北大光华本科微观作业micro-chapter4

pter 4 Chapter 4pIndividual and Market Demand T opics to be Discussed y Individual Demandy Income and Substitution Effects y Market Demandy Consumer Surplusy Empirical Estimation of DemandIndividual Demandy Price Changes◦Using the figures developed in the previouschapter, the impact of a change in the price of food can be illustrated using indifferencecurves◦For each price change, we can determine how much of the good the individual wouldpurchase given their budget lines andindifference curves Effect of a Price ChangeAssume:•I = $20•PC= $2Clothing10Each price leads toC$•P F = $2, $1, $0.50A Each price leads todifferent amounts offood purchased 5DB6U1U34U2Food (unitsper month)1220per month) 4Effect of a Price ChangeThe Price-Consumption Curve traces out the utility Clothing10traces out the utility maximizing market basket for each priceof food Aof foodB5D6U 14U 3U 2Food (unitsper month)1220per month)4Effect of a Price ChangeyBy changing prices andshowing what the Demand Schedule gconsumer will purchase, we can P Q create a demand schedule and demand fh i di id l $2.004curve for the individual yFrom the previous l$1.0012example:$0.5020Effect of a Price ChangePriceIndividual Demand relatesof FoodE$200the quantity of a good that a consumer will buy to the price of that good.$2.00G$100Demand Curve $1.00$Food (nitsH$.50Food (units per month)41220Demand Curves Demand Curves ––Important Properties The level of utility that can be attainedychanges as we move along the curvey At every point on the demand curve, theconsumer is maximizing utility byg y y satisfying the condition that the MRS of food for clothing equals the ratio of the prices of food and clothingEffect of a Price ChangePrice of FoodE$200When the price falls,&MRS also fall$2.002/21P f /P c & MRS also fall G$100•E : P f /P c = 2/2 = 1 = MRS•G: P f /P c = 1/2= .5 = MRS •H:P f /P c = .5/2 = .25 = MRS$1.00$50Food (unitsH$.50Demand CurveFood (units per month)41220Individual DemandyIncome Changes◦Using the figures developed in the previous chapter, the impact of a change in the income can be illustrated using indifference curves ◦Changing income, with prices fixed, causes consumers to change their market basketsEffects of Income ChangesCl thi Clothing (units per month)Assume: P f = $1, P c = $2I = $10, $20, $30An increase in income,with the prices fixed with the prices fixed,causes consumers to altertheir choice of market basket.D75B U 2U 3Food (units 3AU 1per month)41016Individual DemandyIncome Changes◦The income-consumption curve traces out the utility-maximizing combinations of food and clothing associated with every income levelIndividual DemandyIncome Changes◦An increase in income shifts the budget line to the right, increasing consumption along the income-consumption curve◦Simultaneously, the increase in income shifts the demand curve to the rightEffects of Income ChangesCl thi Clothing (units per month)The Income Consumption Curve traces out the utility maximizing market basket for maximizing market basket for each income levelD 7Income Consumption Curve5B U 2U 3Food (units 3AU 1per month)41016Effects of Income ChangesPrice of foodAn increase in income, from $10 to $20 to $30, with the prices fixed, shifts theconsumer’s demand curve to consumer’s demand curve to the right as well.$1.00E G HD 3Food (units D 1D 2(per month)41016Individual DemandyIncome Changes◦When the income-consumption curve has a positive slope:x The quantity demanded increases with income x The income elasticity of demand is positive x The good is a normal goodIndividual DemandyIncome Changes◦When the income-consumption curve has a negative slope:x The quantity demanded decreases with income x The income elasticity of demand is negative x The good is an inferior goodAn Inferior GoodSteak (units per Income-ConsumptionBoth hamburger and steak behave as a normal good month)CCurve10as a normal good, between A and B...U 3…but hamburger becomes an inferior good when the income good when the income consumption curve bends backward between B and C.5BHamburgerAU 1U 2(units per month)3010520Individual DemandyEngel Curves◦Engel curves relate the quantity of good consumed to income◦If the good is a normal good, the Engel curve is upward sloping◦If the good is an inferior good, the Engel curve g g ,g is downward slopingEngel Curves30Income ($ per month)Engel