Lecture 10. Introduction. Tax Incidence. Introduction. Tax Incidence: General Remarks. Tax Incidence: General Remarks. Tax Incidence: General Remarks

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1 Introuction Lecture 0 Tax Incience Many policie center aroun whether the tax buren i itribute fairly. Not a imple a analyzing how much in taxe each peron actually pai, becaue of tax inuce change to price. 2 Introuction Two main concept of how a tax i itribute: Statutory incience who i legally reponible for tax Economic incience the true change in the itribution of income inuce by tax. Thee two concept iffer becaue of tax hifting. Only people can bear taxe Buine paying their fair hare imply hift the tax buren to ifferent people Can tuy people whoe total income conit of ifferent proportion of labor earning, capital income, an o on. Sometime appropriate to tuy incience of a tax acro region. 3 4 Both Source an Ue of Income houl be coniere Tax affect conumer, worker in inutry, an owner of factor of prouction. Economit often ignore the ource ie Incience epen on how price are etermine Inutry tructure matter Short veru long run repone 5 6

2 Incience epen on ipoition of tax revenue Balance buget incience compute the combine effect of levying taxe an government pening finance by thoe taxe. Differential tax incience compare the incience of one tax to another, ignoring how the money i pent. Often the comparion tax i a lump um tax a tax that oe not epen on a peron behavior. There are three baic rule for figuring out who ultimately bear the buren of paying a tax. The tatutory buren of a tax oe not ecribe who really bear the tax. The ie of the market on which the tax i impoe i irrelevant to the itribution of tax buren. Partie with inelatic upply or eman bear the buren of a tax. 7 8 Statutory incience i the buren of the tax borne by the party that en the check to the government. For example, the government coul impoe a 50 per litre tax on upplier of gaoline. Economic incience i the buren of taxation meaure by the change in reource available to any economic agent a a reult of taxation. If ga tation raie gaoline price by 25 per litre a a reult, then conumer are bearing half of the tax. Incience can be analye at a number of level:. Proucer v. conumer (tax on cigarette) 2. Source of income (labour v. capital) 3. Income level (rich v. poor) 4. Region or country (local property taxe) 5. Acro generation (ocial Security reform) 9 0 Key Aumption Two goo economy Only one relative price partial an general equilibrium are ame. Can be viewe a an approx. of incience in a multi goo moel if the market being taxe i mall there are no cloe ubtitute/complement in the utility function Tax revenue i not pent on the taxe goo Tax revenue i ue to buy untaxe goo or thrown away Perfect competition among proucer Relaxe in ome tuie of monopolitic or oligopolitic market Conier, for eae of expoition, a pecific tax. A pecific tax i where the tax i expree a an amount per unit of the goo: e.g. per litre bottle of wine or 20 cent per cigarette. The alternative to a pecific tax i an a valorem tax where the tax i expree a a proportion of the price; hence a tax of 20% on a goo that cot 2 correpon to a tax per unit of 40 cent. For a pecific tax the tax i the ifference between the conumer pai by the conumer P an that receive by the upplier, P. P P = t () 2 2

3 Change in the tax then generate ome combination of change in the two price: P = (2) where the "" i the ifferential operator. To fin out how much quantitie change when the price change we ue the lope of the eman or upply curve: = D p. (3) D p (<0) i the lope of the eman curve, o if we multiply the change in P (the price pai by the conumer) by the lope thi give the correponing change in quantity emane. By the ame logic, where S p (>0) i the lope of the upply curve: = S p. (4) Ue (2) to ubtitute out of (4): = S p.( t) = S p. S p. t (5) So that upply i equal to eman after the tax i introuce it mut be the cae that the change in quantity emane ha to be equal to the change in quantity upplie o: = (6) 3 4 Hence re write (5) a D p. = S p. S p. (7) Rearranging thi give: S p. t = (S p D p ). (8) We get a more intuitive expreion by multiplying above an below by the ratio of price to quantity: S p. P e S P P e e p D p (0) 5 S p (9) S p Dp Thi i an expreion for the incience of the tax on the conumer price an i a poitive number. We get a more intuitive expreion by multiplying above an below by the ratio of price to quantity: 6 where e i the elaticity of upply an e i the elaticity of eman (expree a a negative number). Thi expreion range from to 0. Following imilar tep we get an expreion for the impact on the upply price: () For example, ay a ale tax of 50 per unit i put on a goo. The elaticity of eman i 0.4 an the elaticity of upply i 0.6. Then uing the formulae above the price pai by the conumer rie by 60% of the tax per unit {= 0.6/[0.6 (.4)] = 0.6} that i 30. The price that the eller mut charge fall by 40% of the tax per unit, that i 50 x [.4/(0.6.4)] = 50p x 0.4 = 20. The gap or "wege" between the buyer price an eller' price mut be equal to the tax per unit, 50 in thi cae ince thi i what the government collect per unit. There are four polar cae a we conier high or low value for each elaticity: e 0 e e e

