Reading materials Chapter 5

Transcription

1 9/8/206 Reading materials Chapter 5 The Theor of Demand Besanko and Braeutigam: Chapter 5. Perloff: pp. 6. pp pp I will post these pages on Blackboard. Individual Demand Individual Demand Price Changes: Using the figures developed in the previous chapters, we will be able to analze the effect of a price change on the individual s optimal choice. And the analsis of these effects will give us the demand curve. Clothing (units per month) A U B Assume: I = $20 P C = $2 P F = $2, $, $.50 C U 3 Three separate indifference curves are tangent to each budget line. U 2 Food (units per month)

2 9/8/206 Individual Demand Clothing (units per month) A U B C U 3 The price-consumption curve traces out the utilit maimizing basket for the various prices for food. Deriving an Individual s Demand Curve (a) Indifference Curves and Budget Constraints (b) Demand Curve for Beer Wine, Gallons per ear p b, $ per unit 2.0 e L (p b = $2) e 2 e E I Price-consumption curve I2 I 3 L2 (p b = $6) L3 (p b = $4) Beer, Gallons per ear U E 2 Food (units per month) 4.0 E 3 D, Demand for beer Beer, Gallons per ear 6 Finding a demand curve Eample Consider the Cobb Douglas utilit function, u(,) =, with marginal utilities,, and we leave prices and st ) Budget constraint 2 nd ) MRS,=price ratio income levels as general as possible, i.e., p, p, On our own I Finding a demand curve Eample Consider now a utilit function u 0, where 0,, And assume I=$00, and p =$ but we leave unspecified p since we seek to find the demand curve for good (as a function of its price). Otherwise, we would be obtaining an optimal consumption bundle (a number for the optimal consumption of good, rather than a function of p ). st ) Budget constraint 2 nd ) MRS,=price ratio Net slide 7 2

3 9/8/206 Learning b doing 5.2: U 0 0 and Suppose that I 00 and p p unknow then ) p p 00 p 00 B.L. p 0 2) MRS 0 p plug into p p Plugging (2) into () 00 0p 0p p 00 2p 0p 00 2p P X P Y I Learning b doing 5.2: Hence, the demand for good is positive, 00 0 p 2 p 0 onl if 00-0p p 0 p 00 0 p if p <0 2 p 0 otherwise We can now depict the demand cure for good we just found Effects of Income Changes (Vertical spike). Price of food $.00 E G H An increase in income, from $0 to $20 to $30, with the prices fied, shifts the consumer s demand curve to the right. D 3 D 2 D Food (units per month) 2 3

4 9/8/206 An Inferior Good Steaks 5 (units per month) 0 5 A C B U Income-Consumption Curve U 3 U Both hamburger and steak behave as a normal good, between A and B but hamburger becomes an inferior good when the income consumption curve bends backward between B and C. Hamburgers (units per month) 3 Individual Demand Normal Good vs. Inferior Good Income Changes When the income consumption curve has a positive slope: The quantit demanded increases with income. The income elasticit of demand is positive. The good is a normal good. 4 Individual Demand Normal Good vs. Inferior Good Income Changes When the income consumption curve has a negative slope: The quantit demanded decreases with income. The income elasticit of demand is negative. The good is an inferior good. Effects of Income Changes: Engel Curves Engel curves relate the quantit of goods 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 is downward sloping. Let s look at two eamples: 5 6 4

5 9/8/206 Effects of Income Changes: Engel Curves 30 Income ($ per month) 20 Engel curves slope upward for normal goods. Engel Curves Income ($ per month) Engel curves slope backward bending for inferior goods. Inferior 0 0 Normal Food (units per month) Food (units per month) 7 8 Finding Engel Curves Consider again the Cobb Douglas utilit function Finding Engel Curves Consider again the Cobb Douglas utilit function u (, ) with and p p I is the budget line. In order to find the Engel Curve for good demand curve of : Using the tangenc condition, we obtain p p p p p p, we first need to find the Then, p p p I p p I 2 p I p Solving for, we obtain the demand curve for I 2 p plugging p the above result,, into the budget p line ields 5