curves slope 20g pupward for normal goods.10F d (it Food (units per month)481216Engel Curves30Income ($ per Engel curves are Inferiormonth)backward bending for inferior goods.20Normal10F d (it Food (unitsper month)481216Substitutes & ComplementsT ywo goods are considered substitutes if an increase (decrease) in the price of one leads to an increase (decrease) in the quantity demanded of the other q y◦Ex: movie tickets and video rentalsSubstitutes & ComplementsT ywo goods are considered complements if an increase (decrease) in the price of one leads to a decrease (increase) in the quantity demanded of the other q y◦Ex: gasoline and motor oilSubstitutes & ComplementsIf two goods are independent then ayIf two goods are independent, then a change in the price of one good has no effect on the quantity demanded of the other◦Ex: price of chicken and price of airplane ticketsIncome and Substitution Effects A change in the price of a good has two yeffects:◦Substitution Effect◦Income Effect Income and Substitution Effects y Substitution Effect◦The substitution effect is the change in anitem’s consumption associated with a changein the price of the item, with the level ofutility held constant◦When the price of an item declines, thesubstitution effect always leads to an increase in the quantity demanded of the good◦Why is substitution effect alwaysnonpositive?pIncome and Substitution Effects y Income Effect◦The income effect is the change in an item’sconsumption brought about by the increase in purchasing power, with the price of the itemheld constant◦When a person’s income increases, thequantity demanded for the product mayincrease or decrease Income and Substitution Effects y Income Effect◦Even with inferior goods, the income effect is rarely large enough to outweigh thesubstitution effectIncome and Substitution Effects: Normal GoodClothing (units per month)R When the price of food falls, consumption increases by F1F2as the consumer moves from A to B.CThe substitution effect, F1E,(from point A to D), changes therelative prices but keeps real income1AThe income effect, EF,relative prices but keeps real income(satisfaction) constant.,2,(from D to B) keeps relativeprices constant butincreases purchasing power.C2BDF d(iU1U2 SubstitutionEffectFood (unitsper month)O F1SIncome EffectF2TETotal EffectIncome and SubstitutionEffects: Inferior GoodRClothing(units permonth)Since food is aninferior good, theincome effect isincome effect isnegative. However,the substitution effectis larger than theAincome effect.BDU2U1SubstitutionEffectFood (unitsper month)O F1S F2TETotal EffectIncome EffectIncome and Substitution Effects y A Special Case: The Giffen Good◦The income effect may theoretically be largeenough to cause the demand curve for a good to slope upward◦This rarely occurs and is of little practicalinterestGiffen Goodsx2 A decrease in p1causesd d d fquantity demanded ofgood 1 to fall.x2’’’x2’x1x1’x1’’’Slutsky EquationThe formal expression of the price effect yis the following:Ix x dx ∂∂−∂=xu u x x p I p dp ∂•∂∂=_The Law of DemandThe demand for a normal good (i e theyThe demand for a normal good (i.e., the income effect is positive) increases when its price decreasesyNote that substitution effect is always ti itinegative or nonpositive Another Way of Decomposing PriceEffectHicksian substitution effect: holding the yutility constanty Slutsky substitution effect: holding the purchasing power constantp c s gpo e Slutsky Substitution Effectx 2x 2’x 2’’x 1x 1’x 1’’And Now And Now the the Income Effect Income Effectx 2x 2’(x 1’’’,x 2’’’)x 2’’x 1x 1’x 1’’Rebating A T axOriginal budget:ypx + y = my T axing x and rebate the tax, at optimal consumption (x’y’):consumption (x ,y ):(p+t)x’ + y’ = m + tx’px’ + y’ = my (x’,y’) is on the original budget (x ,y ) is on the original budget y “Getting prices right”Rebating a tax based on final consumptionMarket DemandyMarket Demand Curves◦A curve that relates the quantity of a good that all consumers in a market buy to the price of that good◦The sum of all the individual demand curves in the marketDetermining the Market Demand CurvePrice A B CMarket Demand16101632 2481325 3261018 404711 50246Summing to Obtain aMarket Demand CurvePrice5The market demandcurve is obtained bysumming the consumer’s 4summing the consumer sdemand curves3Market Demand 2Q tit 1D B D CD AQuantity 