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An energy Btu tax alternative
RESOURCE
and ENERGY ELSEVIER
Resource and Energy Economics 17 (1995) 291-305
ECONOMICS
An energy Btu tax alternative Gehuang D. Nan " Economics Department, Energy Division, C.H. Guernsey and Company, 5555 North Grand Boulevard, Okhlhoma City, OK 73112, USA Received March 1994; final ve.~ion received October 1994
Abstract This paper extends the Ramsey tax rule and develops a tax rate by minimizing toial excess burden, subject to government tax revenues. This tax rate is a function of its own and other fuels' price elasticities of comFensated demand and supply, its own price and consumption l e v e l , other fuels' prices and consumption l e v e l s , and governmen: revenues. It is this proposed tax rate, not the Ramsey tax ratio, that guides a government to levy a tax efficiently through a minimization of total excess burden. In the case of an energy tax, this tax rate provides direct guidance for taxation on various feels. Moreover, total excess burden generated by the proposed tax rate is significantly less than that produced by the Clinton Administration's proposal. JEL classification: H21; Q41 Keywords: gamsey r-ale; LaD-ang;aa expression; ~..._m=-,'rey,.Btu tax; Excess burden
1. I n t r o d u c t i o n The theory o f e x c e s s burden and optimal taxation is one o f the oldest subjects in the field o f public finance. It has also been well developed in the literature.
* This is a revised chapter o f my Ph.D. thesis at the University of Oklahoma. I greatly appreciate D.A. Murry and a ~eferee for :heir comments and suggestions. I would also like to thank P.A. Diamond, C.L. Ballard, A.J. Kondonassis, C.K. Liew, J.F. Horrell, W.S. Wei, R.C. Dauffenbacl:, D.A. Huettner, J.C. Hartigan, D.J. Pierce, P.R. Bumett, R.J. Kilway, and B.M. Harrington for their valuable information on this research. ! also gratefully acknowledge research support received from the Sarkeys Energy Center, the University of Oklahoma. 0928-7655/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 8 - 7 6 5 5 ( 9 4 ) 0 0 0 2 7 - 1
292
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
Auerbach (1985) stated that '~ p:obably the most celebrated example ... is that of Ramsey's (1927) derivation of optimal commodity tax formulae, now referred to as the Ramsey rule . . . . " Given an assumption for an infinitesimail) ~small tax and given that the level of government spending is fixed, Ramsey stated that the taxes should be such as to diminish the production of two commodities in the same proportion. In other words, if tilt j = e j / e i, total excess burden is minimized; where t is a tax rate and e is a compensated price elasticity of demand. However, the optimal Ramsey ratio has been criticized on the grounds that the ratio is irrelevant to a government's budget, or analogous to an assumption of negligible income effects when a tax is imposed. For example, the approach of marginal excess burden per additional dollar of tax revenue, such as of Fullerton (1991), Browing (1987), Ballard et al. (1985), and Stuart (1984), has improved Ramsey's shortcoming by selecting optimal government spending in a general equilibrium model. On the other hand, the optimal Ramsey ratio, t i / t j = e j / e i, has infinite solutions. This leaves an unso',ved problem to levy a tax. The Clinton Administration proposed an energy Btu (British thermal units) tax to collect a fixed revenue for economic recovery programs, reduce reliance on imported oil, cut down national deficits, and boost U.S. energy conservation and efficiency. ~ The interest in ncw or additional taxes on energy consumption was first sparked by the 1973-74 oil embargo. The broad-based energy tax has also been explored and suggested, for example, by Hudson and Jorgenson (!974a, 1974b). Given expected government revenues, this paper extends the Ramsey rule and develops a tax rate for all fuels. This tax rate is a function of its own and other fuels' price elasticities of compensated demand and supply, its own price and own consumption level, other fuels' prices and consumption levels, and government revenues. Thus this tax rate overcomes the shortcoming of ignoring government budgets in the Ramsey rule. Moreover, this tax rate has the advantage of simplicity in a partial equilibrium model. In the case of an energy taxation, this tax rate minimizes total excess burden and provides direct guidance for taxation on various fuels.
2. A proposed tax rate This section studies excess burden of taxation and revenues constraints, and develops a tax rate which minimizes total excess burden. ~Given compensated demand and supply curves, the objective is to minimize total excess burden, subject to government revenues required to support government programs. The minimization, in turn, results in a proposed tax rate.
i The Administration estimated that the energy Bm tax, if apl:roved and when fully effective, would produce $22 billion in revenue annually.
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293
2.1. Excess burden When the supply curve is perfectly elastic in a simple partial equilibrium model, the well-known excess burden is - ½pq6t2, where p and q are price and quantity before a tax is imposed, e is the compensated price elasticity of demand with a negative value, and t is a tax rate equal to a tax dividing by p. This excess burden formula is derived under the Harberger's (1974) triangle measure, unfortunately, which has been censured for its approximate, rather than exact, results, e However, ~n the incidence of an energy tax, the triangle measure of excess burden is not inappropriate. 3 Accordingly, this paper assumes that the arc of 'ad' and 'cd' in Fig. 1 is a straight line. This paper assumes a supply curve is upward sloping and that the incidence of a tax is imposed on the demand side. As shown in Fig. 1, an imposed tax will shift the demand curve from D~D~ t o D 2 D 2, where p and q are initial equilibrium price and quantity, Q is the quantity consumed after an imposition of a tax, Pa and Pb are price paid by consumers and price received by suppliers respectively, and ot and /3 are excess burden. Assuming y = 1 / 7 1 - I / c , this paper derives an excess-burden formula: 4 pqt 2
a+fl=~,
(1)
2y
where • and 7/are price elasticities of compeasated demand and supply, respectively. Noticeably, e is a negative value, so that ,~ +/3 has a positive value. If one also assumes the supply curve is perfectly elastic, Eq. (I) reduces to the well-known traditional formula, - ½pqet2, and cor, sumers bear the entire burden. On the other hand, when the compensated demand curve is perfectly elastic, total excess burden ! 2 and suppliers bear the entire burden, in an n-commodities case, becomes ~FqTit one can rewrite Eq. (1) as
( , , + t3),= i=l
~ Piqit~
'
(r)
i=i
2 The use of Hicksian (Hicks, 1946) measures of either compensating or equivalent variation, e.g., King (1983), Hausman (1981), Kay (1980), Rosen (1978), and Diamond and McFadden (1974), has improved this shortcoming. ~ It is estimated that the incidence of an energy Btu tax would resul~I in a very small reduction in energy consumption. As shown by McGraw-Hill, Inc. (1993), the U.S. Department of Energy estimated that the impact of the Clinton Administration's proposed energy Btu tax on energy consumption would be that if the incidence of an energy Btu tax began July 1, 1994, ccnsumption of coal, natural gas, oil, and electricity by the year 2000 would be expected to drop by 1.4, 1.2, 1.9, and 1.9%, respectively. 4 See Appendix A for a detailed derivation. This formula has also been developed by Bishop (1968). However, to develop a proposed fuel tax rate, this paper examines all processes in order to show the audience a complete picture.
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
294
Y
D2
Pa P Ih,
Dx
s
[
i
!
O
Q
i
q
X
Fig. 1. Excess burden of a tax.
2.2. Government revenues After an ~mposition of a tax, quantity consumed will decrease. The consumption difference, q - Q, is expected to be a function of t, e, ~/, and other factors. Before developing a tax-revenue equation, this paper derives Eq. (2): s
q-Q-
qt --.
