good’s Price: Price of X falls U1ASuppose the consumer is maximizing utility at point A.Quantity of yU2BIf the price of good x falls, the consumer will maximize utility at point B.Total increase in xQuantity of x
21 Changes in a Good’s Price: Price of X falls Quantity of yTo isolate the substitution effect, we hold “real” income constant but allow the relative price of good x to changeThe substitution effect is the movementfrom point A to point CACThe individual substitutes x for y because it is now relatively cheaperSubstitution effectU1Quantity of x
22 Changes in a Good’s Price : Price of X falls The income effect occurs because “real” income changes when the price of good x changesQuantity of yBThe income effect is the movementfrom point C to point BIf x is a normal good,the individual will buy more because “real” income increasedIncome effectACU2U1Quantity of xTotal Effect or Price Effect(AB) = Substitution Effect (AC) Income Effect (CB)
23 Changes in a Good’s Price: Price of X rises Quantity of yAn increase in the price of good x meansthat the budget constraint gets steeperCThe substitution effect is themovement from point A to point CSubstitution effectAIncome effectThe income effect is themovement from point Cto point BBU1U2Quantity of xTotal Effect or Price Effect (AB) = Substitution Effect (AC) +Income Effect (CB)
24 Price Changes – Normal Goods If a good is normal, substitution and income effects reinforce one anotherwhen pX :substitution effect quantity demanded of Xincome effect quantity demanded of X when pX :substitution effect quantity demanded of X income effect quantity demanded of X
25 Price Changes – Inferior Goods If a good is inferior, substitution and income effects move in opposite directionswhen pX :substitution effect quantity demanded of X income effect quantity demanded of X when pX :substitution effect quantity demanded of X income effect quantity demanded of X
26 INCOME AND SUBSTITUTION EFFECTS: INFERIOR GOOD Consumer is initially at point A on RS.With a ↓ PFood, the consumer moves to point B.a substitution effect, F1E (associated with a move from A to D),an income effect, EF2 (associated with a move from D to B).In this case, food is an inferior good because the income effect is negative.
27 A Special Case: The Giffen Good Giffen good Good whose demand curve slopes upward because the (negative) income effect is larger than the substitution effect.Food: an inferior goodConsumer is initially at AAfter the ↓P of food, moves to B and consumes less food.The income effect F2F1 > the substitution effect EF2,Income effect dominates over the substitution effectThe ↓Pfood leads to a lower quantity of food demanded.UPWARD-SLOPING DEMAND CURVE: THE GIFFEN GOOD
28 Inferior good and Giffen Paradox For inferior goods, no definite prediction can be made for changes in pricethe substitution effect and income effect move in opposite directionsif the income effect outweighs the substitution effect, we have a case of Giffen’s paradoxGiffen Paradox: If the income effect of a price change is strong enough, there could be a positive relationship between price and quantity demandedan decrease in price leads to a increase in real incomesince the good is inferior, a increase in income causes quantity demanded to fall
29 The Individual’s Demand Curve An individual’s demand for x depends on preferences, all prices, and income:x* = x(px,py,I)It may be convenient to graph the individual’s demand for x assuming that income and the price of y i.e (py) are held constant
30 The Individual’s Demand Curve Quantity of yAs the priceof x falls...pxx’px’U1x1I = px’ + pyx’’px’’U2x2I = px’’ + pyx’’’px’’’x3U3I = px’’’ + pyx…quantity of xdemanded rises.Quantity of xQuantity of x
31 Shifts in the Demand Curve Three factors are held constant when a demand curve is derivedincomeprices of other goods (py)the individual’s preferencesIf any of these factors change, the demand curve will shift to a new positionDifference between a change in quantity demanded and change in demand
32 Compensated Demand Curve The demand curves shown so far have all been uncompensated, or Marshallian, demand curves.Consumer utility is allowed to vary with the price of the good.Alternatively, we have a compensated, or Hicksian, demand curve.It shows how quantity demanded changes when price increases, holding utility constant.
