Taxation and Externalities. - Much recent discussion of policy towards externalities, e.g., global warming debate/kyoto

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1 Taxaton and Externaltes - Much recent dscusson of polcy towards externaltes, e.g., global warmng debate/kyoto - Increasng share of tax revenue from envronmental taxaton 6 percent n OECD - Envronmental taxaton has specfc features: () () () (v) Amed at mprovng envronment Envronment tself s a publc good As a publc good, envronment subect to uncoordnated decsons of many agents Wth no maret, results n externaltes - Dstorton can be corrected wth a Pgovan tax placed on consumpton of a drty good (see Fgure ) - Consumpton creates a prvate margnal beneft (PMB), and a margnal loss due to polluton, the sum generatng socal margnal beneft (SMB)

2 Fgure p MC t p PMB SMB q O q E q

3 Socal optmum where SMB=MC, prvate optmum where PMB=MC, the latter resultng n excessve consumpton of the drty good, q E > q O - If government sets a specfc tax t P on consumpton of the drty good, t P =SMB(q O )- PMB(q O ), then the maret equlbrum wll be PMB(q)- t P =MC(q) - t P the Pgovan tax, brngs economy to the frstbest optmum, the tax beng the margnal loss due to polluton, the tax nternalzng the externalty - In general equlbrum, several ssues arse wth taxaton of externaltes: () () If other taxes exst, what happens wth a Pgovan tax(es)? Is there a double dvdend? Can green taxes be used to reduce other dstortonary taxes as well as mprove the envronment (Pearce, 99)? - Followng Salane (2003), use a general equlbrum settng smlar to the Ramsey taxaton problem

4 - I households have utlty functons U (X,L ), all wth dentcal productvtes facng taxes t on n consumpton goods, and a tax rate on ther labor - Frms produce one unt of good from one unt of labor, and f wage s normalzed to, ts consumer prce s (+t ) - Household faces a budget constrant: = ( + t )X = ( -)L + T () where T s a lump-sum transfer. Government has to rase taxes to fnance lump-sum transfers, and also pay G unts of labor - Assume good s drty, whose total consumpton damages the envronment, where e=f(x ), and f s a smooth decreasng functon, the utlty functon becomng U (X,L,e), U ncreasng n e - Assume I s large so that each household neglects ts own mpact on e; producton sets are not affected by qualty of the envronment; and goods > are clean

5 Optmal Green Taxes: () Frst-best case, wth a set of Pareto weghts v, and maxmzng: I = v U (X,L,e) (2) gven e=f(x ), and the producton constrant: n I = = X + G L (3) The frst-order condton on = s: U I U v + v f (X ) = X e = (4) For other goods, >: U v = X and for labor L : U v + = 0 L (5) (6)

6 Substtute (6) nto (4) and (5), for clean goods >: U X - = U L (7) and for =: I U X U e - - f (X ) = U L = U L (8) (8) dffers from standard frst-order condton, as margnal rate of substtuton between the drty good and lesure s corrected for by margnal dsutlty caused by extra consumpton of drty good,.e., left-hand sde of (8) s the socal margnal rate of substtuton Assume government can redstrbute through lump-sum transfers, Pareto optmum can be decentralzed usng approprate tax system, consumer prces are q, and net wage s (-) For all and : U X q - = U L - (9)

7 Suppose =0 and q =+t, then we can choose t =0 for >, and: I U e t = f (X ) = U L (0) Snce U L < 0 and f s decreasng, the tax t >0,.e., the Pgovan tax n general equlbrum when the government can use arbtrary lump-sum transfers () Second-best case, f government has to use unform lump-sum transfers, frst-best no-longer attanable, and t has to choose a vector of tax t rates on goods, where the tax rate on wages s set at zero, and a unform lump-sum transfer T, to maxmze a Bergson-Samuelson socal welfare functon: I W(V,...,V ) () subect to: n IT + G t X (2) =

