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Taxation of profits when there are profits
Economics Letters 107 (2010) 145–147
Contents lists available at ScienceDirect
Economics Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o l e t
Taxation of profits when there are profits Mark Gersovitz ⁎ Department of Economics, Johns Hopkins University, Baltimore, MD 21218, United States
a r t i c l e
i n f o
Article history: Received 21 May 2009 Received in revised form 21 December 2009 Accepted 7 January 2010 Available online 14 January 2010
a b s t r a c t Profits taxes fall on both pure profits and the use of capital as an input. Simulations of a Cournot oligopoly suggest that gains from the former are not outweighed by losses from the latter. © 2010 Elsevier B.V. All rights reserved.
JEL classification: H21 Keywords: Profits taxation Cournot
1. Introduction Two rules for optimal taxation are: (1) tax any pure profits before anything else and (2) tax final consumption rather than inputs to production (Diamond and Mirrlees, 1971). Statutory profits taxes do not, however, allow the full deductibility of capital costs. If firms have market power, profits taxes combine taxation of pure profits with a distortion to the use of capital. Does deadweight loss from this distortion undermine the attraction of taxing pure profits? The question is inherently about magnitudes and so this paper simulates a Cournot oligopoly. The findings are broadly in accord with Guo and Lansing (1999) but derive from a very different specification. 2. The model
There are no fixed costs and unit cost, c, is independent of production but dependent on factor prices and input taxes. Firms use labor, l, and capital, k, costing w and r before taxes to produce a unit of output; w and r are exogenous to the industry. Firms pay a tax on final sales at rate t, receiving (1 − t)P per unit sold. Firms pay profits tax at rate τ. The profits tax allows deduction of a fraction, δ, of capital cost and the whole of labor cost; unit cost after taxes is c = (1 − τ) wl + (1 − δτ) rk.2 Firms' total after-tax profits, Π, are: Π = ð1−τÞð1−t ÞPM−½ð1−τÞwl + ð1−δτÞrkM:
ð2Þ
Firms choose capital and labor to minimize unit cost subject to the unit isoquant, F(k, l) = 1, and choose production scale, m, as standard Cournot oligopolists. Revenues from the sales and profits taxes are:
The model is partial equilibrium and demand is linear. Consumers demand quantity M at price P:
R = tPM + τ½ð1−t ÞP−ðwl + δrkÞM:
P ðM Þ = a−bM;
Government chooses taxes, t and τ, to maximize social welfare, V, the sum of consumer's surplus, S, after-tax profits, Π, and tax revenue, R, adjusted by the social value of revenue, γ:
ð1Þ
a, b N 0. N symmetric Cournot oligopolists each produce m units supplying total quantity M = Nm.1 ⁎ Tel.: + 1 410 516 7612. E-mail address: [email protected]. 1 Atkinson and Stiglitz (1980) assume a fixed markup on costs inclusive of taxes in a general equilibrium model of imperfect competition and taxation. A specific tax on unit cost that is passed forward raises the price of final goods by more than the tax because it is marked up. When Cournot oligopolists face linear demand, however, price rises only by the faction N/(N + 1) so the markup on the tax is negative, mitigating rather than exacerbating deadweight loss.
0165-1765/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2010.01.008
V = S + Π + γR:
ð3Þ
ð4Þ
Because w and r are exogenous, there are no inframarginal losses from taxes to factor owners. Taxes are shifted forward onto 2 For 36 countries, Mintz et al. (2005) estimate δs from negative (the marginal effective rate on capital exceeds the statutory rate primarily because capital goods are not exempt from sales taxes) to 0.79. If capital goods are subject to sales taxation, then the sales tax, t, should apply to capital as well as final goods, inducing further distortion.