(2)
y
In Fig. 1, government revenues (R 1) equal Q(Pa-Pb), which are derived from a single fuel's taxation. In turn, based on a tax wedge assumption, t - (pa -Pb)/P, one will find that R 1 equals Qpt. Therefore, when there are n fuels' taxes, government revenues (R) equal E~=lQipiti. After substituting Eq. (2)into the government revenues equation, R = E~'= iQipiti, this paper derives Eq. (3): n
R= ~Qipiti i=1
= ~piti[qi-(qi-Qi)] i=l
= Epiqiti - ~ i=l i=l
s Se~. Eqs. (A.12) and (A.13) in Appendix A for a detailed derivation.
piqit-----~'. 2j ~i
(3)
G.D. N a n / R e s o u r c e and Energy Economics 17 (1995) 291-305
295
2.3. Tax rates
To derive proposed tax rates, this research minimizes total excess burden of Eq. (1'), subject to total government revenues of Eq. (3). Combining Eqs. (1') and (3), this paper forms the Lagrangian expression to choose proposed tax rates t i for all fuels: piqit 2 dp= £ i=l
( ~ 1 £ ) p i q i t 2 + A Rpiqiti +
2"Yi
i=
i=1
(4) "~i
'
where A is the Lagrange multiplier. To get the proposed tax rate, this paper follows the classical first-order conditions needed for minimization: adp/at~ = 0 (i = 1,... ,n) and a~/~A = 0. By taking O~/at~ = ~dp/Stj = 0 (i,j = 1,... ,n; i j), this paper derives Eq. (5): 6 ti -
tj
y~- 2t~
=
3'j- 2tj
.
(5)
Rearranging Eq. (5), this paper derives a tax ratio: t~
~,~ = ~,j
1 / % - 1/E~ / = 1/rlj - 1 / e j . ,
( i , j = 1,2,... ,n; i :# j ) .
(6)
If one also a~sumes that a supply curve is perfectly elastic, Eq. (6) reduces to the conventional Ramsey rule (1927); that is, t i / t j = Ej/e i. A difficulty of applying Eq. (6) in taxation is that there are infinite solutions to thh equation. Thus the application of this tax ratio is limited in practice. To develop a useful tool in practice, a further step should be taken. After substituting Eq. (6) into Odp/aA = R - ~ ~p, qit~ + E~-_ l(Piqit~/~'i ) = 0, this paper derives a general formula of tax rates for all fuels (see Appendix B for a detailed derivation):
t i = ~- 1 _+
1-
--
(i= 1,2,...,n),
(7)
lPi qi Ti
where ~,~= 1/7/i - 1/~. Given market prices, quantities consumed, expected government revenues, and price elasticities of compensated demand and supply, the tax rate for all fuels is known. Again, Eq. (7) is derived under the assumption that the Harbetg,er's (1974) triangle measure of excess burden is not inappropriate. Moreover, ihe expected
6 .. i)4j/Oti = piqiti/"/i ti / ( ~ - 2ti).
- Piqi A +
2p, q i a t i / 7 i = O. " A p i q i [ 1 - 2 t i / Y i ]
= Piqiti/7/- Taus a =
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G.D. Nan / Resource and Energy Economics 17 (1995) 291-305
government revenue (R) should be a global case covering all sectors in the economy so that it is a minimization of all sectors' total excess burden. Otherwise, Eq. (7) will present local optima only.
2.4. A sensitivity analysis There are two solutions in Eq. (7): one is the ' + ' term and the other is the ' - ' term. This section provides a sensitivity analysis on these two solutions. There are two examples in this analysis. One case is an increase of government revenues, and the other case is a decrease of all supply elasticities. Changes of other factors can be analyzed in the same way. A major conclusion in this section is that the solution with the ' + ' term in Eq. (7) is unreasonable. Thus this paper discards it and will not show it any more. 7
2.4.1. An increase of government revenues (R) An increase in R, all other factors remaining constant, will increase all t i. The reasons are: (1) an increase in R will increase at least one t~; (2) based upon Eq. (6), the tax ratio should remain constant because all price elasticities of compensated demand and supply do not change. Since all tax ratios of Eq. (6) remain constant and at least one t~ will increase, all ti will increase when expected government revenues increase. In Eq. (7), the 1 - (4R/Y~= l p i q i y i ) t e r m under the square root will decrease because R increases. Thus the solution at the right-hand side of Eq. (7) with the ' - ' term, ½y~(1 - ( - ) , can ensure that all t~ increase when R increases. On the other hand, the solution at the right-hand side 1 of Eq. (7) with the ' + term, ~y~(1 + v/--), will make all t~ fall. Therefore, the solution with the ' + ' term in Eq. (7) is not reasonable. 2.4.2. All supply elasticities decrease All fuels' supply elasticities decrease, but the other factors remain constant. 1 There are two terms, ~Yi and (1 + ¢'-), on the right-hand side of Eq. (7). The 1 - (4R/E~__ i PiqiT~) term under the the square root will increase when all supply elasticities decrease (assuming total expenditure for all fuels does not change); so will the 7Ti term. In turn, the (1 + ~ - ) term increases but the ( 1 - Vr-) term decreases. Based on Eq. (6), one knows that any tax ratio may increase, decrease, or remain constant when all supply elasticities decrease. In other words, when all supply elasticities decrease, some tax rates will increase, others will decrease. This will be ensured by the solution with the 6 -- , term in Eq. (7) because the ~1 Ti term increases but the (! - O r - ) term decreases. The solution with the ' + ' term will ! result in an increase of a!! :, because the ~% term increases and the (1 + ,,/--) term increases also.
7 In the California case, the solution with the " + ' term has a tax-rate range o f 3 1 9 - 6 4 1 % .
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Table 1 California residential and commercial energy consumption data: 1990 Natural gas
Petroleum prd.
Electricity
5.60 2973.8 531035 714
12.00 272.0 22666667
29.26 6646.0 "~ " 1 3 6 0 2 2 ,.2, 0.6719
Residential
Price a Expenditure a Quantity b Budget share
0.3006
0.0275
fli~
-
- 0.098
- 0.612
- 0.016
fli,n
1.029
1.173
0.975
4.96
Commercial
Price a Expenditure ~ Quantity b Budget share
6.28
26.31
1459.7 2 9 4 2 9 4 355
289.8 46146 497
7934.3 3 0 1 5 6 9 745
0.1507
0.0299
0.8193
fl:~
- 0.407
- 0.841
- 0.001
flim
0.994
0.964
1.004
The unit for price and expenditure is $/MBtu and million dollars, respectively. Quantity equals expenditufe ($) dividing by price ($/MBtu), and the unit for quantity is MBtu. Sources: Energy Information Administration (1992b) and Nan and Murry (1992).
a
b
In addition, dividing t i by tj (i =~j) in Eq. (7), one obtains Eq. (6). That is, the (1 - Vr ) term in Eq. (7) is a common factor to all fuels' tax rates. However, the multiplication of ~)'i i and ( 1 - x/- ) may result in an increased, decreased, or constant result. This implies that even though it is a common factor to all fuels' tax rates, the (1 - Vr-) term in Eq. (7) is one of the key factors that adjusts the change, either rise or fail, of tax rates for all fuels when some fa~:tors changes. Additionally, to derive a real-number tax rate, it is required thaL 4R .g. ~'__ ~piq~%. Most importantly, the proposed tax rate developed in this paper is a function of price elasticities of compensated demand and supply, its own price and consumption level, other fuels' prices and consumption levels, and government :evenues. Thus this proposed tax rate overcomes the shortcoming of ignoring government budgets in the Ramsey rule. Therefore it is this proposed tax rate, not the optimal R:~msey tax ratio, that guides a government to levy a tax through a minimization of total excess burden.
3. AR
--~r.~'--~,-,,I .... e . , . v - - app|ication
This Clinton million million
section examines the proposed tax rates developed in this paper. The Administration proposed a broad-based energy Btu tax of 25.7 cents per Btu (MBtu) on coal, natural gas, and nuclear energy, and 59.9 cents per Btu (MBtu) on oil. Hydro power would be taxed on the basis of Btu
298
G.D. Nan ~Resource and Energy Economics 17 (1995) 291-305
Table 2 Compensated elasticities Natural gas
Petroleum prd.
