Presentation on theme: "Chapter 5: Applying Consumer Theory"— Presentation transcript:
1Chapter 5: Applying Consumer Theory From chap 2&3, we learned that supply & demand curves yield a market equilibrium.From chap 4, we learned that a consumer maximizes his/her utility subject to constraints.This chapter does:Derive demand curves from one’s u-max problemHow Δin income shifts demand (income elasticity)Two effects of a price change on demandDeriving labor supply curve using consumer theoryInflation adjustment
25.1 Deriving Demand Curves A consumer chooses an optimal bundle of goods subject to budget constraints.From the consumer’s optimum choice, we can derive the demand function:x1= x1(p1, p2, Y)By varying own price (p1), holding both p2 and Y constant, we know how much x1 is demanded at any price. →Use this info to draw the demand curve.
3Figure 5.1 Deriving an Individual’s Demand Curve Suppose that the price of beer changes while the price of wine remains constant Y = pbeerQbeer + pwineQwine Original prices: pbeer=12, pwine=35 Income: Y = 419 The consumer can consume 12 (=419/35) units of wine or 35 (=419/12) units of beer if she consumes only one of the two. Draw the budget line. The price of beer changes: pbeer=6, pbeer=4 She can now consume 70 (=419/6) or 105(=419/4) units of beer.
4Figure 5. 1 Continued. Change Pbeer holding Pwine and Y constant Figure Continued. Change Pbeer holding Pwine and Y constant. → New budget constraint → New optimal bundle of goods. Tracing these optimal xbeer*, we can draw the demand curve for beer on Price-Quantity space.
55.2 How changes in Income shift demand curves How does demand curve change when income shifts, holding prices constant?
6Figure 5.2 Effect of Budget Increase on an Individual’s Demand Curve Suppose that the income of the consumer increases.Income increases to $628 and $837 for same prices.She can now consume 18 (=628/35) units of wine or 52 (=628/12) units of beer if she consumes either one.Or she can now consume 24 (=837/35) units of wine or 70 (=837/12) units of beer if she consumes either one.The budget line expands outward, and she consumes more wine and beer because she can!
7Figure 5. 2 Continued. Change Y holding Pbeer and Pwine constant Figure 5.2 Continued. Change Y holding Pbeer and Pwine constant. → Budget line shifts outward → New optimal bundle of goods Demand curves shifts outward as Y increases if the good is normal. Engel curve summarizes the relationship between income and quantity demanded, holding prices constant.
8Income Elasticity of Demand = How much quantity demanded changes when income increases.Normal goodη≥ 0As Y rises, Qd also risesLuxuryη> 1Qd increases by a greater proportion than YNecessityη< 1Qd increases by a lesser proportion than YInferior goodη< 0As Y rises, Qd decreases
9Figure 5.3 Income-Consumption Curves and Income Elasticities
10Figure 5.4 A Good that is both Inferior and Normal
115.3 Effects of a Price Change A decrease in p1 holding p2 & Y constant has two effects on individual’s demand:Substitution effect: Change in Qd due to consumer’s behavior of substituting good 1 for good 2 (because x1 now relatively cheap), holding utility constant.Income effect: Change in Qd due to effectively-increased income (lower p1 = higher buying power), holding prices constant.Total effect = Substitution effect + Income effect
12Total Effect Suppose the consumer is maximizing utility at point A. BTotal increase in x1If the price of good x1 falls, the consumerwill maximize utility at point B.This can be decomposed into two effects.
13Substitution Effect To isolate the substitution effect, we hold the utility level constant but allow therelative price of good x1 to changeU1x1x2ASubstitution effectCThe substitution effect is the movementfrom point A to point CThe individual substitutesgood x1 for good x2because good x1 is nowrelatively cheaper
14Income Effect The income effect occurs because the individual’s “real” income changes whenthe price of good x1 changesBU1U2x1x2ACIncomeeffectThe income effect is the movementfrom point C to point BIf x is a normal good,the individual will buymore because “real”income increasedSubstitutioneffectWhat if x1 is an inferior good?Total effect
15Ordinary Goods and Giffen Goods Ordinary Goods: As P decreases, Qd increases. ∂x1/∂p1 < 0Giffen Goods: As P decreases, Qd decreases. ∂x1/∂p1 > 0
165.5 Deriving Labor Supply Curve We normally use consumer theory to derive demand behavior. But here, we derive labor supply curve using consumer theory.Individuals must decide how to allocate the fixed amount of time they have.The point here is “time is money.” When we do not work, we sacrifice or forgo wage income. That is, the opportunity cost of time is equal to the wage rate.
17Model Utility function: u= U(Y, N) where N= Leisure time and Y is the consumption of other goods, which is equal to the labor income (wages).Time constraint: H (labor time) + N = 24 hoursMax u = U(Y, N)Subject to Y = w1 H = w1 (24 – N)
18The Budget Line The time constraint: H + N =24 Y = 24wThe time constraint:H + N =24Y = wHLeisureN (Leisure)H (Labor time)The labor time determines how muchthe consumer can consumes the other goods.
19Figure 5.8 Demand for leisure Given 24hrs and wage w1Original optimum at e1To derive demand for leisure, increase wage to w2New optimum at e2A higher wage means a higher price of leisureDemand curve for leisure on Price-Quantity space
21Substitution and Income Effects Both effects occur when w changesSubstitution effect: When w rises, the price for leisure increases due to higher opportunity cost, and the individual will choose less leisureIncome effect: Because leisure is a normal good, with increased income, she will choose more leisureThe income and substitution effects move in opposite directions if leisure is a normal good.
22Figure 5.10 Income and Substitution Effects of a Wage Change
23Case 1: Substitution effect > Income effect Leisure （N)Consumption（Y)ABCSubstitution effectIncome effectTotal effectThe substitution effect is the movementfrom point A to point CThe income effect is the movementfrom point C to point BThe individual chooses less leisure at B as a result of the increase in w
24Case 2: Substitution effect < Income effect The substitution effect is the movementfrom point A to point CConsumption（Y)U1U2Leisure（N)ABCSubstitution effectIncome effectTotal effectThe income effect is the movementfrom point C to point BThe individual chooses more leisure at B as a result of the increase in w
25Figure 5.11 Labor Supply Curve that Slopes Upward and then Bends Backward Application: Will you stop working if you win a lottery?
26Tax revenue and Tax rates Application: What is the optimal (i.e., maximizes the tax revenue) marginal tax rate?Sweden 58% (vs. actual 65%) Japan: 54 % (vs. 24 %)
27Child-Care Subsidies: The same resource for subsidy and the lump-sum payment. This means that the budgets lines go through e2.
285.4 Cost of Living Adjustments Nominal price: Actual price of a goodReal price: Price adjusted for inflationConsumer Price Index (Laspeyres index): Weighted average of the price increase for each good where weights are each good’s budget share in base year
29ExampleYearP1P2Price index2000\120\5001002007\240\1,000200YearP1P2Price index2000\120\5001002007\108\550??In the first case, both relative and real prices remain unchanged.Real price = Nominal price / Price index, e.g., \240/2.00.In the second case, it is not clear how we should compute the price index (P).One reasonable way may bewhere s: budget share
30Price Index Laspeyres index (Lp) weight: base year quantity = (Cost of buying the base-year’s bundles in the current year) / (Actual cost in the base year)Paasche index (Pp)weight: current year quantity