8 Each ndrect utlty functon V (q,e,t) s defned by maxmzng the utlty functon U (.) subect to the budget constrant q.x L + T Assumng that demand functons for varous goods are ndependent of e, the frst-order condton for q s: I W V V X + f (X ) V q e q = n X = -X + tl q l= l (3) Denote as the margnal utlty of ncome of, and = W V as ther socal margnal utlty of ncome, then: I n X X = X + tl q = l= I W V X + f (X ) V e q = l l (4)

9 I W V Now denote =, and defne a new = V e tax system on goods by t = t for >, and t = t +f (X ) The frst-order condton becomes: I n X X = X + tl q = l= l (5) Where (5) s smlar to the commodty taxaton result, except for the defnton of t P Let t =f (X )>0, t follows that the optmal commodty taxes only vary from the Ramsey optmal rates t R by the addton of the Pgovan tax t P to the tax rate for the drty good: R P R t = t + t, and t = t for > Result due to Sandmo (975) mples that government should not attempt to tax complements to drty good(s) more heavly n second-best optmum

10 () Is there a double-dvdend? What f the green tax t s ncreased and tax on labor s cut to mantan government revenue constrant? Assume ntal pont s not optmal, and that there s only one representatve consumer, wth no lump-sum transfer. Utlty functon U(X,L,e) s maxmzed subect to, n ( + t )X = ( -)L = Snce de = f (X )dx, the tax reform changes utlty: du = U X.dX + ULdL + Uef (X )dx (6) If s the margnal utlty of ncome, then U X =( + t) and U L = -( -), then dvdng through by : du = ( + t).dx - ( -)dl - t p dx (7) where t = U f (X ) p e s the Pgovan tax

11 The producton constrant s n t follows that n = change n utlty s: = X + G = L, so dx = dl, and the normalzed du = t.dx +dl - t p dx (8) The fnal term on the rght-hand sde s the frst dvdend due to mprovement n the qualty of the envronment, whle the frst and second-terms on the rght-hand sde s the second dvdend D = t.dx +dl = n = t dx +dl To get an ntuton of whether there s a double dvdend, assume n fact taxes are optmal, then by defnton du=0, but as the frst-dvdend s always postve, the second dvdend must be negatve Now start from Ramsey optmal taxes when there s no externalty, then by defnton the second dvdend s zero. It follows that the second dvdend can only be postve when the orgnal tax system favors the pollutng good more than the Ramsey-optmal tax system

12 To be more precse, gven D, and the government s budget constrant of: G = n t = X +L (9) As only t and are modfed, revenue stayng constant, then: n = dt X + t dx +dl + Ld = 0 (20) so that D = -Xdt - Ld, but no concluson can be drawn as dt >0 and d<0 To smplfy, assume externaltes are separable n the utlty functon and that utlty over X and L s Cobb-Douglas: ( n - ) = U(X,L,e) = U X ( - L),e (20) where = n =. Computaton shows L=, and therefore does not depend on tax rates, and for each, - X = (2) + t

13 Dfferentatng: dt d dx = -X - + t + t (22) Substtutng n the dfferentated government budget constrant: dt t dtx - tx - d +d = 0 + t + t n = (23) or usng = n =, dt n X + d = 0 + t + t = (24) Substtute n for n -Xdt = d( + t ) + t = n the expresson for D, and usng = n agan, then: n = = t - t D = d (25) + t

14 Wth a Cobb-Douglas utlty functon, all the Ramsey taxes, t s, are equal. If government already has a green tax, then, t > t for all >, and snce d < 0, t follows that the doubledvdend s negatve n ths case Ramsey taxaton by defnton s optmal, and the Pgovan tax s good for the envronment (the frst dvdend), but t s more dstortonary than the labor tax Note, n LDCs, the startng pont may be where t < t for some >, so that the tax system subsdzes drty goods relatve to clean goods, hence D > 0