Electricity
- 0.407
- 0.644
- 0.671
- 0.557
- 0.870
- 0.824
Residential • i~
Cc'mmercial 6i~"
content of electricity. 8 Nan and Mu~,'W(1992) developed a flexible double-logarithmic functional form and applied annual residential and commercial data, 1970-1987, to examine demand for natural gas, petroleum products, and electricity in California. Given estimates in Nan and Murry (1992), this paper estimate.: fuels' tax rates in the residentiaTt and commercial sectors of California. Of course, to reach global optima, this res,~:arch sums up both sectors' expected government revenues, treats this sum as one single value, and applies it to Eq. (7). One purpose of this study is to develop tax rates that satisfy the Clinton Administration's energy B~u tax revenues goals and minimize total excess burden. Thus, firstly, the government revenues generated by the Clinton Administration's proposed energy Btu tax should be derived. Because coal consumption in both sectors is insignificant, this study excludes it in the analysis. The updated residential and commercial energy data are summarized in Table 1. The compensated elasticity of demand developed by Nan and Murry (1992) is expressed as Ei~ =//i~ - s~/3~m, where//~ and //~m are constants which are estimated through a model, and si is a budget share. Thus ~* wi.il change as s~ changes. Given 1990 budget shares shown in Table 1, this paper derives price elasticities of compensated demand and reports them in Table 2. On the other hand, there is a term of fuels' supply elasticity in Eq. (7). Unlike demand elasticities, unfortunate!y, energy supply elasticities are less explored in the literature. Edmonson (1975) applied aggregate U.S. energy data, from 1901 to 1968, and reported an aggregate U.S. mineral energy supply elasticity of 0.5. This paper assumes that supply elasticity c~f natural gas is 0.25.9 I~ accordance with Kaufmann (1991) and Kaufmann et al. (1994), this paper assumes oil supply elasticity is approximately equal to 0.3. This paper further assumes the supply elasticity of electricity equals 0.5. Based on fuels' data shown in Energy Information Administration (1992b) and on the Clinton Administration's energy Btu tax proposal, this paper derives
s See, for example, page 32 of Studness (1993). 9 A note from R.B. Kalisch of American Gas Association to the author on June 9, 1993, c o m m e n t e d on the elasticity of natural gas supplies: " . . . In the short run ... there is some evidence thet monthly natural gas production has about a 0.25 elasticity to short-run wellhead price .... ".
G.D. Nan ~Resource and Energy Economics 17 (1995) 291-305
299
1'~le 3 Proposed tax rates Natur,~! gas
The Clinton Administration Residential 4.59% (0.257) Commercial 5.18% (0.257) This study Residential Commercial
3.67% (C.206) 3.30% (0.104)
Petroleum prd.
Electricity
4.99% (0.599) 9.54% (0.599)
1.25% (0.366) 1.39% (0.366)
2.78% (0.334) 2.55% (0.160)
1.99% (0.582) 1.83% (0.481)
l'he value in parentheses is a Pa:-i's tax ($/MBtu).
total tax revenues of $233266625 and $213757908 for the residential and the commercial sectors, respectively. Thus total tax revenues derived from both sectors are $447 024 533. ~0 Thus all variables on the right-hand side of Eq. (7) are known. The proposed tax rates are summarized in Table 3. The results show that natural gas, petroleum products, and electricity in the residential sector have proposed tax rates of 3.67, 2.78, and 1.99%, respectively. In the commercial sector, the proposed tax rates for natural gas, petroleum products, and electricity are 3.30, 2.55, and 1.83%, respectively.
4. Comparison Based on the Clinton Administration's energ3' Btu tax revenues, this study attempts to develop proposed fuels" tax rates that minimize total excess burden. Consequently, it is interesting to compare two approaches' results. Certainly, a comparison of total excess burden generated by both approaches is highly desirable in this study. In accordance with Eq. (1), an excess burden because of an imposed tax is equal to pqtZ/{2[(1/rl)-(1/e)]}. The Clinton Administration's energy taxation is based on an energy Btu content. Thus one needs to develop tax rates for the Clinton Administration's approach to derive total excess burden. By a tax wedge assumption of a tax incidence, a t~x rate is defined as a ratio of a tax to the price before a tax is imposed. Given an energy Btu tax of $0.257 and $0.599 for natural gas and petroleum products, respectively, and given prices of these two fuels reported in Table 1, one can derive the Clinton Administration's tax rates for natural gas and
l0 See Appendix C for a detailed derivation.
300
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
Table 4 Total excess burden Residential
The Clinton Administration Natural gas $484999 Petro. prod. $69353 Electricity $149 255
Commercial
Total
$338110 $294075 $239 363
$823109 $363428 $388 618 $1575155
$137146 $21019 $413 419
$447 304 $42530 $790 446 $1280 280
This study Natural gas Petro. prod. Electricity
$310158 $21511 $377 027
petroleum products, equal to 4.589 and 4.992%, respectively. In addition, based on appendix C, tax revenues for electricity consumption are $83213113 and $110482508 for the residential and the commercial sectors, respectively. In accordance with Table 1, total electricity consumption is 227136022 and 301569745 MBtu for the residential and the commercial sector, respectively. Thus one can derive a tax of $0.366/MBtu for electricity consumption for both sectors under the Clinton Administration's proposal. Given electricity price shown in Table 1 and a tax of $0.366/MBtu, one can derive tax rates for electricity consumption in both sectors. The derived tax rates under the Clinton Administration's proposal are reported in Table 3. Substituting all individual numbers into Eq. (1), one can derive an excess burden of taxation for each fuel. This study summarizes all fuels' excess burden in Table 4. Total excess burden results from tax rates developed in this study is $1 280280 and $1575 155 for the Clinton Administration's proposal. Based upon the excess burden of $1 280280 generated by this study, the excess burden produced by the Clinton Administration's proposal is higher by 23%.
5. Conc~csion This paper extends Ramsey tax rule and develops a tax rate by minimizing total excess burden, subject to government tax revenues. This proposed tax rate is a f:mction of its own and other fuels' price elasticities of compensated demand and supply, its own price and consumption level, other fuels' prices and consumption levels, and government revenues. Thus this proposed tax rate overcomes the shortcoming of ignoring government budgets in the Ramsey rule. Most importantly, it is this proposed tax rate, not the optimal tax ratio of Ramsey rule, that guides the government to levy a tax through a minimization of total excess burden.
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
301
Moreover, this proposed tax rate has the advantage of simplicity in a partial equilibrium model. In the case of an energy tax, this proposed tax rate provides direct guidance for taxation on various fuels. By using California data, this paper estimates tax rates for natural gas, petroleum products, and electricity consumed in the residential and commercial sectors. Based on the Clinton Administration's proposed energy Btu tax and on Nan and Murry (1992), this paper derives expected government tax revenues and develops price elasticities of compensated demand in the residential and commercial sectors. The results show that the highest proposed tax rate is 3.67% for the residential natural gas consumption. The lowest proposed tax rate is 1.83% for the commercial electricity consumption. On the other hand, the Clinton Administration's energy Btu tax proposal generates a highest tax rate of 9.54% for the commercial petroleum products consumption; the lowest tax rate is 1.25% for the residential electricity consumption. In addition, total excess burden generated by the Clinton administration's proposal is 23% higher t!.'an that produced by this study. Moreover, one of the big objections to the energy Btu tax was its effect on competitiveness. In other words, U.S. firms would loose market share to nations that did not impose the tax. Unfortunately, the proposed tax rate developed in this research was unab!e to capture this argument. Certainly, it is a good topic for further research.
Appendix A: Excess burden derivation By definition of price elasticities of compensated demand (e) and supply (r/), one obtains Eqs. (A.1) and (A.2): E=(Sq/Sp)(p/q)
= [(Q-q)/(Pa-P)](P/q).
rl = ( i)q/Op)( p / q ) = [(Q - q ) / ( Pb - - P ) ] ( P / q)"
Rearranging Eqs. (A.1) and (A.2), one derives Eqs. (A.I') and (A.2'): q-Q--q~(pa -p)/p. q - Q = qn( P - Pb ) / P . Dividing Eq. (A.1) by Eq. (A.2), one derives Eq. (A.3): e/n=(p--pb)/(p--p~).