6 9/8/206 Finding Engel Curves Since the Engel curve has the amount of the good on the horizontal ais and income (I) on the vertical ais If, for instance p $, then the curve I 2p becomes I 2 : Engel I = 2 I we first need to solve for I in the demand curve, 2 p ielding an Engel curve of I 2 p 2 Slope of the Engel curve Engel Curve in corner solutions What if, instead, we face a utilit function for perfect substitutes, such as u(,) = +, which we know ields optimal consumption bundles at a corner? Let s practice: U (, ) its MRS, is MRS, if p, P P p then MRS P P P P which implies that this consumer would be still willing to consume more units of and less of. Graph on net slide. Of course, the Engel curve of good implies = 0 for all income levels. That is, the equation of the Engel curve would be I = 0 for all, as depicted in the figure. What about the Engel curve for good? 6

7 9/8/206 Income and Substitution Effects A fall in the price of a good has two effects: Substitution & Income Substitution Effect Consumers will tend to bu more of the good that has become relativel cheaper, and less of the good that is now relativel more epensive. Engel Curve, Positivel sloped for all income levels. Slope of : Ever etra dollar is spent on good. 26 Income and Substitution Effects Income and Substitution Effects A fall in the price of a good has two effects: Substitution & Income Income Effect Consumers eperience an increase in real purchasing power when the price of one good falls. Substitution Effect The substitution effect is the change in an item s consumption associated with a change in its price, holding the utilit level constant. When the price of an item declines, the substitution effect alwas leads to an increase in the quantit of the item demanded

8 9/8/206 Income and Substitution Effects Substitution and Income Effects with NORMAL Goods Clothing BL2 Income Effect The income effect is the change in an item s consumption brought about b the increase in purchasing power, with the price of the item held constant. When a person s purchasing power increases, the quantit demanded for the product ma increase or decrease. BL BLd A B I C I 2 0 Substitution effect Income effect Total effect Food Clothing Income and Substitution Effects: INFERIOR Good A C Since food is an inferior good, the income effect is negative. However, the substitution effect is larger than the income effect. Clothing BL2 BL BLd Income and Substitution Effects: GIFFEN Good C I 2 A B I 2 O Substitution Effect Total Effect Income Effect I Food B Total effect Substitution effect Income effect I Food

9 9/8/206 Income and Substitution effects For a decrease in prices: Demand curve is negativel sloped (as usual) Potatoes (in Ireland during the XIX centur) and Tortillas (Meico, 990s). Demand curve is positivel sloped Normal good Inferior good Giffen good SE IE TE Income and Substitution effects Note that if the total effect of a price decrease is positive (TE >0), the demand curve is negativel sloped. Indeed, a decrease in p implies an increase in the quantit demanded. This applies for both normal and inferior goods But NOT for Giffen goods: The would have a positivel sloped demand curve, i.e., a more epensive good would lead to an increase in the quantit demanded (the are a rare species of goods!) Please note that all signs would change if we analze an increase in prices. 33 Learning b doing 5. 4 Consider again the Cobb Douglas utilit function U with marginal utilities and Suppose that I $72 and p $. In addition, assume that the initial p 9 then decreases to p 4. Basket A (at initial price p 9): ) 9 p 72 p 9 2) MRS 9 plug into p plug into 9(4) 36 A (4,36) 2 Learning b doing 5. 4 (cont d): Basket C (at final prices p 2 $4) : ) 4 p 72 p 4 2) MRS 4 plug into p plug into 9(4) 36 C (9,36) AC 49 of, thus impling a total effect of TE=9 4 9