4 : Diagram : Diagram 9 20 : Diagram : Diagram If a market i not perfectly competitive then thi analyi oe not apply. There are lot of form of imperfect competition (uopoly, oligopoly, monopolitic competition an o on) o there are no real general reult here. We look at perhap the implet cae, imple monopoly, which how one intereting poibility. It will be hown that it i poible to have over hifting, that i the egree of tax hifting can be greater than 00%. For example, if the government introuce a tax of on a goo an the price to buyer roe by.20 the egree of hifting i 20%. To ee how thi happen conier the implet cae of a monopoly, a market with a ingle firm, that ha contant marginal cot an face a eman curve with a contant elaticity of eman. 24 After tax profit are given by P. c. T. T i the amount of tax pai per unit an c i the marginal cot (that i of proucing one extra unit). We can re write after tax profit a: P. ( T c). The marginal cot to the firm of an extra unit i effectively the marginal cot of prouction plu the amount it mut pay the government. 4

5 Deman i given by a contant elaticity eman function: P where η (>0) i the elaticity of eman. Remember that a monopolit will never operate on an inelatic part of the eman curve, that i where 0<η<. Why? If it i then aume it increae the price by %. Deman woul fall by le than % by aumption. So revenue woul increae, approximately by ( η)%. Since eman (i.e. quantity) ha fallen the firm' cot have alo fallen. With an increae in revenue an a ecreae in cot it profit mut have rien. So thi cannot be equilibrium. A long a eman i inelatic (η<) the firm can make greater profit by raiing the price. So in a profit maximizing equilibrium it mut be the cae that η>. Let u examine how a monopolit maximie it profit. With the above equation we get. MR MC T c T ( P ) MR P.. P. P. P P A the elaticity of eman i P : Overhifting of Taxe Setting Marginal Revenue equal to Marginal Cot (incluing the tax) implie: c T P T c P T Since η>, it follow that the lat term i greater than : the enominator in {brace} i poitive but le than. In other wor the increae in price i greater than the amount of the tax (per unit). Thi i preciely what we mean by over hifting. A the elaticity of eman goe towar infinity the egree of hifting fall towar one. In other wor it i the firm' market power which enable it to pa on the tax. Pt P t MR c+t c AR curve : Linear eman curve : Linear eman curve For the linear cae, ay. a bp P ( a ) / b Then the lope of the eman curve i b Pt 2 Total Revenue i given by P by TR ( a ) / b The Marginal Revenue i MR ( a2) / b The lope of the Marginal Revenue curve i: MR 2 b So for the linear cae the marginal revenue lope own twice a fat a the eman curve. Thi correpon to Figure below. P T t MR curve c+t c AR eman)curve

