EC426 Class 5, Question 3: Is there a case for eliminating commodity taxation? Bianca Mulaney November 3, 2016

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1 EC426 Class 5, Questio 3: Is there a case for elimiatig commodity taxatio? Biaca Mulaey November 3, 2016

2 Aswer: YES Why? Atkiso & Stiglitz: differetial commodity taxatio is ot optimal i the presece of a optimal oliear icome tax Kaplow: eve whe icome taxatio is ot optimal, differetial commodity tax is ot optimal. Give ANY commodity tax ad icome tax system, differetial commodity taxatio ca be elimiated i a maer that results i a Pareto improvemet

3 Atkiso ad Stiglitz (1971) o Idirect Taxatio Idividual budget costrait: (where q i = cosumer price of good x i = p i + t i ), L = amout of labour supplied Govermet budget costrait: (sum of tax reveues for each commodity = govermet spedig) Govermet maximizes SWF Where U k = U(x,L) is the utility of a represetative idividual Max Lagragia: FOC: Where alpha = margial utility of icome, H k = sum of elasticities of margial utility of x k Result: i a model where all commodities are taxable but leisure is ot, t* k represets the optimal tax rates the govermet will choose (for all k) to maximize cosumer surplus, coditioal o raisig reveue R

4 Key result: Atkiso ad Stiglitz (1971) o Idirect Taxatio Further ituitio: If the utility is homothetic (idifferece curves are idetical i shape, just proportioal resizigs of a give idifferece curve), the H k = 0 for all k ad we have a uiform optimal tax If we assume costat margial disutility of labor, the H 0 = 0 ad the optimal tax rate is iversely proportioal to the price elasticity of demad (Ramsey result) If the margial utility of leisure is idepedet of the cosumptio of every commodity, ad if labor supply is completely ielastic, we have a uiform optimal tax (whe there is a factor that is completely ielastically supplied, it should bear all the tax) If the utility fuctio is directly additive, the utility fuctio depeds iversely o the icome elasticity of demad (optimal tax will be high o goods that are ecessities ad low o luxury goods)

5 The Atkiso-Stiglitz Theorem (1976) h idividuals each choose levels of cosumptio of commodities, x 1,...,x, ad of labor effort L to max utility U h (x, L) s.t. budget costrait qx = w h L h weak separability of labor This gives us the idirect utility fuctio V h (q,w h ) SWF made up of idividual utility fuctios G(U 1,,U N ) Max SWF s.t. govermet reveue costrait Lagragia: With optimal icome tax, gov t reveue costrait becomes Hamiltoia: Set x 2,,x, L as cotrol variables, U as state variable Key result: ß Tax rates are proportioal to the rate at which the MRS betwee good i ad good 1 chages with a chage i the cosumptio of leisure

6 Atkiso & Stiglitz (1976) results - ituitio Tax rates are proportioal to the rate at which the margial rate of substitutio betwee two goods chages with a chage i the cosumptio of leisure Goods that are substitutes with leisure should be taxed more heavily; goods that are complemets with leisure should be taxed less A proportioal tax o labor icome is simply a uiform commodity tax Further, if labor supply is ielastic, we have a lump-sum tax This is i cotrast to Atkiso & Stiglitz (1972): price ad icome elasticities do ot ifluece the optimal idirect taxatio The role of commodity taxatio is greatly reduced whe o-liear icome tax is available If household utility fuctios are separable i goods ad leisure, differetial commodity taxes should ot be used

7 Kaplow (2006) o the udesirability of commodity tax Idividuals choose levels of cosumptio of commodities, x 1,..., x, ad of labor effort l to max utility u(v(x 1,...,x ), l) weak separability of labor Idividual budget costrait: (where (p i + T i ) = et price of good x i, x i (wl) = amout of commodity chose for idividual with icome wl; T = icome tax) Govermet budget costrait: (sum of icome ad commodity tax reveues = govermet spedig) Differetiated vs. Udifferetiated Differetiated: differet proportioal tax rates o goods; vs. udifferetiated:

8 Kaplow (2006) Sceario 1 Differetiated tax t* What happes whe we get rid of it? (t* à 0) Defie a ew icome tax schedule T (wl) that keeps utility uchaged from iitial tax, provided l remais same V(t*, T, wl) = V(0, T, wl) for all wl We fid that T (wl) > T(wl) + t i x i (wl) Reveue is greater tha it was uder the iitial regime Idividuals choose the same amout of labor l (sice T is chose) (Why? Because cosumers ca o loger afford their iitial cosumptio budles, so they must be payig more tax)