10 9/8/206 Learning b doing 5.4 (cont.) In order to disentangle the SE and IE from the TE = 5 we just found, we need to first find the decomposition Basket B. We know that the decomposition bundle B satisfies two properties: First, B must give the same utilit level as the initial basket A. Hence, since basket A = (4, 36) ields a utilit level of u = = 4 (36) = 44, then basket B must also satisf = 44. Learning b doing 5.4 (cont.) Second, BL d must be tangent to IC. Since the slope of BL d is the same as BL 2, then p 4 p slope of BL slope of IC d Combining the information we found from both properties, Hence, B 6, 24 Decomposition Basket B Learning b doing 5.4 (cont.) We can now summarize our results with a figure depicting the units consumed of good (the good whose price changed): A B C SE IE { TE =5 Summar of learning b doing 5.4: As price of good X decreases The SE leads us to an increase in consumption of good X from 4 to 6. The IE will measure the consumption from decomposition basket B to basket C (From 6 to 9) SE X B X A IE X C X B (normal good) Note: When ou eamine the SE remember that at B ou reach the same indifference curve as at A, but our BL has the same slope at bundle C. 0

11 9/8/206 Special Case: What happens with the SE and IE when we deal with a quasilinear utilit functions, such as U (, ) Special Case: SE and IE with quasilinear utilit functions X is neither a normal good nor an inferior good. SE=X B X A >0 IE=X C X B =0 (no income effect) SE IE=0 Hence, SE=E since IE =0 SE IE=0 Hence, SE=E since IE =0 Learning b doing 5.6, where IE = 0 Let s now consider a Quasi linear utilit function U 2 and I 0, p 0.5, p 0.2, p 2 (At initial prices) Basket A : ) p 0.5 2) MRS 4 p A (4,8) Learning b doing 5.6, where IE = 0 (At final prices) Basket C: ) p 0.2 2) MRS 25 p C (25,5)

12 9/8/206 Learning b doing 5.6 (cont.) Decomposition Basket B. It must satisf two properties: ) Same utilit level as basket A=(4,8), so U Thus we know, 2 2 2) BL d must be tangent to IC and parallel to BL 2 p p 5 Hence, the decomposition bundle B is slope of IC slope of BL2 (and BL d ) B 25, 2 Learn b doing 5.6 (cont.) We can now summarize our results about SE and IE: SE = B A = 25 4 = 2 IE = C B = = 0 B coincides with C Notice there is no IE because she consumes the same amount of good at bundles B and C. A more compact representation of the SE and IE using the compensated demand curve From Perloff s tetbook (posted on Blackboard) Let us use the Compensated Demand Curve to analze SE and IE: In our eercise from the ependiture minimization problem we obtain the compensated (or Hicksian) demand. (See the last part of the Ch. 4 lectures) Using h(p, p 2,U ) we obtain the minimal ependiture that the consumer needs to incur in order to reach indifference curve U at prices p and p 2, X X 2 Min subject to p p _ u ( ) u 2 2 h(p,p 2,, ū) Hence,,,,,,, E p p U p h p p U p h p p U E p h ( p, p 2,U ) This is just an amount of good bought b this consumer, i.e., equivalent to q. 2

13 9/8/206 A more compact representation of the SE and IE using the compensated demand curve Plugging the minimal ependiture into the consumer s income level I we obtain hp, p2, U D p, p2, Ep, p2, U minimal ependiture to reach U And differentiating with respect to p, h D D E p p E p h D D q p p E This equation is often regarded on the Slutsk equation and describes the SE and IE as follows: h D D q p p E SE TE IE That is, SE = TE + IE h Note that p captures the SE since the compensated demand operates on a target indifference curve,u for different price levels. D D Second, q reflects the IE since indicates how an E E increase in ependiture increases the demand for good. p Multipling all terms b E and the last b, we obtain q E h p D p D p E q p q p q E q E * D E pq E q E q, I where: ) ε is the standard definition of price elasticit of demand 2) ε * is the definition of price elasticit applied to the compensated demand curve 3) ε q,i is the income elasticit of demand, and 4) θ is the budget share of that good. Hence, we can summarize the above big epression more compactl as follows * QI, And rearranging, * QI, TE SE IE 3