33 Compensated Demand Curves The actual level of utility varies along the demand curveAs the price of x falls, the individual moves to higher indifference curvesit is assumed that nominal income is held constant as the demand curve is derivedthis means that “real” income rises as the price of x falls
34 Compensated Demand Curves An alternative approach holds real income (or utility) constant while examining reactions to changes in pxthe effects of the price change are “compensated” so as to force the individual to remain on the same indifference curvereactions to price changes include only substitution effects
35 Compensated Demand Curves A compensated (Hicksian) demand curve shows the relationship between the price of a good and the quantity purchased assuming that other prices and utility are held constantThe compensated demand curve is a two-dimensional representation of the compensated demand functionx* = xc(px,py,U)
36 Compensated Demand Curves Holding utility constant, as price falls...Quantity of ypxx’px’Xc…quantity demandedrises.U2x’’px’’x’’’px’’’Quantity of xQuantity of x
37 Compensated & Uncompensated Demand x’’px’’At px’’, the curves intersect because the individual’s income is just sufficient to attain a certain utility levelpxxxcQuantity of x
38 Compensated & Uncompensated Demand x*x’px’At prices above px’’, income compensation is positive because the individual needs more income to remain on a certain utility levelpxpx’’xxcQuantity of x
39 Compensated & Uncompensated Demand pxx***x’’’px’’’At prices below px’’, income compensation is negative to prevent an increase in utility from a lower pricepx’’XxcQuantity of x
40 Compensated & Uncompensated Demand For a normal good, the compensated demand curve is less responsive to price changes than is the uncompensated demand curvethe uncompensated demand curve reflects both income and substitution effectsthe compensated demand curve reflects only substitution effects
41 The Response to a Change in Price We will use an indirect approach using the expenditure functionminimum expenditure = E(px,py,U)Then, by definitionxc (px,py,U) = x [px,py,E(px,py,U)]
42 The Response to a Change in Price xc (px,py,U) = x[px,py,E(px,py,U)]We can differentiate the function and get
43 The Response to a Change in Price The first term is the slope of the compensated demand curvethe mathematical representation of the substitution effect
44 The Response to a Change in Price The second term measures the way in which changes in px affect the demand for x through changes in purchasing powerthe mathematical representation of the income effect
45 The Slutsky Equation The substitution effect can be written as The income effect can be written as
46 The Slutsky EquationThe utility-maximization hypothesis shows that the substitution and income effects arising from a price change can be represented by
47 The Slutsky Equation The first term is the substitution effect always negativeThe second term is the income effectif x is a normal good, entire income effect is negativeif x is an inferior good, entire income effect is positive
48 Marshallian Demand Elasticities Most of the commonly used demand elasticities are derived from the Marshallian demand function x(px,py,I)Price elasticity of demand (ex,px)Income elasticity of demand (ex,I)Cross-price elasticity of demand (ex,py)
49 Price Elasticity of Demand The own price elasticity of demand is always negativethe only exception is Giffen’s paradoxThe size of the elasticity is importantif ex,px < -1, demand is elasticif ex,px > -1, demand is inelasticif ex,px = -1, demand is unit elastic
50 Compensated Price Elasticities It is also useful to define elasticities based on the compensated demand functionIf the compensated demand function isxc = xc(px,py,U)we can calculatecompensated own price elasticity of demand (exc,px)compensated cross-price elasticity of demand (exc,py)
51 Price ElasticitiesThe Slutsky equation shows that the compensated and uncompensated price elasticities will be similar ifthe share of income devoted to x is smallthe income elasticity of x is small
52 Consumer Welfare Consumer Surplus Suppose we want to examine the change in an individual’s welfare when price changesConsumer WelfareIf the price rises, the individual would have to increase expenditure to remain at the initial level of utilityexpenditure at px0 = E0 = E(px0,py,U0)expenditure at px1 = E1 = E(px1,py,U0)In order to compensate for the price rise, this person would require a compensating variation (CV) ofCV = E(px1,py,U0) - E(px0,py,U0)
53 Consumer Welfare Suppose the consumer is maximizing Quantity of ySuppose the consumer is maximizingutility at point A.U1BIf the price of good x rises, the consumer will maximize utility at point B.The consumer’s utility falls from U2 to U1AU2Quantity of x
54 Consumer Welfare Quantity of y The consumer could be compensated so that he can afford to remain on U2CCV is the amount that the individual would need to be compensatedCVABU2U1Quantity of x
55 Consumer Welfare When the price rises from px0 to px1, the consumer suffers a loss in welfarewelfare losspx1x1px0x0xc(px…U0)Quantity of x
56 Consumer WelfareA price change generally involves both income and substitution effectsshould we use the compensated demand curve for the original target utility (U0) or the new level of utility after the price change (U1)?