0510********Market DemandFrom this analysis one can see twoyimportant points:◦The market demand will shift to the right asmore consumers enter the market◦Factors that influence the demands of manyconsumers will also affect the market demand Market DemandAggregation is important to be able to ydiscuss regarding demand for different groups◦Households with children◦Consumers aged 20 –30, etc.Market DemandyPrice Elasticity of DemandMeasures the percentage change in the◦quantity demanded resulting from a percent change in price%P Q Q/Q Q E P Δ=Δ=Δ=QP P/P P %ΔΔΔPrice Elasticity of DemandyInelastic Demand◦E p is less than 1 in absolute value◦Quantity demanded is relatively unresponsive to a change in price ◦|%ΔQ| < |%ΔP|◦otal expenditure (P*Q) increases when price T otal expenditure (P Q) increases when price increasesPrice Elasticity of DemandyElastic Demand◦E p is greater than than 1 in absolute value◦Quantity demanded is relatively responsive to a change in price ◦|%ΔQ| > |%ΔP|◦otal expenditure (P*Q) decreases when T otal expenditure (P Q) decreases when price increasesPrice Elasticity and Consumer ExpenditurePrice Elasticity of DemandyIsoelastic Demand◦When price elasticity of demand is constantalong the entire demand curve◦Demand curve is bowed inward (not linear)Revenue and Own Revenue and Own--Price Elasticity of DemandIf raising a commodity’s price causes little yIf raising a commodity s price causes little decrease in quantity demanded, then sellers’ revenues rise.◦Hence own-price inelastic demand causes sellers’ revenues to rise as price rises.pyIf raising a commodity’s price causes a large decrease in quantity demanded, then sellers’ q y ,revenues fall.◦Hence own-priceelastic demand causes p sellers’ revenues to fall as price rises.Revenue and Own Revenue and Own--Price Elasticity of Demand)*Sellers’ revenue is R p p X p ()().=×Sellers revenue isRevenue and Own Revenue and Own--Price Elasticity of Demand)*Sellers’ revenue is R p p X p ()().=×Sellers revenue isdR **Sodp X p p dX dp=+())*Sellers’ revenue is R p p X p ()().=×Sellers revenue isdR **Sodp X p p dXdp=+()⎤⎡+=dXp 1X **⎥⎥⎦⎢⎢⎣dp )p (X )p (*)*Sellers’ revenue is R p p X p ()().=×Sellers revenue isdR **Sodp X p p dXdp =+()⎤⎡+=dX p 1X **⎥⎥⎦⎢⎢⎣dp )p (X )p (*[]=+X p *().1εRevenue and Own Revenue and Own--Price Elasticity of DemanddR*[]dpX p =+()1εRevenue and Own Revenue and Own--Price Elasticity of DemanddR*[]dpX p =+()1εso ifε=−1thendR=0dpand a change to price does not alter ll ’sellers’ revenue.dR*[]dpX p =+()1εbut if−<≤10εthendR>0dpand a price increase raises sellers’revenue.dR*[]dpX p =+()1εAnd ifε<−1thendR<0dpand a price increase reduces sellers’revenue.Marginal Revenue and Own Marginal Revenue and Own--Price Elasticity of DemandyA seller’s marginal revenue is the rate atwhich revenue changes with the number of units sold by the seller.dR q ()MR q dq().=Marginal Revenue and Own Marginal Revenue and Own--Price Elasticity of Demand ()dhll ’ id df i i hip(q) denotes the seller’s inverse demand function; i.e. the price at which the seller can sell q units. ThendR q dp q ()()==R q p q q()()=×MR q dq dqq p q ()()+=+⎡⎣⎢⎤⎦⎥p q q p q dp q dq ()()().1Marginal Revenue and Own Marginal Revenue and Own--Price Elasticity of DemandMR q p q q dp q ()()().=+⎡⎢⎤⎥1p q dq ()⎣⎦dq ε=×dp p qandsoMR q p q ()().=+⎡⎤11⎣⎢⎦⎥εMarginal Revenue and Own Marginal Revenue and Own--Price Elasticity of DemandMR q p q ()()=+⎡⎣⎢⎤⎦⎥11εsays that the rateat which a seller’s revenue changeswith the number of units it sellsdepends on the sensitivity of quantity d d dii hdemanded to price; i.e ., upon the of the own-price elasticity of demand.Marginal Revenue and Own Marginal Revenue and Own--Price Elasticity of Demand⎡1⎥⎦⎤⎢⎣ε+=1)q (p )q (MR If =−1then =εMR q ().0If −<≤10εthen MR q ().<0Ifε<−1thenMR q ().>0Marginal Revenue and Own Marginal Revenue and Own--Price Elasticity of Demand An example with linear inverse demand.a bq .=−p q q ()Then R q p q q a bq q ()()()==−andM R q a bq ().