14 9/8/206 Eamples ) Garlic, θ 0. Hence IE 0, and TE=SE 2) Housing, θ=0.4 (40% of monthl ependitures), ε Q,I =.38, ε= 0.6 Then we can find the value of ε * b using the above epression ε * =ε+θ ε Q,I = -0.6+(0.4*.38) = Intuitivel, if the consumer is not compensated for a % price increase in housing, his demand drops b 0.6%. If, however, he is compensated (so he reaches his initial indifference curve at the new prices) his demand onl decreases b 0.04%. For an inferior good, ε Q,I < 0, impling * Q, I Since SE IE for inferior (not Giffen) goods. Hence, ε<0 which implies that a consumer s demand is negativel sloped (as usual). For a Giffen good, ε Q,I < 0 (and etremel negative), impling that * Q, I Because SE IE for Giffen goods. Hence, ε> 0 which implies that demand is positivel sloped! (onl true for Giffengoods). Can all goods be inferior? NO!! The figure represents an increase in income, shifting the consumer s budget line from BL to BL 2. If his optimal consumption bundle under BL is e, where does his optimal bundle under BL 2 lie? Another wa to show this result, b using elasticities: Consider a list of optimal consumption bundles (p, I), 2 (p, I),, n (p, I). Hence, this consumer s budget is ehausted at this optimal consumption bundle, that is Budget Line P X P X... P X I 2 2 n n for n goods In order to eamine what s the effect of an income change let s differentiate with respect to I, Here? d d2 dn P P2... Pn di di di Some good must be normal (not all inferior): If the consumer was buing less of both and, he would pick a bundle inside BL, thus not ehausting all his income. 4

15 9/8/206 We can now multipl and divide b i *I Rearranging, P X I d X I di... For a setting with onl two goods (as in the above figure): or or, I 2 2, I, 0 Can all goods be inferior? Let s see what would happen if the were all inferior: I 0 and, I 0, 2 P X d I I di X... { {, I If that was the case, we wouldn t be able to obtain a sum that adds up to : I 2 I, 2, Eample Consider ou work for a firm selling a good in a developing countr. For simplicit, assume that most households onl spent mone on food (f) and other goods (o), which is the goods ou sell. In addition, consider ou know the income elasticit of demand for food, f ], I [0, but ou don t know the income elasticit of other goods,. However, from the above equation; we know that o,i [ f, I] f, I ( ) 0, I.Hence, 0, Iis0, I Don t know: 0,I Consider that ou have information about the average budget share spent on food: as the countr developed, it decreased from = 0.6 to = We can then evaluate the upper bound for these values of, as follows: IF f Upper bound for o, I since (0,) 0 0, I, I IF f 0, I o,, I lower bound for I. IF 0.6 In In Upper bound In In

16 9/8/206 Measuring Welfare Changes Consumer Surplus Price ($ per ticket) The consumer surplus of purchasing 6 concert tickets is the sum of the surplus derived from each one individuall Consumer Surplus = 2 Market Price While still imprecise, the range for O,I became more accurate as declined. Business strateg: a % in GDP in the developing countr will lead to a maimum increase in our sales of.59% Rock Concert Tickets 62 Learning b doing (Consumer Surplus): Q=# of gallons of milk purchased at P dollars Q=40 4p > But we want p to be in the ais, then we need to solve for p (obtaining the indirect demand function), as follows: Q 4 p 40 Q p { A Learning b doing (cont.) ) Point A is the crossing of the demand function p=0 and market price p=3. Then, Q Q 30 7Q 28 point A ($3, 28 units) 4 4 2) CS is the shaded blue triangle G in the previous slide CS (28)(0 3) 98 2 { height Q 4 { 28 6

17 9/8/206 So far we measure CS using the area of the triangle below the Demand curve, because demand curve was linear (straight line) What if it is not? Eample of a non linear demand curve: 80 p What if the demand function is not a straight line? Consumer Surplus with a Cobb Douglas Utilit Function Consider the following Cobb Douglas utilit function U And assume that, while income remains constant at I = 300, the price of good increases from p 5 to p 20 I 300 ) Find the consumer s demand curve for an P, As a practice, use the tangenc condition to find that the market demand for good is 0.6I 0.6(300) 80 p p p What if the demand function not a straight line? Hence, the decrease in CS when p increases from $5 to $20 is Measuring CS of a Cobb Douglas Utilit Function (which ields a Non Linear Demand) Not a straight line CS d p 80ln p 80ln 20 ln p 5 7

