Presentation on theme: "Chapter 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."— Presentation transcript:
Chapter 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 ones u-max problem –How Δin income shifts demand (income elasticity) –Two effects of a price change on demand –Deriving labor supply curve using consumer theory –Inflation adjustment
A consumer chooses an optimal bundle of goods subject to budget constraints. From the consumers optimum choice, we can derive the demand function: x 1 = x 1 (p 1, p 2, Y) By varying own price (p 1 ), holding both p 2 and Y constant, we know how much x 1 is demanded at any price. Use this info to draw the demand curve. 5.1 Deriving Demand Curves
Figure 5.1 Deriving an Individuals Demand Curve Suppose that the price of beer changes while the price of wine remains constant. Y = p beer Q beer + p wine Q wine Original prices: p beer =12, p wine =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: p beer =6, p beer =4 She can now consume 70 (=419/6) or 105(=419/4) units of beer.
Figure 5.1 Continued. Change P beer holding P wine and Y constant. New budget constraint New optimal bundle of goods. Tracing these optimal x beer *, we can draw the demand curve for beer on Price- Quantity space.
5.2 How changes in Income shift demand curves How does demand curve change when income shifts, holding prices constant?
Figure 5.2 Effect of Budget Increase on an Individuals 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!
Figure 5.2 Continued. Change Y holding P beer and P wine 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 goodη 0η 0As Y rises, Q d also rises Luxuryη> 1Q d increases by a greater proportion than Y Necessityη< 1Q d increases by a lesser proportion than Y Inferior goodη< 0As Y rises, Q d 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 Change A decrease in p 1 holding p 2 & Y constant has two effects on individuals demand: Substitution effect: Change in Q d due to consumers behavior of substituting good 1 for good 2 (because x 1 now relatively cheap), holding utility constant. Income effect: Change in Q d due to effectively- increased income (lower p 1 = higher buying power), holding prices constant. Total effect = Substitution effect + Income effect
Total Effect Suppose the consumer is maximizing utility at point A. If the price of good x 1 falls, the consumer will maximize utility at point B. This can be decomposed into two effects. x1x1 x2x2 U1U1 A U2U2 B Total increase in x 1
Substitution Effect To isolate the substitution effect, we hold the utility level constant but allow the relative price of good x 1 to change The substitution effect is the movement from point A to point C The individual substitutes good x 1 for good x 2 because good x 1 is now relatively cheaper U1U1 x1x1 x2x2 A Substitution effect C
Income Effect The income effect occurs because the individuals real income changes when the price of good x 1 changes The income effect is the movement from point C to point B If x is a normal good, the individual will buy more because real income increased What if x 1 is an inferior good? B U1U1 U2U2 x1x1 x2x2 AC Income effect Substitution effect Total effect
Ordinary Goods and Giffen Goods Ordinary Goods: As P decreases, Q d increases. x 1 /p 1 < 0 Giffen Goods: As P decreases, Q d decreases. x 1 /p 1 > 0
5.5 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.
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 hours Max u = U(Y, N) Subject to Y = w 1 H = w 1 (24 – N) Model
The Budget Line The time constraint: H + N =24 Leisure Y = 24w N (Leisure)H (Labor time) Y = wH The labor time determines how much the consumer can consumes the other goods.
Figure 5.8 Demand for leisure Given 24hrs and wage w 1 Original optimum at e 1 To derive demand for leisure, increase wage to w 2 New optimum at e 2 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 Effects Both effects occur when w changes –Substitution effect: When w rises, the price for leisure increases due to higher opportunity cost, and the individual will choose less leisure –Income 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 movement from point A to point C The individual chooses less leisure at B as a result of the increase in w The income effect is the movement from point C to point B Case 1: Substitution effect > Income effect U1U1 U2U2 Leisure N) Consumption Y) A B C Substitution effect Income effect Total effect
Consumption Y) The substitution effect is the movement from point A to point C The individual chooses more leisure at B as a result of the increase in w The income effect is the movement from point C to point B Case 2: Substitution effect < Income effect U1U1 U2U2 Leisure N) A B C Substitution effect Income effect Total 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 rates Application: What is the optimal (i.e., maximizes the tax revenue) marginal tax rate? Sweden 58% (vs. actual 65%) Japan: 54 % (vs. 24 %)
Child-Care Subsidies: The same resource for subsidy and the lump-sum payment. This means that the budgets lines go through e 2.
5.4 Cost of Living Adjustments Nominal price: Actual price of a good Real 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
Example 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 be where s: budget share YearP1P1 P2P2 Price index 2000\120\ \240\1, YearP1P1 P2P2 Price index 2000\120\ \108\550 ??
Price Index Laspeyres index (L p ) weight: base year quantity = (Cost of buying the base- years bundles in the current year) / (Actual cost in the base year) Paasche index (P p ) weight: current year quantity