57 Consumer WelfareIs the consumer’s loss in welfare best described by area px1BApx0 [using xc(...,U1)] or by area px1CDpx0 [using xc(...,U0)]?pxIs U1 or U0 the appropriate utility target?CBpx1Apx0Dxc(...,U1)xc(...,U0)x1x0Quantity of x
58 Consumer WelfareWe can use the Marshallian demand curve as a compromisepxThe area px1CApx0 falls between the sizes of the welfare losses defined by xc(...,U1) and xc(...,U0)Cx(px,…)Bpx1Apx0Dxc(...,U1)xc(...,U0)x1x0Quantity of x
59 Consumer SurplusWe will define consumer surplus as the area below the Marshallian demand curve and above the prevailing market priceshows what an individual would pay for the right to make voluntary transactions at this pricechanges in consumer surplus measure the welfare effects of price changes
60 Compensating Variation versus Equivalent Variation p1 rises.Q: What is the least extra income that, at the new prices, just restores the consumer’s original utility level?A: The Compensating Variation.
61 Compensating Variation p1=p1’p2 is fixed.x2u1x1
62 Compensating Variation p1=p1’ p1=p1” (Price rise)p2 is fixed.x2u1u2x1
69 The effect on (behaviour and) welfare of a change in a price. Let us now look at these two variations with quasi-linear preferences....
70 Compensating vs. Equivalent Variation Quasi –linear Preferences
71 From Individual Demand to Market Demand The market demand function is the horizontal sum of the individual (or segment) demands.In other words, market demand is obtained by adding the quantities demanded by the individuals (or segments) at each price and plotting this total quantity for all possible prices.
72 Market Demand P P P 10 P = 10 - Q P = 4 – 0.2Q 4 Q Q Q Segment 1
73 Market Demand Two points should be noted: 1.The market demand curve will shift to the right as more consumers enter the market.2. Factors that influence the demands of many consumers will also affect market demand.The aggregation of individual demands into market becomes important in practice when market demands are built up from the demands of different demographic groups or from consumers located in different areas.
74 Network Externalities Up to this point we have assumed that people’s demands for a good are independent of one another.This assumption has led to obtain the market demand curve simply by summing individual’s demand.For some goods, one person’s demand also depends on the demands of other peopleIf one consumer's demand for a good changes with the number of other consumers who purchased the good, there are network externalitiesNetwork externality: When each individual’s demand depends on the purchases of other individuals.