18 9/8/206 What if we incorrectl assume linear demand (i.e., so CS=rectangle+triangle): ) Area of A=(20 5)9=45 (Rectangle) 2) Area of B=(20 5)*(/2)*6=5 (Triangle) 3) Total loss in CS= 45+5= 60>5.79 (overestimation of the loss in CS) X=80/p Quer # Suppose the consumer s demand curve for a good can be epressed as P=50-4Q d. Suppose that the market is initiall in equilibrium at a price of $0. What is the consumer surplus at the original equilibrium price? a) 00 b) 50 c) 200 d) 250 Quer # Answer Answer: C ($200) The consumer surplus is the difference between the maimum amount a consumer is willing to pa for a good ( intercept) and the amount the must actuall pa (equilibrium price) below the demand curve. From the demand curve, we see that when Q d = 0, P=$50. When P=0, Q d =2.5. Those are our and intercepts, respectivel. From there, we can subtract the maimum price consumers are willing to pa, $50, form the equilibrium price, $0, which gives us a difference of $40. When we plug P*=$0, the equilibrium given to us, into the demand curce, we find that Q*=0 Consumer surplus is simpl the area of the triangle CS=(.5)(40)(0)=$200 Quer # - Answer Graphicall P=50 4Q CS=/2 *(50 0)*0= (/2) *40*0=$200 8

19 9/8/206 Measuring Welfare Changes After a price decrease, the consumer is better off. But how can we measure b how much? Compensating Variation: A measure of how much mone a consumer would be willing to give up after a reduction in the price of a good to be just as well off as before the price decrease. If prices increase, then I need more income to maintain { p p{ the same level of utilit. How much mone would I need? CV If prices decrease, then I don t need all m original income to remain at m original utilit. How much mone would I be willing to give up in order to remain at the original utilit level? CV Measuring Welfare Changes Equivalent Variation: A measure of how much additional mone a consumer would need before a price reduction to be as well off as after the price decrease. If prices are going to decrease, then consumers are going to be better off because the can purchase more. p How much income should we give them toda, to make them just as well off as the will be tomorrow after the price decrease? EV If prices are going to increase, then consumers are going to be worse off. p How much mone would we need to take from the consumer toda, before the price increase, in order for him to be just as worse off as he is going to be tomorrow? EV Compensating Variation of a price decrease In order to provide a graphical representation of CV and EV, we normalize the price of good, so that p = $. This allows us to identif the vertical intercept of an budget line as the individual income. Wh? Recall that the vertical intercept of BL is, so if p = $, becomes I. CV 0K consumer s income 0L income needed to purchase basket B at the new prices of 0K 0L=KL is the CV Definition: The amount of mone that the consumer will be willing to give up, after the price change, in order to maintain the original utilit that he had before the price change. 9

20 9/8/206 Equivalent Variation of a price decrease EV 0J income needed to bu basket E at the old prices of. 0J 0K=JK is the EV Definition: The amount of mone that we need to give to the consumer, before the price change, in order to make him just as well off as he will be after the price change. Generall, CV EV, ecept with quasilinear utilities (where we will find that CV = EV). Quer #2 Compensating variation is: a) the change in income necessar to hold the consumer at the final level of utilit as price changes b) alwas the area under the demand curve and above the price paid c) the change in income necessar to restore the consumer to the initial level of utilit d) the difference in the consumer s income between the purchase of the original basket and the new basket at the old prices Quer #2 Answer Answer C Compensation variation is a measure of how much mone a consumer would be willing to give up after a reduction in the price of a good, just to be as well off before the price decrease. Answer A describes the Equivalent variation. The income effect causes the magnitude of the compensation and equivalent variations to be different. Eample CV and EV with quasi linear utilit CV and EV with no Income effect: Consider the following quasi linear utilit function U 2 I 0, p 0.5, p 0.2, p 2 Assume that I = 0 and p =, but the price of good decreases from p = 0.5 to p 2 = 0.2. Compensating Variation (CV) CV= Cost of initial basket A ($0) Cost of the decomposition basket B (0.2(25)+2=$7) CV= 0 7=$3 Recall that basket B=(25,2) 20