(A.1) (A.2) (A.I') (A.2') (A.3)
By a tax wedge assumption of a tax incidence, one has Eq. (,~.4): t=(pa-Pb)/P.
(A.4)
Rewriting Eq. (A.4), one has Eqs. (A.4') and (A.4"): p a = t p + Pb"
(A.4')
Pb = P~ -- tp.
(a.4")
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302
Substituting Eq. (A.4') into Eq. (A.3) and Eq. (A.4") into Eq. (A.3), respectively, one derives Eqs. (A.5) and (A.6): p - p~ = tp(~/( ~. - 7)).
(A.5)
po - p = - t p n / (
(A.6)
n).
By definition, one has Eqs. (A.7) and (A.8): a=(q-Q)(pa-p)/2
(A.7)
fl= ( q - Q)( p - p b ) / 2
(A.8)
Substituting Eqs. (A.I') and (A.6) into Eq. (A.7), and Eqs. (A.2') and (A.5) into Eq. (A.8), one derives Eqs. (A.9) and (A.IO): a = [ - q , ( Pa - P ) 2 ] / 2 P
= -Pqer/z.t2/[2( " - ,/)2].
(A.9)
/3= [qr/( p - - p b ) E ] / 2 p = p q r / , 2 t 2 / [ 2 ( , - ,)2].
(A.10)
Adding up Eqs. (A.9) and (A.10), one derives Eq. (.4,.11): a +/3= (pqr/,2t2-pqer/2t2)/[2(
7/)2]
,-
= pq,rlt2/[2( ,--,))] =pq,'2/{2[(1/))) - ( 1 / ~ ) ] }.
(A.11)
Thus fi,qs paper derives Eq, (1). Based 9n Eqs. (A.7) a~,d (A,.9), one derive.,.; Eq. (A.12): ( q - Q)( pa - p) / 2 = - p q e r / 2 t 2 / [ 2 ( e - ,/)2].
(A.12)
After substituting Eq. (A.6), P a - P = -tpr//(~--r/), into Eq. (A.12), one derives Eq. (A.!3): q-Q=
--pqEr/2 t 2
qer/t
(e-- r/)2(pa --p)
~ - 7/
qt =
l / r / - 1/e
.
(A.13)
Thus this paper derives Eq. (2).
Appendix B: Derivation of the proposed tax rate
Given O~b/OA= R - E~= l piqiti + E'~= l(Piqit2/Ti) = 0, one rewrites this as: R = ~,piqiti 1 i
~--i
=
Plqltl
1-
-~--
+
1=
pjqjtj 1
-- . ~1
(B.1)
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
303
Rewriting Eq. (6) as tj = t i Y j / y 1 or tj/Tj = ti/)q ( j = 2,3,...,n) and substitming these into Eq. (B.1), one derives Eq. (B.2):
R = p t q t t s 1---yl
t 't
=t i 1-~
~tl
+
Pjqjtl ~ +
Yl
j=2
1---yt
"~1
(B.2)
=t I 1--~ YJ
i= I
Y~
Rearranging Eq. (B.2), one derives a quadratic equation:
1 ~t2--tt+
Y!
n
Ry !
=0.
(B.3)
E Piqi~'i t=l
The solutk ~l to Eq. (B.3) is:
t I = -~- 1 +
J
1 - i~l piqi~/i
)
(Bo4)
Rewriting Eq. (6) as t,-= y , t ~ / y ~ (i = 2,3,...,n) and substituting Eq. (B.4) into it, this paper derives Eq. (7).
Appendix C: Energy Btu t a x e s revenues For gas and petroleum products, Btu taxes revenues equal total consumption (MBtu) shown in Table 1, multiplying by 0.257 ($/MBtu) for gas and by 0.599 ($/MBtu) for petroleum products. Thus total tax revenues from gas and petroleum products consumption in the residential and commercial sectors are $150053 512 and $103 275 401, respectively. Electricity Btu tax revenues are more com#icated than those for oil and gas. As data show in Table 14 of Energy Information Administration (1992a), energy sources for electric generation in California include gas, oil, nuclear fuel, and hydro power. Additionally, gas, oil, and nuclear fuel are taxed based on heat content. However, hydro power is taxed based on electricity content, rather than heat content. In accordance with Nan (1994), only approximately 34% of heat content will be converted into electricity content. Dividing expenditure ($) by price ($/MBtu) in the electric sector of Energy Information Administration (1992b), one will find gas, petroleum products, and nuclear fuel contribute
304
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
471617162, 46192661, and 349861 111 MBtu, respectively, in heat content for power generation. Based on Table 14 of Energy Information Administration (1992a) and on a conversion factor, MBtu = 293 Kwh, hydro power generates 81211604 MBtu in electricity content. Thus multiplying $0.599 for petroleum products and $0.257 for the rest, the government can obtain Btu taxes of $121205 611, $27 669404, $89914 306, and $20871382 from gas, petroleum products, nuclear fuel, and hydro power, respectively. Thus total Btu tax revenues received from electricity generation in California are $259660702. However, these tax revenues, $259 660 702, should distribute to the residential, commercial induetrial, and transportation sectors. To derive the residential and commercial electricity consumption tax revenues, one needs a further calculation. Given price ($/MBtu) and expenditure ($) of electricity in four sectors shewn in Energy Information Administration (1992b), one derives 227136022, 301569745, 179241218, and 815094 MBtu in electricity content in the residential, commercial, industrial, and transportation sectors, respectively. Thus total amount is 708762079 MBtu. In turn, one can derive MBtu shares in electricity content in the residential, commercial, industrial, and transportation sectors, which are 0.3205, 0.4255, 0.2529, and 0.0012, respectively. Multiplying $259 660 702 by these MBtu shares, one will derive tax revenues of $83 213 113 and $110482508 received from residential and commercial electricity comamption, respectively. Therefore total tax revenues received from consuming gas, pc*roleum products, and electricity are $233 266625 and $213 757 908 for the residential and commercial sectors, respectively. In the empirical analysis, the sum, $447 024 533, i:, applied to get global optima.
References Auerbach, A.J., 1985, The theory of excess burden and optimal taxation, in: AJ. Auerbach and M. Feldstein, eds., Handbook of public economics, Vol. I (North-Holland, Amsterdam). Ballard, C.L., J.B. Shoven and J. Whalley, 1985, General equilibrium computations of the marginal welfare costs of taxes in the United States, American Economic Review 75, 128-138. Bishop, R.L., 1968, The effects of specific and ad valorem taxes, Quarterly Journal of Economics, May, 198-218. Browning, E.K., 1987, On the marginal welfare cost of taxation, American Economic Review 77, 11-23.
Diamond, P.A. and D.L. McFadden, 1974, Some uses of the expenditure function in public finance, Journal of Public Economics 3, 3-21. Edmonson, N., 1975, Real price and the consumption of mineral energy in the United States: 1901-1968, Journal of Induslrial Economics 22, 161-74. Energy Information Administration, 1992a, Electric power annual 1990, Department of Energy, January. Energy Information Administration, 1992b, State energy price and expenditure report 1990, Department of Energy, September. Fullerton, D., 1991, Reconciling recent estimates of the marginal welfare cost of taxation, American Economic Review 81, 302-308.