9 Kaplow (2006) Sceario 2 Differetiated tax t* What happes whe we reduce it? (t* à αt*, α (0,1)) Defie a ew icome tax schedule T (wl) that keeps utility uchaged from iitial tax, provided l remais same V(t*, T, wl) = V(αt*, T, wl) for all wl We fid that T (wl) + αt * x (wl) > T(wl) + t * x (wl) i i i i Eve whe simply movig towards a more udifferetiated system, reveue is greater tha it was uder the iitial regime

10 So why do we still have a commodity tax? Thik o-ecoomic reasos Admiistrative: Coutries that do t have the admiistrative wherewithal to set up a icome tax might fid it easier to impose broad-based commodity taxes Political: Vehicle excise duty vs. petrol tax i UK Iformatio: A commodity tax gives the govermet useful iformatio o what people are cosumig Visibility: People might ot see a commodity tax as blatatly as icome tax (especially if icome tax is ot PAYE system) otoriously called stealth taxes Reveue-raisig: Govermet: let s ot abolish the taxes we already have, sice implemetig a ew oe could be very difficult

11 SUMMARY OF MAIN CONTRIBUTIONS TO OPTIMAL TAXATION Author Model (chages) Fidigs Ramsey (1927) Diamod ad Mirrlees (1971a, 1971b) Mirrlees (1971) GENERAL MODEL: maximize SWF s.t. tax reveue costrait; (oe) cosumer allocates budget betwee leisure ad multiple goods ASSUMPTIONS: - Costat producer prices, o profits - Zero icome tax (proportioal icome tax allowed) - Liear tax system T(z) = t x z (o lump-sum/oliear taxes) Relax Ramsey s assumptio of fixed producer prices (model productio) ASSUMPTIONS: - Govermet has the ability to tax each iput ad output differetially ad fully tax pure profits (or CRS i productio = zero profits, so profits are t i SWF) - Zero icome tax (commodity taxes oly) Cotrol theoretic optimal o-liear icome tax model Icorporates behavioral respose (equity-efficiecy tradeoff) ASSUMPTIONS: - Idividuals differ i ability - Idetical cosumer prefereces - Noliear tax system T(z) = f(z) Iverse elasticity rule: we should tax ielastic goods to miimize efficiecy costs At the optimum, a icrease i all idirect taxes will decrease compesated demad by the same proportio for all goods (Oly characterizes properties of the optimum; does t provide guidace o what the optimum tax structure would look like) Commodity taxes should ot be uiform (except i special cases) A. Productio efficiecy (eve i a ecoomy where first-best is ot attaiable, optimal policy maitais productio efficiecy): itermediate goods should ot be taxed, (so as ot to distort productio decisios), ad ay public sector producig goods should also be efficiet (ad have the goal of maximizig profits, just as i the private sector, ot geeratig govermet reveue) B. Ramsey rule ca be applied with edogeous prices (eve whe producer prices are ot costat just replace p s with p s that arise i equilibrium) FOC: 0 < T (.) 1, ad T (.) = 0 at the top ad bottom of the skill distributio. (Taxes are flat at the eds ad icreasig otherwise.) Importat for models with asymmetric iformatio (i.e. tax authority ca oly discer people s icomes, ot abilities)

12 SUMMARY OF MAIN CONTRIBUTIONS TO OPTIMAL TAXATION cot d. Author Model (chages) Fidigs Atkiso ad Stiglitz (1976) Combiatio of o-liear icome tax (from Mirrlees) ad proportioal idirect (commodity) taxes (from Ramsey) ASSUMPTIONS: - Weak separability betwee commodities ad leisure - No-liear commodity tax fuctio t i (x i ) Differetial commodity taxatio is ot optimal i the presece of a optimal oliear icome tax (icludig lump-sum icome tax). Optimal o-liear commodity taxes will all be zero, ad optimal redistributio is achieved by icome tax aloe. The Ramsey result is merely a artifact of the restrictio that icome taxes must be liear. Chamley (1983) Kaplow (2006) [ot discussed i lecture] Exteded to o-optimal icome tax fuctios (relax Atkiso ad Stiglitz s assumptio that preexistig icome tax is set optimally) ASSUMPTIONS: - Weak labor separability No capital taxatio i ifiite horizo models Ay o-uiform idirect tax structure ca be replaced with zero or uiform commodity taxes with a Pareto improvemet A-S s 1976 argumet holds regardless of whether the icome tax is optimal Additioal geeral assumptios: - Utility fuctio is cotiuously differetiable, strictly cocave, icreasig i commodities, ad decreasig i labor effort - Commodity prices > 0