75 Network Externalities Network externalities can be positive or negativeA positive network externality exists if the quantity of a good demanded by a consumer increases in response to an increase in purchases by other consumersNegative network externalities are just the opposite
76 Positive Network Externalities Bandwagon effect: A positive network externality that refers to the increase in each consumer’s demand for a good as more consumers buy the goodE.g: Toys for kids
77 Positive Network Externality: Bandwagon Effect Price($ perunit)D202040D4060D6080D80100D100When consumers believe morepeople have purchased theproduct, the demand curve shiftsfurther to the the right.Quantity(thousands per month)
78 Positive Network Externality: Bandwagon Effect Price($ perunit)D202040D4060D6080D80100D100The market demandcurve is found by joiningthe points on the individualdemand curves. It is relativelymore elastic.DemandQuantity(thousands per month)
79 Positive Network Externality: Bandwagon Effect Price($ perunit)D202040D4060D6080D80100D100But as more people buythe good, it becomesstylish to own it andthe quantity demandedincreases further.Suppose the price fallsfrom $30 to $20. If therewere no bandwagon effect,quantity demanded wouldonly increase to 48,000$30Demand48$20BandwagonEffectPure PriceEffectQuantity(thousands per month)
80 Network Externalities Snob effect: A negative network externality that refers to the decrease in each consumer’s demand as more consumers buy the goodThe snob effect refers to the desire to own exclusive or unique goodsThe quantity demanded of a “snob” good is higher the fewer the people who own it
81 Network Externality: Snob Effect Price($ perunit)DemandOriginally demand is D2,when consumers think 2,000people have bought a good.$30,000468D4D6D8However, if consumers think 4,000people have bought the good,demand shifts from D2 to D6 and itssnob value has been reduced.$15,000D2Pure Price EffectQuantity (thousandsper month)214
82 Network Externality: Snob Effect Quantity (thousandsper month)Price($ perunit)2DemandD2$30,000$15,00014468D4D6D8Pure Price EffectThe demand is less elastic and as a snob good its value is greatly reduced if more people own it.Net EffectSnob Effect
83 Revealed Preference Hypothesis The theory of revealed preference was proposed by Paul Samuelson in the year 1938.Considered major breakthrough in the theory of demand .It establishes law of demand without using IC and their respective assumptions.Assumptions:1) Rationality2) Consistency3) Transitivity4) Revealed Preference axiom
84 Revealed Preference Axiom Consider two bundles of goods: A and BIf the individual can afford to purchase either bundle but chooses A, we say that A had been revealed preferred to BThe chosen basket A maximizes (axiomatically) his utility and rest of the baskets on the budget line are revealed inferior.
85 Revealed Preference Hypothesis: Derivation of Demand Curve Initially consumer at B with budget line RS.A ↓ PF shifts budget line from RS to RT.The new market basket chosen must lie on line segment BT' of budget line R′T' (which intersects RS to the right of B), and the quantity of food consumed must be greater than at B.
86 The Weak and the Strong Axioms of the Revealed Preference Theory While listing the assumptions of the RPT, the ordering principles (consistency and transitivity) of consumer preferences are mentionedWe combine the ordering principles with the RP axioms to state and establish1) Weak Axiom of Revealed Preference (WARP)2) Strong Axiom of Revealed Preference (SARP)
87 Weak Axiom of Revealed Preference (WARP) If bundle (x1, y1) is directly revealed preferred to bundle (x2, y2), the two bundles being different from each other, it cannot happen that bundle (x2, y2) would be directly revealed preferred to bundle (x1, Y1).That is: If (x1,y1) is revealed preferred when (x2,y2) was affordable then (x1,y1) is preferred always (or at all prices).
88 Weak Axiom of Revealed Preference (WARP) If (x1, y1) is directly revealed preferred to (x2,y2), and the two bundles are not the same, then it cannot happen that (x2,y2) is directly revealed preferred to (x1, y1).This is the weak axiom of revealed preference (WARP)If this occurs then WARP is violated
89 Strong Axiom of Revealed Preference If commodity bundle 0 is revealed preferred to bundle 1, and if bundle 1 is revealed preferred to bundle 2, and if bundle 2 is revealed preferred to bundle 3,…, and if bundle K-1 is revealed preferred to bundle K, then bundle K cannot be revealed preferred to bundle 0If (x1,y1) is revealed preferred to (x3,y3) either directly or indirectly) then (x3,y3) cannot be directly or indirectly revealed preferred to (x1,y1)SARP is a necessary and sufficient condition for observed behaviour to be consistent with the underlying model of consumer choice