21 9/8/206 Eample CV and EV with quasi linear utilit Equivalent Variation (EV) EV= Cost of buing basket E at initial prices Cost of buing initial basket A ($0) But, where is basket E? In search of basket E We know that basket E must reach the same utilit level as basket C. Since basket C is C = (25, 5), its associated utilit is u = = (2*5) + 5 = 5. Hence, we need that basket E satisfies 2 + = 5. In search of basket E We also know that at E, the slope of U 2 = slope of BL (old price ratio) Plugging this result, = 4, into the condition we found above 2 + = 5, ields E (4,) Therefore Basket E is E = (4, ). Hence, the cost of buing E is (0.5)4+=3 As a consequence EV = Cost of basket E Cost of basket A = 3 0 = $3 In summar, the CV and EV coincide, i.e., CV=EV= $3, when the IE is absent (which occurs when we have a quasilinear utilit function). $3=EV $3=CV { { 3 2

22 9/8/206 What if we use CS to measure change in welfare that arises from the decrease in the price of good? If we did U 2 I 0, p 0.5, p 0.2, p 2 The demand for is. 2 p Hence, since the demand function is a curve, the increase in CS is given b the integral: d p 2 p 0.5 p 0.5 CS which is eactl the same as the CV and EV since we have a quasilinear utilit function. Gain in CS Note: Using CS onl ields the same welfare change as CV and EV if income effects are absent, i.e, IE = 0. Otherwise CV EV CS. What if IE > 0? Consider the following Cobb Douglas utilit function U(,)= I = $72 P = $ P = $9P = $4 From L.D. 5.4 we found A= (4,36) C= (9, 36) B= (6, 24) What if IE > 0? a) CV CV= Cost of initial bundle A Cost of decomp. basket B at the final prices = = 72 (4 6)+( 24)= 72 48= $24 A B C SE = 2 IE = 3 Since IE 0 we can then epect that CV EC CS. Cost of bundle A $9*4+$*36=$72 Cost of bundle B(6,24) at the final prices 22

23 9/8/206 B) EV EV= Cost of basket E of final prices Cost of initial basket A We know that the cost of buing basket A is $72, but Where is basket E? ) On one hand, we know that E reaches the same utilit level U2 as basket C. Since basket C is C = (9, 36), its utilit level is U2 = 9*36 = 324. Hence, basket E must satisf * = 324. On the other hand, we know that at E, slope of U 2 = slope of BL 9 9 Combining = 9 with the condition we found above, = 324, ields (9) = 324, or = 6 units. This entails that = 9 = 9*6 = 54 units. Therefore, basket E is E = (6, 54). Hence, the cost of buing basket E at initial prices (recall initial prices were P =$9 and P Y =$) is (9 6)+( 54)= $08 Then, EV= 08 72= 36 c) Comparing CV and EV in this eercise, CV= 24 EV= 36 What if we measure the change in consumer welfare using CS? First, we find the demand curve for good when utilit function is U(,)= I=$72 P =$ I p 2p p Hence, the gain in CS resulting from the decrease in the price of good from $9 to $4 is given b integral: 9 36 CS dp p 9 36ln( P ) 36ln9 ln 4 $ $9 Gain in CS (non linear in p ) 23

24 9/8/206 Summarizing: CS 29 CV 24 These measures of welfare change are different (Since IE>0), but is this usual? EV 36 Not so much since and QI, are low (making income effects low for man goods). C Q, p Q, P Q, I TE SE IE Application: Automobile eport restrictions for Japanese cars in 984 Prices when up about 20% for JPN cars sold in U.S. CV=$4 billion: additional income needed after the prices change (due to the eport restrictions) is $4 billion. Since in 984 there were million new cars bought, the CV per car buer is 4,000 $,272 Y, Goods per da Application: Should I reall pa m workers more? Income and Substitution effects in the labor market BL2 I 2 I BLd BL B A C If the income effect is sufficientl small, total effect of an increase in the wage rate would be still positive. (more working hours applied) However, if IE is reall large, TE would be negative (workers would suppl less working hours). 0 N * N N H * H H 2 0 Substitution effect Total effect (-) Income effect N, Leisure hours per da H, Work hours per da 95 24