G.D. Nan/Resource and Energy Ecol,~omics 17 (1995) 291-305
305
Harberger, A.C., ed., 1974, Taxation, resource allocation, ~nd welfare, in: Taxation and welfare (Little Brown, Boston). Hausman, J.A., 1981, Exact consumer's surplus and deadweight loss, American Economic Review 71, 662-676. Hicks, J.R., 1946, Value and capital, 2nd Ed. (Oxford University Press, Oxford). Hudson, E.A. and D.W. Jorgenson, 1974a, U.S. energy policy and economic growth: 1975-2000, The Bell Journal of Economics and Management Science 5, 461-514. Hudson, E.A. and D.W. Jorgenson, 1974b, Tax policy and energy conservation, Testimony before the Committee of Finance, U.S. Senate, Jan. 29. Kaufmann, R.K., 1991, Oil production in the lower 48 states: Reconciling curve fitting and econometric techniq,~es, Resourcvs and Energy 13, 111-127. Kaufmann, R.K., W. Gruen, and R. Montesi, 1994, Drilling rates and expected oil prices: The own price elasticity of L~S. oil supply, Energy Sources 16, 39-58. Kay, J°A., 1980, The deadweight loss from a tax system, Journal of Public Economics 13, 111-120. King, M.A., 1983, Welfare analysis of tax reforms using household data, Journal of Public Economics 21, 183-214. McGraw-Hill, Inc., 1993, Clinton energy tax proposal sets stage for major battle in congress, Electric Utility Week, Feb. 22, 3-4. Nan, G.D., 1994, Sulfur dioxide emissions and U.S. new regulation, Resources Policy 20, 71-75. Nan, G.D. and D.A. Murry, 1992, Energy demand with the flexible double-logarithmic functional form, The Energy Journal 13, 149-159. Ramsey, F.P., 1927, A contribution to the theory of taxation, Economic Journal 37, 47-61. Rosen, H., 1978, The measurement of excess burden with explicit utility functions, Journal of Political Economy 86, $121-136. Studness, C.M., 1993, An energy tax and the electric utilities, Public Utilities Fortnightly, April 1, 32. Stuart, C.E., 1984, Welfare costs per dollar of additional tax revenue in the United Sta~es, American Economic Review 74, 352-362.
and ENERGY ELSEVIER
Resource and Energy Economics 17 (1995) 291-305
ECONOMICS
An energy Btu tax alternative Gehuang D. Nan " Economics Department, Energy Division, C.H. Guernsey and Company, 5555 North Grand Boulevard, Okhlhoma City, OK 73112, USA Received March 1994; final ve.~ion received October 1994
Abstract This paper extends the Ramsey tax rule and develops a tax rate by minimizing toial excess burden, subject to government tax revenues. This tax rate is a function of its own and other fuels' price elasticities of comFensated demand and supply, its own price and consumption l e v e l , other fuels' prices and consumption l e v e l s , and governmen: revenues. It is this proposed tax rate, not the Ramsey tax ratio, that guides a government to levy a tax efficiently through a minimization of total excess burden. In the case of an energy tax, this tax rate provides direct guidance for taxation on various feels. Moreover, total excess burden generated by the proposed tax rate is significantly less than that produced by the Clinton Administration's proposal. JEL classification: H21; Q41 Keywords: gamsey r-ale; LaD-ang;aa expression; ~..._m=-,'rey,.Btu tax; Excess burden
1. I n t r o d u c t i o n The theory o f e x c e s s burden and optimal taxation is one o f the oldest subjects in the field o f public finance. It has also been well developed in the literature.
* This is a revised chapter o f my Ph.D. thesis at the University of Oklahoma. I greatly appreciate D.A. Murry and a ~eferee for :heir comments and suggestions. I would also like to thank P.A. Diamond, C.L. Ballard, A.J. Kondonassis, C.K. Liew, J.F. Horrell, W.S. Wei, R.C. Dauffenbacl:, D.A. Huettner, J.C. Hartigan, D.J. Pierce, P.R. Bumett, R.J. Kilway, and B.M. Harrington for their valuable information on this research. ! also gratefully acknowledge research support received from the Sarkeys Energy Center, the University of Oklahoma. 0928-7655/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 8 - 7 6 5 5 ( 9 4 ) 0 0 0 2 7 - 1
292
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
Auerbach (1985) stated that '~ p:obably the most celebrated example ... is that of Ramsey's (1927) derivation of optimal commodity tax formulae, now referred to as the Ramsey rule . . . . " Given an assumption for an infinitesimail) ~small tax and given that the level of government spending is fixed, Ramsey stated that the taxes should be such as to diminish the production of two commodities in the same proportion. In other words, if tilt j = e j / e i, total excess burden is minimized; where t is a tax rate and e is a compensated price elasticity of demand. However, the optimal Ramsey ratio has been criticized on the grounds that the ratio is irrelevant to a government's budget, or analogous to an assumption of negligible income effects when a tax is imposed. For example, the approach of marginal excess burden per additional dollar of tax revenue, such as of Fullerton (1991), Browing (1987), Ballard et al. (1985), and Stuart (1984), has improved Ramsey's shortcoming by selecting optimal government spending in a general equilibrium model. On the other hand, the optimal Ramsey ratio, t i / t j = e j / e i, has infinite solutions. This leaves an unso',ved problem to levy a tax. The Clinton Administration proposed an energy Btu (British thermal units) tax to collect a fixed revenue for economic recovery programs, reduce reliance on imported oil, cut down national deficits, and boost U.S. energy conservation and efficiency. ~ The interest in ncw or additional taxes on energy consumption was first sparked by the 1973-74 oil embargo. The broad-based energy tax has also been explored and suggested, for example, by Hudson and Jorgenson (!974a, 1974b). Given expected government revenues, this paper extends the Ramsey rule and develops a tax rate for all fuels. This tax rate is a function of its own and other fuels' price elasticities of compensated demand and supply, its own price and own consumption level, other fuels' prices and consumption levels, and government revenues. Thus this tax rate overcomes the shortcoming of ignoring government budgets in the Ramsey rule. Moreover, this tax rate has the advantage of simplicity in a partial equilibrium model. In the case of an energy taxation, this tax rate minimizes total excess burden and provides direct guidance for taxation on various fuels.
2. A proposed tax rate This section studies excess burden of taxation and revenues constraints, and develops a tax rate which minimizes total excess burden. ~Given compensated demand and supply curves, the objective is to minimize total excess burden, subject to government revenues required to support government programs. The minimization, in turn, results in a proposed tax rate.
i The Administration estimated that the energy Bm tax, if apl:roved and when fully effective, would produce $22 billion in revenue annually.
G.D. Nan/Resource and Enerey Economics 17 (1995) 291-305
293
2.1. Excess burden When the supply curve is perfectly elastic in a simple partial equilibrium model, the well-known excess burden is - ½pq6t2, where p and q are price and quantity before a tax is imposed, e is the compensated price elasticity of demand with a negative value, and t is a tax rate equal to a tax dividing by p. This excess burden formula is derived under the Harberger's (1974) triangle measure, unfortunately, which has been censured for its approximate, rather than exact, results, e However, ~n the incidence of an energy tax, the triangle measure of excess burden is not inappropriate. 3 Accordingly, this paper assumes that the arc of 'ad' and 'cd' in Fig. 1 is a straight line. This paper assumes a supply curve is upward sloping and that the incidence of a tax is imposed on the demand side. As shown in Fig. 1, an imposed tax will shift the demand curve from D~D~ t o D 2 D 2, where p and q are initial equilibrium price and quantity, Q is the quantity consumed after an imposition of a tax, Pa and Pb are price paid by consumers and price received by suppliers respectively, and ot and /3 are excess burden. Assuming y = 1 / 7 1 - I / c , this paper derives an excess-burden formula: 4 pqt 2
a+fl=~,
(1)
2y
where • and 7/are price elasticities of compeasated demand and supply, respectively. Noticeably, e is a negative value, so that ,~ +/3 has a positive value. If one also assumes the supply curve is perfectly elastic, Eq. (I) reduces to the well-known traditional formula, - ½pqet2, and cor, sumers bear the entire burden. On the other hand, when the compensated demand curve is perfectly elastic, total excess burden ! 2 and suppliers bear the entire burden, in an n-commodities case, becomes ~FqTit one can rewrite Eq. (1) as
( , , + t3),= i=l
~ Piqit~
'
(r)
i=i
2 The use of Hicksian (Hicks, 1946) measures of either compensating or equivalent variation, e.g., King (1983), Hausman (1981), Kay (1980), Rosen (1978), and Diamond and McFadden (1974), has improved this shortcoming. ~ It is estimated that the incidence of an energy Btu tax would resul~I in a very small reduction in energy consumption. As shown by McGraw-Hill, Inc. (1993), the U.S. Department of Energy estimated that the impact of the Clinton Administration's proposed energy Btu tax on energy consumption would be that if the incidence of an energy Btu tax began July 1, 1994, ccnsumption of coal, natural gas, oil, and electricity by the year 2000 would be expected to drop by 1.4, 1.2, 1.9, and 1.9%, respectively. 4 See Appendix A for a detailed derivation. This formula has also been developed by Bishop (1968). However, to develop a proposed fuel tax rate, this paper examines all processes in order to show the audience a complete picture.
