Chapter 5: Applying Consumer Theory
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Transcript of Chapter 5: Applying Consumer Theory
Chapter 5:Applying Consumer TheoryFrom 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 ones u-max problemHow in income shifts demand (income elasticity)Two effects of a price change on demandDeriving labor supply curve using consumer theoryInflation adjustment
5.1 Deriving Demand CurvesA consumer chooses an optimal bundle of goods subject to budget constraints.
From the consumers 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.
Figure 5.1 Deriving an Individuals Demand Curve
Suppose that the price of beer changes while the price of wine remains constant.
Y = pbeerQbeer + pwineQwineOriginal prices: pbeer=12, pwine=35Income: Y = 419The 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.
Figure 5.1 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.
5.2 How changes in Income shift demand curvesHow does demand curve change when income shifts, holding prices constant?
Figure 5.2 Effect of Budget Increase on an Individuals Demand CurveSuppose 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!
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.
Income Elasticity of Demand= How much quantity demanded changes when income increases.
Normal good 0As Y rises, Qd also risesLuxury> 1Qd increases by a greater proportion than YNecessity< 1Qd increases by a lesser proportion than YInferior good< 0As Y rises, Qd decreases
Figure 5.3 Income-Consumption Curves and Income Elasticities
Figure 5.4 A Good that is both Inferior and Normal
5.3 Effects of a Price ChangeA decrease in p1 holding p2 & Y constant has two effects on individuals demand:
Substitution effect: Change in Qd due to consumers 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
Total EffectSuppose the consumer is maximizing utility at point A.If the price of good x1 falls, the consumer will maximize utility at point B.This can be decomposed into two effects.
Substitution EffectTo isolate the substitution effect, we holdthe utility level constant but allow the relative price of good x1 to changeThe substitution effect is the movementfrom point A to point CThe individual substitutes good x1 for good x2 because good x1 is now relatively cheaper
Income EffectThe income effect occurs because theindividuals real income changes whenthe price of good x1 changesThe income effect is the movementfrom point C to point BIf x is a normal good,the individual will buy more because realincome increasedWhat if x1 is an inferior good?
Ordinary Goods and Giffen GoodsOrdinary Goods: As P decreases, Qd increases. x1/p1 < 0 Giffen Goods: As P decreases, Qd decreases. x1/p1 > 0
5.5 Deriving Labor Supply CurveWe 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.
ModelUtility 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 hours
Max u = U(Y, N)Subject to Y = w1 H = w1 (24 N)
The Budget LineThe time constraint: H + N =24LeisureY = 24wN (Leisure)H (Labor time)Y = wHThe labor time determines how muchthe consumer can consumes the other goods.
Figure 5.8 Demand for leisureGiven 24hrs and wage w1Original optimum at e1
To derive demand for leisure, increase wage to w2New optimum at e2
A higher wage means a higher price of leisure
Demand curve for leisure on Price-Quantity space
Figure 5.9 Supply Curve of Labor
Substitution and Income EffectsBoth 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 leisure
The income and substitution effects move in opposite directions if leisure is a normal good.
Figure 5.10 Income and Substitution Effects of a Wage Change
The substitution effect is the movementfrom point A to point CThe individual chooses less leisure at B as a result of the increase in wThe income effect is the movementfrom point C to point BCase 1: Substitution effect > Income effect
ConsumptionY)The substitution effect is the movementfrom point A to point CThe individual chooses more leisure at B as a result of the increase in wThe income effect is the movementfrom point C to point BCase 2: Substitution effect < Income effect
Application: Will you stop working if you win a lottery?Figure 5.11 Labor Supply Curve that Slopes Upward and then Bends Backward
Tax revenue and Tax ratesApplication: What is the optimal (i.e., maximizes the tax revenue) marginal tax rate? Sweden 58% (vs. actual 65%) Japan: 54 % (vs. 24 %)
The same resource for subsidy and the lump-sum payment. This means that the budgets lines go through e2.
5.4 Cost of Living AdjustmentsNominal price: Actual price of a goodReal price: Price adjusted for inflation
Consumer Price Index (Laspeyres index): Weighted average of the price increase for each good where weights are each goods budget share in base year
ExampleIn 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 be where s: budget share
Price IndexLaspeyres index (Lp)weight: base year quantity= (Cost of buying the base-years bundles in the current year) / (Actual cost in the base year)
Paasche index (Pp)weight: current year quantity