25 9/8/206 Backward bending Labor Suppl Curve Analsis of labor suppl Consider a worker with utilit function u ( wh) (24 H) Where H :# hours worked per da w : Wage per hour The first term represents utilit function from the goods that the worker can purchase with their total salar, while the second term represents the utilit from leisure, i.e., remaining hours in a da that he/ she doesn t work. Rearranging, 24 H ( )H 24 H H H H * 24 Taking F.O.C. in utilit function u = (wh) (24 H) with respect to the number of hours worked, H; u ( wh) H w(24h) ( wh) ( )(24H) 0 b) Consider, What is H*? 3 H* 24 8 hours 3 ( wh) (24 wwh H) ( wh) ( )(24H) ( ) (24 H) (24 H) H 25

26 9/8/206 Ta Revenue and Labor Suppl Since labor suppl is insensitive to variations in the wage rate, w, then the substitution and income effects must completel offset each other, i.e., SE = IE, impling a null total effect, TE = 0. The above analsis about SE and IE in labor markets can be used to analze ta polic. TaRevenue wh( ) where h( ) is the number of hours worked when wage net of taes is (- ) w Some people argue that increasing ta rates would reduce incentives to work. We all agree with that, but the question is b how much. If the reduction in working hours is sufficientl large, total ta revenue will actuall decrease. If, in contrast, such a reduction is onl minor, total ta revenue will increase. This relationship is graphicall represented with the Laffer curve, depicting ta rates on the horizontal ais and total ta collection on the vertical ais. The Laffer curve T 0 T T 0 T Ta Revenue and Labor Suppl Let us analze under which conditions we are in the increasing or decreasing portion of the Laffer curve. TaRevenue wh( ) where h( ) is the number of hours worked when wage net of taes is (- ) w T dh 2 wh ( w) w dw positive effect on T from higher rate negative effect on T from fewer hours worked T For 0 (a decrease in ta rates to cause an increase in revenue), we need 2 dh dh w wh( ) w d d h ( ) 26

27 9/8/206 Ta Revenue and Labor Suppl dh w d h( ) Multipling both terms b ( ), we obtain dh w d h( ) dh d h( ) More compactl: elasticit of suppl of labor suppl, A % increase in net wages, w, produces an ε suppl,w percentage increase in working hours. Hence, for total ta collection,t, to raise from a small fall in the ta rate, we need suppl, Eample : 25% if our income is about average $35,000 a ear 0.25 suppl, 3 Unlikel: Bush admin. or nowadas Eample 2: τ=80% Suppl, w 0.25 Likel: Japan, and Sweden 90s, US during Kenned τ τ * Maimum Additional Ta Revenue United States 28 63(!) 30 EU Ireland United Kingdom Portugal Spain German Netherlands Greece France Ital Belgium Finland Austria Sweden Denmark Onl recommended decrease Source: Trabandt and Uhlig (2009) Market Demand We now seek to aggregate the individual demands of all consumers in a given industr to obtain the market (or aggregate) demand. We will need to horizontall sum their individual demands. That is, for a given price, we add up the units demanded b each consumer. Let us look at one eample 27

28 9/8/206 Market Demand We horizontall sum the individual demand of casual consumers and health conscious consumers, obtaining the aggregate demand. Onl h consumes 5 3 p if p5 Qh ( p) 0 if p 5 62 p if p3 Qc ( p) 0 if p 3 The market demand will be 25 p if p3 (Both) QM ( p) 5 3 p if 3 p5 (Onl h consumes) 0 if p 5 (Neither consumes) Both consume, so D m >D h Neither Consumes Overlap of D h and Market Demand since onl H consumes Network Eternalities Eample Bandwagon effect: A positive network eternalit that refers to the increase in aggregate demand for a good as more consumers bu the good. (e.g., online games) Snob effect: A negative network eternalit that refers to the decrease in aggregate demand for a good as more consumers bu the good. (e.g., gm memberships) 28