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
294
Y
D2
Pa P Ih,
Dx
s
[
i
!
O
Q
i
q
X
Fig. 1. Excess burden of a tax.
2.2. Government revenues After an ~mposition of a tax, quantity consumed will decrease. The consumption difference, q - Q, is expected to be a function of t, e, ~/, and other factors. Before developing a tax-revenue equation, this paper derives Eq. (2): s
q-Q-
qt --.
(2)
y
In Fig. 1, government revenues (R 1) equal Q(Pa-Pb), which are derived from a single fuel's taxation. In turn, based on a tax wedge assumption, t - (pa -Pb)/P, one will find that R 1 equals Qpt. Therefore, when there are n fuels' taxes, government revenues (R) equal E~=lQipiti. After substituting Eq. (2)into the government revenues equation, R = E~'= iQipiti, this paper derives Eq. (3): n
R= ~Qipiti i=1
= ~piti[qi-(qi-Qi)] i=l
= Epiqiti - ~ i=l i=l
s Se~. Eqs. (A.12) and (A.13) in Appendix A for a detailed derivation.
piqit-----~'. 2j ~i
(3)
G.D. N a n / R e s o u r c e and Energy Economics 17 (1995) 291-305
295
2.3. Tax rates
To derive proposed tax rates, this research minimizes total excess burden of Eq. (1'), subject to total government revenues of Eq. (3). Combining Eqs. (1') and (3), this paper forms the Lagrangian expression to choose proposed tax rates t i for all fuels: piqit 2 dp= £ i=l
( ~ 1 £ ) p i q i t 2 + A Rpiqiti +
2"Yi
i=
i=1
(4) "~i
'
where A is the Lagrange multiplier. To get the proposed tax rate, this paper follows the classical first-order conditions needed for minimization: adp/at~ = 0 (i = 1,... ,n) and a~/~A = 0. By taking O~/at~ = ~dp/Stj = 0 (i,j = 1,... ,n; i j), this paper derives Eq. (5): 6 ti -
tj
y~- 2t~
=
3'j- 2tj
.
(5)
Rearranging Eq. (5), this paper derives a tax ratio: t~
~,~ = ~,j
1 / % - 1/E~ / = 1/rlj - 1 / e j . ,
( i , j = 1,2,... ,n; i :# j ) .
(6)
If one also a~sumes that a supply curve is perfectly elastic, Eq. (6) reduces to the conventional Ramsey rule (1927); that is, t i / t j = Ej/e i. A difficulty of applying Eq. (6) in taxation is that there are infinite solutions to thh equation. Thus the application of this tax ratio is limited in practice. To develop a useful tool in practice, a further step should be taken. After substituting Eq. (6) into Odp/aA = R - ~ ~p, qit~ + E~-_ l(Piqit~/~'i ) = 0, this paper derives a general formula of tax rates for all fuels (see Appendix B for a detailed derivation):
t i = ~- 1 _+
1-
--
(i= 1,2,...,n),
(7)
lPi qi Ti
where ~,~= 1/7/i - 1/~. Given market prices, quantities consumed, expected government revenues, and price elasticities of compensated demand and supply, the tax rate for all fuels is known. Again, Eq. (7) is derived under the assumption that the Harbetg,er's (1974) triangle measure of excess burden is not inappropriate. Moreover, ihe expected
6 .. i)4j/Oti = piqiti/"/i ti / ( ~ - 2ti).
- Piqi A +
2p, q i a t i / 7 i = O. " A p i q i [ 1 - 2 t i / Y i ]
= Piqiti/7/- Taus a =
296
G.D. Nan / Resource and Energy Economics 17 (1995) 291-305
government revenue (R) should be a global case covering all sectors in the economy so that it is a minimization of all sectors' total excess burden. Otherwise, Eq. (7) will present local optima only.
2.4. A sensitivity analysis There are two solutions in Eq. (7): one is the ' + ' term and the other is the ' - ' term. This section provides a sensitivity analysis on these two solutions. There are two examples in this analysis. One case is an increase of government revenues, and the other case is a decrease of all supply elasticities. Changes of other factors can be analyzed in the same way. A major conclusion in this section is that the solution with the ' + ' term in Eq. (7) is unreasonable. Thus this paper discards it and will not show it any more. 7
2.4.1. An increase of government revenues (R) An increase in R, all other factors remaining constant, will increase all t i. The reasons are: (1) an increase in R will increase at least one t~; (2) based upon Eq. (6), the tax ratio should remain constant because all price elasticities of compensated demand and supply do not change. Since all tax ratios of Eq. (6) remain constant and at least one t~ will increase, all ti will increase when expected government revenues increase. In Eq. (7), the 1 - (4R/Y~= l p i q i y i ) t e r m under the square root will decrease because R increases. Thus the solution at the right-hand side of Eq. (7) with the ' - ' term, ½y~(1 - ( - ) , can ensure that all t~ increase when R increases. On the other hand, the solution at the right-hand side 1 of Eq. (7) with the ' + term, ~y~(1 + v/--), will make all t~ fall. Therefore, the solution with the ' + ' term in Eq. (7) is not reasonable. 2.4.2. All supply elasticities decrease All fuels' supply elasticities decrease, but the other factors remain constant. 1 There are two terms, ~Yi and (1 + ¢'-), on the right-hand side of Eq. (7). The 1 - (4R/E~__ i PiqiT~) term under the the square root will increase when all supply elasticities decrease (assuming total expenditure for all fuels does not change); so will the 7Ti term. In turn, the (1 + ~ - ) term increases but the ( 1 - Vr-) term decreases. Based on Eq. (6), one knows that any tax ratio may increase, decrease, or remain constant when all supply elasticities decrease. In other words, when all supply elasticities decrease, some tax rates will increase, others will decrease. This will be ensured by the solution with the 6 -- , term in Eq. (7) because the ~1 Ti term increases but the (! - O r - ) term decreases. The solution with the ' + ' term will ! result in an increase of a!! :, because the ~% term increases and the (1 + ,,/--) term increases also.
7 In the California case, the solution with the " + ' term has a tax-rate range o f 3 1 9 - 6 4 1 % .
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297
Table 1 California residential and commercial energy consumption data: 1990 Natural gas
Petroleum prd.