13 (For referece - i case you eed it) EXTRA BACKGROUND

14 What are commodity taxes? Tax o the sale of commodities (specific goods or services) Atkiso (1977): direct taxes = adjusted to idividual characteristics of taxpayer idirect taxes = levied o trasactios irrespective of circumstaces of the buyer or seller VAT/sales tax = ad valorem (i proportio to price of good); excise tax = per uit Direct Taxes Icome tax Corpora.o tax Wealth tax Capital gais tax Idirect Taxes Sales tax Excise duty Service tax

15 Why have a commodity tax? Three reasos (Coady ad Drèze 2002) Reveue collectio Iterpersoal redistributio Resource allocatio Kaplow (2006): it is likely that redistributive labor icome taxatio is ot first-best; commodity taxatio may offset this distortio (but it would, o the other had, itroduce distortios i commodity choices)

16 What priciples should guide tax desig? Three criteria (Cowell 2008) Allocative efficiecy Distributioal equity Effective admiistratio

17 Optimum taxatio Goal: maximize SW (miimize DWL) s.t. reveue costrait First best solutio: perfect iformatio à lump-sum taxes (but this is impossible!) Secod best solutio: we have efficiecy costs See: Ramsey, Diamod & Mirrlees, Atkiso & Stiglitz, Chamley/Judd

18 Optimum taxatio Ramsey rule Ramsey: how should tax rates be adjusted to miimize utility loss (give a required reveue to be raised)? A: the taxes should dimiish i the same proportio the productio of each commodity taxed Math: (ext slide)

19 Optimum taxatio Ramsey rule Maximize welfare Solve usig Lagragia: q (p ) max p (q)dq C(q) s.t. R(p,q) C(q) = Π = 0 0 R(p,q) = p q (p ) ad C(q) = C(q 1,q 2,...,q ) L = max q (p ) 0 p (q)dq C(q) + λ ( R(p,q) C(q) ) FOC: L = p C (q) + λ R C (q) q q = 0

Optimum taxatio Ramsey rule Elasticity of demad for good : (Cot d): p C (q) = λ p 1 1 C (q) ε p C (q) = λp 1 1 + λc (q) ε 1 p + λp C (q) λc (q) = λp ε 1 (1 + λ)(p C

20 Optimum taxatio Ramsey rule Elasticity of demad for good : (Cot d): p C (q) = λ p 1 1 C (q) ε p C (q) = λp λc (q) ε 1 p + λp C (q) λc (q) = λp ε 1 (1 + λ)(p C (q)) = λp = λ p ε ε λ p p C (q) = 1 + λ p C (q) p = λ 1 + λ ε 1 ε, λ 1 + λ < 1 **RESULT: tax (=price markup over margial cost) is iversely propor.oal to elas.city of demad

21 Atkiso & Stiglitz (1976) displace Ramsey (1927) guidelies Also, the Ramsey result dictates that we would be heavily taxig more ielastic goods. Why is this a problem? Larger DWL whe the same tax is levied o a more elastic good

22 Sources Atkiso (1977). Optimal Taxatio ad the Direct versus Idirect Cotroversy. **Atkiso ad Stiglitz (1976). The desig of tax structure: Direct versus idirect taxatio Coady, David ad Drèze, Jea (2002). Commodity Taxatio ad Social Welfare: The Geeralized Ramsey Rule. Diamod ad Mirrlees (1971). Optimal taxatio ad public productio I: productio efficiecy. AER [lik] **Kaplow (2006). O the udesirability of commodity taxatio eve whe icome taxatio is ot optimal. [Lik] Mirrlees (1971). A exploratio i the theory of the optimal icome tax. [lik] Ramsey (1927). A cotributio to the theory of taxatio [Lik] ** = mai sources

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