6 Extenion of Baic Partial Equilibrium Analyi With price floor, incience can iffer Conier incience of ocial ecurity taxe with minimum wage Statutory incience: 2% on employer an 8% on employee Share of each houl not matter a long a total i contant becaue wage will fall to ajut But with bining minimum wage, employer cannot cut wage further o tatutory incience etermine economic incience on the margin Extenion of Baic Partial Equilibrium Analyi Market rigiitie Imperfect competition Overhifting: poible to get an increae in after tax price > level of the tax A valorem an excie taxation are no longer equivalent Effect on other market: Increae in cigarette tax! ubtitute cigarette for cigar, increaing price of cigar an hifting cigarette eman curve Revenue effect on other market: tax increae make agent poorer; le to pen on other market Thi motivate general equilibrium analyi of incience 3 32 Harberger Two Sector Moel 33 Trace out full incience of taxe back to original owner of factor Partial equilibrium:.proucer. v. conumer General equilibrium: capital owner v. labor v. lanlor, etc. Two type of moel: Static: many ector or many factor of prouction Baic analytical moel: Harberger (962): 2 ector an 2 factor of prouction. Alo many ector an factor. Dynamic Intergenerational incience: Soc Sec reform Aet price effect: capitalization 34. Fixe total upply of labor L an capital K (hort run, cloe economy) 2. Contant return to cale in both prouction ector 3. Full employment of L an K 4. Firm are perfectly competitive 5. All conumer are ientical with homothetic utility function Implicit aumption: no ajutment cot for capital an labor, when the are relocate from one ector to the other Harberger Two Sector Moel: Setup Harberger Two Sector Moel: Setup Prouction in ector (foo) an 2 (car): X = F (K, L) = Lf (k) X2 = F 2 (K2, L2) = L2f (k2) with full employment conition K + K2 = K an L + L2 = L Factor w an L fully mobile o return mut be equal: w = pfl = p2f2l r = pfk = p2f2k Deman function for goo an 2: X = X(p/p2) an X2 = X2(p/p2) Note: Since all conumer are ientical reitribution of income via tax ytem oe not affect eman via a feeback effect Sytem of ten equation an ten unknown: K i, L i, p i,x i,w, r, i=,2. Introuce mall tax on rental of capital in ector 2 (K2) All eqn the ame a above except r = ( )p2f2k Linearize the 0 eq n aroun initial equilibrium to compute the effect of on all 0 variable (w, r, L,...) Labor income = wl with L fixe, rk = capital income with K fixe Therefore change in price w/ an r/ ecribe how tax i hifte from capital to labor Change in price p/, p2/ ecribe how tax i hifte from ector 2 to ector

7 Harberger Two Sector Moel: Main Effect Subtitution effect: capital bear incience Tax on K2 hift prouction in Sector 2 away from K o aggregate eman for K goe own Becaue total K i fixe, r fall o K bear ome of the buren Harberger Two Sector Moel: Main Effect Output effect: capital may not bear incience Tax on K2 implie that ector 2 output become more expenive relative to ector one Therefore eman hift towar ector Cae : K/L < K2/L2 (: foo, 2: car) Sector i le capital intenive o aggregate eman for K goe own Output effect reinforce ubtitution effect: K bear the buren of the tax Cae 2: K/L > K2/L2 (: car, 2: foo) Sector i more capital intenive, aggregate eman for K increae Subtitution an output effect have oppoite ign; labor may bear ome or all the tax Harberger Two Sector Moel: Main Effect Subtitution + Output = Overhifting effect Cae : K/L < K2/L2 Can get overhifting of tax, r < an w > 0 Capital bear more than 00% of the buren if output effect ufficiently trong Taxing capital in ector 2 raie price of car which implie more eman for foo, le eman for car With very elatic eman (two goo are highly ubtitutable), eman for labor rie harply an eman for capital fall harply Capital loe more than irect tax effect an labor upplier gain Harberger Two Sector Moel: Main Effect Subtitution + Output = Overhifting effect Cae 2: K/L > K2/L2 Poible that capital i mae better off by capital tax Labor force to bear more than 00% of incience of capital tax in ector 2 E.g. Conier tax on capital in foo ector: eman for foo fall, eman for car rie Capital in greater eman than it wa before. Thu price of labor fall ubtantially, capital owner actually gain Bottom line: taxe factor may bear le than 0 or more than 00% of tax Harberger Two Sector Moel Theory not very informative: moel mainly ue to illutrate negativereult that anything goe. More interet now in eveloping metho to ientify what actually happen Original Application of thi framework by Harberger: ector = houing an corporation Capital in thee ector taxe ifferently becaue of corporate income tax an many tax ubiie to houing E.g: Deuction for mortgage interet an Harberger mae aumption about elaticitie an calculate incience of corporate tax given potential to ubtitute into houing 42 Computable General Equilibrium Moel Harberger analyze two ector; Subequent literature expane analyi to multiple ector Analytical metho infeaible in multi ector moel Intea, ue numerical imulation to invetigate tax incience effect after pecifying full moel Pioneere by Shoven an Whalley (972). See Kotlikoff ansummer ection 2.3 for a review Prouce a voluminou boy of reearch in PF, trae, an evelopment economic 7