Electricity
5.60 2973.8 531035 714
12.00 272.0 22666667
29.26 6646.0 "~ " 1 3 6 0 2 2 ,.2, 0.6719
Residential
Price a Expenditure a Quantity b Budget share
0.3006
0.0275
fli~
-
- 0.098
- 0.612
- 0.016
fli,n
1.029
1.173
0.975
4.96
Commercial
Price a Expenditure ~ Quantity b Budget share
6.28
26.31
1459.7 2 9 4 2 9 4 355
289.8 46146 497
7934.3 3 0 1 5 6 9 745
0.1507
0.0299
0.8193
fl:~
- 0.407
- 0.841
- 0.001
flim
0.994
0.964
1.004
The unit for price and expenditure is $/MBtu and million dollars, respectively. Quantity equals expenditufe ($) dividing by price ($/MBtu), and the unit for quantity is MBtu. Sources: Energy Information Administration (1992b) and Nan and Murry (1992).
a
b
In addition, dividing t i by tj (i =~j) in Eq. (7), one obtains Eq. (6). That is, the (1 - Vr ) term in Eq. (7) is a common factor to all fuels' tax rates. However, the multiplication of ~)'i i and ( 1 - x/- ) may result in an increased, decreased, or constant result. This implies that even though it is a common factor to all fuels' tax rates, the (1 - Vr-) term in Eq. (7) is one of the key factors that adjusts the change, either rise or fail, of tax rates for all fuels when some fa~:tors changes. Additionally, to derive a real-number tax rate, it is required thaL 4R .g. ~'__ ~piq~%. Most importantly, the proposed tax rate developed in this paper is a function of price elasticities of compensated demand and supply, its own price and consumption level, other fuels' prices and consumption levels, and government :evenues. Thus this proposed tax rate overcomes the shortcoming of ignoring government budgets in the Ramsey rule. Therefore it is this proposed tax rate, not the optimal R:~msey tax ratio, that guides a government to levy a tax through a minimization of total excess burden.
3. AR
--~r.~'--~,-,,I .... e . , . v - - app|ication
This Clinton million million
section examines the proposed tax rates developed in this paper. The Administration proposed a broad-based energy Btu tax of 25.7 cents per Btu (MBtu) on coal, natural gas, and nuclear energy, and 59.9 cents per Btu (MBtu) on oil. Hydro power would be taxed on the basis of Btu
298
G.D. Nan ~Resource and Energy Economics 17 (1995) 291-305
Table 2 Compensated elasticities Natural gas
Petroleum prd.
Electricity
- 0.407
- 0.644
- 0.671
- 0.557
- 0.870
- 0.824
Residential • i~
Cc'mmercial 6i~"
content of electricity. 8 Nan and Mu~,'W(1992) developed a flexible double-logarithmic functional form and applied annual residential and commercial data, 1970-1987, to examine demand for natural gas, petroleum products, and electricity in California. Given estimates in Nan and Murry (1992), this paper estimate.: fuels' tax rates in the residentiaTt and commercial sectors of California. Of course, to reach global optima, this res,~:arch sums up both sectors' expected government revenues, treats this sum as one single value, and applies it to Eq. (7). One purpose of this study is to develop tax rates that satisfy the Clinton Administration's energy B~u tax revenues goals and minimize total excess burden. Thus, firstly, the government revenues generated by the Clinton Administration's proposed energy Btu tax should be derived. Because coal consumption in both sectors is insignificant, this study excludes it in the analysis. The updated residential and commercial energy data are summarized in Table 1. The compensated elasticity of demand developed by Nan and Murry (1992) is expressed as Ei~ =//i~ - s~/3~m, where//~ and //~m are constants which are estimated through a model, and si is a budget share. Thus ~* wi.il change as s~ changes. Given 1990 budget shares shown in Table 1, this paper derives price elasticities of compensated demand and reports them in Table 2. On the other hand, there is a term of fuels' supply elasticity in Eq. (7). Unlike demand elasticities, unfortunate!y, energy supply elasticities are less explored in the literature. Edmonson (1975) applied aggregate U.S. energy data, from 1901 to 1968, and reported an aggregate U.S. mineral energy supply elasticity of 0.5. This paper assumes that supply elasticity c~f natural gas is 0.25.9 I~ accordance with Kaufmann (1991) and Kaufmann et al. (1994), this paper assumes oil supply elasticity is approximately equal to 0.3. This paper further assumes the supply elasticity of electricity equals 0.5. Based on fuels' data shown in Energy Information Administration (1992b) and on the Clinton Administration's energy Btu tax proposal, this paper derives
s See, for example, page 32 of Studness (1993). 9 A note from R.B. Kalisch of American Gas Association to the author on June 9, 1993, c o m m e n t e d on the elasticity of natural gas supplies: " . . . In the short run ... there is some evidence thet monthly natural gas production has about a 0.25 elasticity to short-run wellhead price .... ".
G.D. Nan ~Resource and Energy Economics 17 (1995) 291-305
299
1'~le 3 Proposed tax rates Natur,~! gas
The Clinton Administration Residential 4.59% (0.257) Commercial 5.18% (0.257) This study Residential Commercial
3.67% (C.206) 3.30% (0.104)
Petroleum prd.
Electricity
4.99% (0.599) 9.54% (0.599)
1.25% (0.366) 1.39% (0.366)
2.78% (0.334) 2.55% (0.160)
1.99% (0.582) 1.83% (0.481)
l'he value in parentheses is a Pa:-i's tax ($/MBtu).
total tax revenues of $233266625 and $213757908 for the residential and the commercial sectors, respectively. Thus total tax revenues derived from both sectors are $447 024 533. ~0 Thus all variables on the right-hand side of Eq. (7) are known. The proposed tax rates are summarized in Table 3. The results show that natural gas, petroleum products, and electricity in the residential sector have proposed tax rates of 3.67, 2.78, and 1.99%, respectively. In the commercial sector, the proposed tax rates for natural gas, petroleum products, and electricity are 3.30, 2.55, and 1.83%, respectively.
4. Comparison Based on the Clinton Administration's energ3' Btu tax revenues, this study attempts to develop proposed fuels" tax rates that minimize total excess burden. Consequently, it is interesting to compare two approaches' results. Certainly, a comparison of total excess burden generated by both approaches is highly desirable in this study. In accordance with Eq. (1), an excess burden because of an imposed tax is equal to pqtZ/{2[(1/rl)-(1/e)]}. The Clinton Administration's energy taxation is based on an energy Btu content. Thus one needs to develop tax rates for the Clinton Administration's approach to derive total excess burden. By a tax wedge assumption of a tax incidence, a t~x rate is defined as a ratio of a tax to the price before a tax is imposed. Given an energy Btu tax of $0.257 and $0.599 for natural gas and petroleum products, respectively, and given prices of these two fuels reported in Table 1, one can derive the Clinton Administration's tax rates for natural gas and
l0 See Appendix C for a detailed derivation.
300
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
Table 4 Total excess burden Residential
The Clinton Administration Natural gas $484999 Petro. prod. $69353 Electricity $149 255
Commercial
Total
$338110 $294075 $239 363
$823109 $363428 $388 618 $1575155
$137146 $21019 $413 419
$447 304 $42530 $790 446 $1280 280
This study Natural gas Petro. prod. Electricity
$310158 $21511 $377 027
petroleum products, equal to 4.589 and 4.992%, respectively. In addition, based on appendix C, tax revenues for electricity consumption are $83213113 and $110482508 for the residential and the commercial sectors, respectively. In accordance with Table 1, total electricity consumption is 227136022 and 301569745 MBtu for the residential and the commercial sector, respectively. Thus one can derive a tax of $0.366/MBtu for electricity consumption for both sectors under the Clinton Administration's proposal. Given electricity price shown in Table 1 and a tax of $0.366/MBtu, one can derive tax rates for electricity consumption in both sectors. The derived tax rates under the Clinton Administration's proposal are reported in Table 3. Substituting all individual numbers into Eq. (1), one can derive an excess burden of taxation for each fuel. This study summarizes all fuels' excess burden in Table 4. Total excess burden results from tax rates developed in this study is $1 280280 and $1575 155 for the Clinton Administration's proposal. Based upon the excess burden of $1 280280 generated by this study, the excess burden produced by the Clinton Administration's proposal is higher by 23%.
5. Conc~csion This paper extends Ramsey tax rule and develops a tax rate by minimizing total excess burden, subject to government tax revenues. This proposed tax rate is a f:mction of its own and other fuels' price elasticities of compensated demand and supply, its own price and consumption level, other fuels' prices and consumption levels, and government revenues. Thus this proposed tax rate overcomes the shortcoming of ignoring government budgets in the Ramsey rule. Most importantly, it is this proposed tax rate, not the optimal tax ratio of Ramsey rule, that guides the government to levy a tax through a minimization of total excess burden.