=−2Marginal Revenue and Own Marginal Revenue and Own--Price Elasticity of Demandpap q a bq()=−a/b qa/2bM R q a bq()=−2Marginal Revenue and OwnMarginal Revenue and Own--PriceElasticity of DemandapM R q a bq()=−2p q a bq()=−a/b qa/2b$R(q)qa/ba/2bIncome Elasticity*m ** ,i iX mi d XX d m η=×y Normal good: η>0y Inferior good: η<0y Luxury good: η>1y Necessary good: 0<η<1Consumer SurplusConsumers buy goods because it makes ythem better offy Consumer Surplus measures how much better off they areyConsumer SurplusyConsumer Surplus◦The difference between the maximum amount a consumer is willing to pay for a good and the amount actually paid◦Can calculate consumer surplus from the demand curveConsumer Surplus Consumer Surplus --ExampleStudent wants to buy concert tickets yy Demand curve tells us willingness to pay for each concert ticket◦1st ticket worth $20 but price is $14 so student generates $6 worth of surplus ◦Can measure this for each ticket◦T otal surplus is addition of surplus for each ti k t h d ticket purchasedConsumer Surplus Consumer Surplus --ExampleP i The consumer surplus of purchasing 6 concert tickets is the sum of the surplus derived from Price($ perticket)1920surplus derived from each one individually.1718Consumer Surplus6+5+4+3+2+1=211516 6 + 5 + 4 + 3 + 2 + 1 21 1314Market PriceWill not buy more than 7because surplus is negativeRock Concert Tickets2345601Consumer SurplusThe stepladder demand curve can be yconverted into a straight-line demand curve by making the units of the good smallery Consumer surplus is the area under the demand curve and above the priceConsumer SurplusP i Consumer Surplus for the Market DemandPrice($ per ticket)19201718CS = ½ ($20 -$14)*(1600) = $19,500Consumer Surplus1516Demand Curve1314Market Price Actual Expenditure Rock Concert Tickets2345601Applying Consumer SurplusCombining consumer surplus with the yaggregate profits that producers obtain, we can evaluate:1.Costs and benefits of different market structures2.Public policies that alter the behavior of consumers and firmsThe Value of Clean AirEmpirical data determined estimates for ythe demand for clean airy No market exists for clean air, but can see people are willing to pay for it p p g p y◦Ex: People pay more to buy houses where the air is cleanThe Value of Cleaner AirUsing these empirical estimates we canyUsing these empirical estimates, we can measure people’s consumer surplus for pollution reduction from the demand curveValuing Cleaner AirThe shaded area represents the consumer surplus generatedwhen air pollution is2000Valuep reduced by 5 parts per 100million of nitrous oxide at a cost of $1000 per part red ced part reduced.1000ANOX (pphm)1005(pp )Pollution ReductionValue of Cleaner AirA full cost benefit analysis would include yA full cost-benefit analysis would include total benefit of cleanupy T otal benefits would be compared to totalcosts to determine if the clean up wasp worthwhileEmpirical Estimation of DemandThe most direct way to obtainyinformation about demand is through interviews where consumers are askedhow much of a product they would bep y willing to buy at a given priceEmpirical Estimation of DemandyProblem◦Consumers may lack information or interest, or be misled by the interviewerEmpirical Estimation of Demand In direct marketing experiments actual y In direct marketing experiments, actual sales offers are posed to potential customers and the responses of customers are observed Empirical Estimation of Demand The Statistical Approach to DemandyEstimation◦Properly applied, the statistical approach todemand estimation can enable one to sortout the effects of variables on the quantitydemanded of a product◦“Least-squares” regression is one approachDemand Data for Raspberries Empirical Estimation of Demandy Assuming only price determines demand:◦Q = a -bP◦Q = 28.2 -1.00PEstimating DemandPrice 25D represents demandif only P determines 20demand and then from the data: Q =28.2-1.00P15d 1105d 2d 3D Quantity 0510152025Estimating Demand Estimating Demand ––Changes in IncomePrice 25d 1,d 2,d 3represent the demand for each income level. Including income in the demand equation:Q =a -bP +cI or 20the demand equation: Q a bP + cI or Q = 8.08 -.49P + .81I15d 1105Dd 2d 3Quantity510152025Empirical Estimation of Demandy Estimating Elasticities◦For the demand equation: Q = a -bPyElasticity:)/()/)(/(Q P b Q P P Q E P −=ΔΔ=Empirical Estimation of DemandyAssuming: Price and income elasticity are constant◦The isoelastic demand =)log()log()log(I c P b a Q +−=The slope, -b = price elasticity of demand Constant, c = income elasticity of demandEmpirical Estimation of Demandy Using the Raspberry data:log(I )P−=−Q+.081log().146)4.2log(Price elasticity = -0.24 (Inelastic)Income elasticity = 1.46I l ti it146。