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
301
Moreover, this proposed tax rate has the advantage of simplicity in a partial equilibrium model. In the case of an energy tax, this proposed tax rate provides direct guidance for taxation on various fuels. By using California data, this paper estimates tax rates for natural gas, petroleum products, and electricity consumed in the residential and commercial sectors. Based on the Clinton Administration's proposed energy Btu tax and on Nan and Murry (1992), this paper derives expected government tax revenues and develops price elasticities of compensated demand in the residential and commercial sectors. The results show that the highest proposed tax rate is 3.67% for the residential natural gas consumption. The lowest proposed tax rate is 1.83% for the commercial electricity consumption. On the other hand, the Clinton Administration's energy Btu tax proposal generates a highest tax rate of 9.54% for the commercial petroleum products consumption; the lowest tax rate is 1.25% for the residential electricity consumption. In addition, total excess burden generated by the Clinton administration's proposal is 23% higher t!.'an that produced by this study. Moreover, one of the big objections to the energy Btu tax was its effect on competitiveness. In other words, U.S. firms would loose market share to nations that did not impose the tax. Unfortunately, the proposed tax rate developed in this research was unab!e to capture this argument. Certainly, it is a good topic for further research.
Appendix A: Excess burden derivation By definition of price elasticities of compensated demand (e) and supply (r/), one obtains Eqs. (A.1) and (A.2): E=(Sq/Sp)(p/q)
= [(Q-q)/(Pa-P)](P/q).
rl = ( i)q/Op)( p / q ) = [(Q - q ) / ( Pb - - P ) ] ( P / q)"
Rearranging Eqs. (A.1) and (A.2), one derives Eqs. (A.I') and (A.2'): q-Q--q~(pa -p)/p. q - Q = qn( P - Pb ) / P . Dividing Eq. (A.1) by Eq. (A.2), one derives Eq. (A.3): e/n=(p--pb)/(p--p~).
(A.1) (A.2) (A.I') (A.2') (A.3)
By a tax wedge assumption of a tax incidence, one has Eq. (,~.4): t=(pa-Pb)/P.
(A.4)
Rewriting Eq. (A.4), one has Eqs. (A.4') and (A.4"): p a = t p + Pb"
(A.4')
Pb = P~ -- tp.
(a.4")
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
302
Substituting Eq. (A.4') into Eq. (A.3) and Eq. (A.4") into Eq. (A.3), respectively, one derives Eqs. (A.5) and (A.6): p - p~ = tp(~/( ~. - 7)).
(A.5)
po - p = - t p n / (
(A.6)
n).
By definition, one has Eqs. (A.7) and (A.8): a=(q-Q)(pa-p)/2
(A.7)
fl= ( q - Q)( p - p b ) / 2
(A.8)
Substituting Eqs. (A.I') and (A.6) into Eq. (A.7), and Eqs. (A.2') and (A.5) into Eq. (A.8), one derives Eqs. (A.9) and (A.IO): a = [ - q , ( Pa - P ) 2 ] / 2 P
= -Pqer/z.t2/[2( " - ,/)2].
(A.9)
/3= [qr/( p - - p b ) E ] / 2 p = p q r / , 2 t 2 / [ 2 ( , - ,)2].
(A.10)
Adding up Eqs. (A.9) and (A.10), one derives Eq. (.4,.11): a +/3= (pqr/,2t2-pqer/2t2)/[2(
7/)2]
,-
= pq,rlt2/[2( ,--,))] =pq,'2/{2[(1/))) - ( 1 / ~ ) ] }.
(A.11)
Thus fi,qs paper derives Eq, (1). Based 9n Eqs. (A.7) a~,d (A,.9), one derive.,.; Eq. (A.12): ( q - Q)( pa - p) / 2 = - p q e r / 2 t 2 / [ 2 ( e - ,/)2].
(A.12)
After substituting Eq. (A.6), P a - P = -tpr//(~--r/), into Eq. (A.12), one derives Eq. (A.!3): q-Q=
--pqEr/2 t 2
qer/t
(e-- r/)2(pa --p)
~ - 7/
qt =
l / r / - 1/e
.
(A.13)
Thus this paper derives Eq. (2).
Appendix B: Derivation of the proposed tax rate
Given O~b/OA= R - E~= l piqiti + E'~= l(Piqit2/Ti) = 0, one rewrites this as: R = ~,piqiti 1 i
~--i
=
Plqltl
1-
-~--
+
1=
pjqjtj 1
-- . ~1
(B.1)
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
303
Rewriting Eq. (6) as tj = t i Y j / y 1 or tj/Tj = ti/)q ( j = 2,3,...,n) and substitming these into Eq. (B.1), one derives Eq. (B.2):
R = p t q t t s 1---yl
t 't
=t i 1-~
~tl
+
Pjqjtl ~ +
Yl
j=2
1---yt
"~1
(B.2)
=t I 1--~ YJ
i= I
Y~
Rearranging Eq. (B.2), one derives a quadratic equation:
1 ~t2--tt+
Y!
n
Ry !
=0.
(B.3)
E Piqi~'i t=l
The solutk ~l to Eq. (B.3) is:
t I = -~- 1 +
J
1 - i~l piqi~/i
)
(Bo4)
Rewriting Eq. (6) as t,-= y , t ~ / y ~ (i = 2,3,...,n) and substituting Eq. (B.4) into it, this paper derives Eq. (7).
Appendix C: Energy Btu t a x e s revenues For gas and petroleum products, Btu taxes revenues equal total consumption (MBtu) shown in Table 1, multiplying by 0.257 ($/MBtu) for gas and by 0.599 ($/MBtu) for petroleum products. Thus total tax revenues from gas and petroleum products consumption in the residential and commercial sectors are $150053 512 and $103 275 401, respectively. Electricity Btu tax revenues are more com#icated than those for oil and gas. As data show in Table 14 of Energy Information Administration (1992a), energy sources for electric generation in California include gas, oil, nuclear fuel, and hydro power. Additionally, gas, oil, and nuclear fuel are taxed based on heat content. However, hydro power is taxed based on electricity content, rather than heat content. In accordance with Nan (1994), only approximately 34% of heat content will be converted into electricity content. Dividing expenditure ($) by price ($/MBtu) in the electric sector of Energy Information Administration (1992b), one will find gas, petroleum products, and nuclear fuel contribute
304
G.D. Nan/Resource and Energy Economics 17 (1995) 291-305
471617162, 46192661, and 349861 111 MBtu, respectively, in heat content for power generation. Based on Table 14 of Energy Information Administration (1992a) and on a conversion factor, MBtu = 293 Kwh, hydro power generates 81211604 MBtu in electricity content. Thus multiplying $0.599 for petroleum products and $0.257 for the rest, the government can obtain Btu taxes of $121205 611, $27 669404, $89914 306, and $20871382 from gas, petroleum products, nuclear fuel, and hydro power, respectively. Thus total Btu tax revenues received from electricity generation in California are $259660702. However, these tax revenues, $259 660 702, should distribute to the residential, commercial induetrial, and transportation sectors. To derive the residential and commercial electricity consumption tax revenues, one needs a further calculation. Given price ($/MBtu) and expenditure ($) of electricity in four sectors shewn in Energy Information Administration (1992b), one derives 227136022, 301569745, 179241218, and 815094 MBtu in electricity content in the residential, commercial, industrial, and transportation sectors, respectively. Thus total amount is 708762079 MBtu. In turn, one can derive MBtu shares in electricity content in the residential, commercial, industrial, and transportation sectors, which are 0.3205, 0.4255, 0.2529, and 0.0012, respectively. Multiplying $259 660 702 by these MBtu shares, one will derive tax revenues of $83 213 113 and $110482508 received from residential and commercial electricity comamption, respectively. Therefore total tax revenues received from consuming gas, pc*roleum products, and electricity are $233 266625 and $213 757 908 for the residential and commercial sectors, respectively. In the empirical analysis, the sum, $447 024 533, i:, applied to get global optima.
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