146
M. Gersovitz / Economics Letters 107 (2010) 145–147
Table 1 Simulation results. Social value of taxes
Profit tax rate
Sales tax rate
Taxes per unit output
Output
After-tax profits
Fraction of max Δ V
Profit tax rate
Sales tax rate
Taxes per unit output
Output
After-tax profits
Fraction of max Δ V
γ
τ
t
T/M
M
Π/(PM)
Φ
τ
t
T/M
M
Π/(PM)
Φ
0.157 0.348
1.558 1.222
0.051 0.028
0.491 0.841
0.151 0.347
1.548 1.205
0.061 0.036
0.435 0.817
1.601 1.267
0.019 0.011
0.793 0.940
1.571 1.238
0.040 0.021
0.572 0.871
1.613 1.264
0.056 0.031
0.483 0.839
1.554 1.216
0.055 0.031
0.468 0.832
1B. Sales tax only: τ = 0
1A. Base case 1.30 2.20
0.207 0.276
0.091 0.210
2A. Number of firms: N = 3 1.30 2.20
0.349 0.462
1.30 2.20
0.113 0.163
0.000 0.128
0.138 0.342
0.154 0.347
1.408 1.119
0.118 0.061
0.220 0.647
1.553 1.214
0.056 0.032
0.461 0.829
0.316 0.398
0.103 0.231
0.170 0.365
1.639 1.290
0.047 0.025
0.537 0.861
0.304 0.381
0.070 0.186
0.160 0.348
0.135 0.242
0.176 0.351
0.403 0.476
0.078 0.198
0.164 0.348
4B. Share of capital: 2 = 0.375
5A. Elasticity of substitution: σ = 0.5 1.30 2.20
0.090 0.134
3B. Deductibility of capital cost: δ = 0.75
4 Share of capital: 2 = 0.125 1.30 2.20
0.123 0.249
2B. Number of firms: N = 27
3A. Deductibility of capital cost: δ = 0.25 0.101 0.220
0 0
0.175 0.237
0.095 0.217
0.163 0.361
5B. Elasticity of substitution: σ = 2.0 1.564 1.229
0.046 0.025
0.523 0.853
1.438 1.161
0 0
0.295 0.670
0.129 0.184
0.105 0.226
0.155 0.348
6. Fixed costs and free entry 1.30 2.20
0.274 0.263
0.105 0.198
0.192 0.334
consumers. If, instead, factor supplies were fixed, taxes would be shifted onto factors without inducing any deadweight loss, a bias in favor of the profits tax I want to avoid. 3. Simulations Table 1 reports the simulations. The base simulation (1A) assumes: a = 2, b = 0.5, N = 9, δ = 0.5, w = 0.75, and r = 0.25. The unit isoquant −1 is CES, ½2 k−ρ + ð1− 2Þl−ρ ρ = 1 with σ = 1 / (1 + ρ), the elasticity of substitution. In the base simulation, σ = 1, which biases in favor of deadweight loss,3 and 2 = 0.25. The social value of revenue is controversial and simulations are done for a low and high γ. In the absence of taxes, the share of profits in the value of output (Π/PM) is 9.1%, but the optimal taxes lower it sharply. I have juggled N, a, b, w and r to produce moderate after-tax pure profits to avoid a bias in favor of the profits tax.4 Maximization of Eq. (4) was by grid search over t and τ from 0.0000 to 0.9995 in steps of 0.0005. Taxes are thereby non-negative, consistent with statutes. The non-negativity constraint could bind for the sales tax because subsidies may be optimal for low γ, certainly for γ=1. Optimal taxes in Table 1 are, however, strictly positive except when market power is highest (N=3) and the social value of revenue is lowest (γ=1.30). Table 1 reports: the social-welfare maximizing tax rates, total taxes paid per unit output, output, the share of after-tax profits in the value of sales, and a welfare indicator for each policy package: Φ=
ðV of a Tax PackageÞ−ðV without any TaxesÞ : ðV of the Ideal PackageÞ−ðV without any TaxesÞ
ð5Þ
3 Chirinko's (2002) survey supports σ = 0.5, but the range is wide including lower estimates producing even less deadweight loss. The values of w and r are chosen so that absent taxes the unit isoquants of all CES production functions share a common point for the wage rental ratio tangency when 2 = 0.25, a starting point for the simulations that change the elasticity of substitution. 4 Industries with lower rates of pure profits due to easier entry and hence a lower optimal rate of profits taxation other things equal also likely have a lower capital intensity (2) so that other things are not equal and the distortion from any level of profits taxation is less (Table 1, 4A and B).
V is the relevant value of social welfare, Eq. (4). Linear transforms of V do not change Φ. In the Ideal Package, firms price at constant average cost plus a socially-optimal ad valorem sales tax because government revenue cannot be raised in a non-distortionary way. The index measures how much of the gap between an Ideal without market power and doing nothing is closed by any simulated policy package. In the base simulation, 1A, the profits tax, τ, is significant (20.7% to 27.6%), rising with γ but well below the 100% implied by δ = 1. Simulation 1B sets τ = 0, so the government only has the ad valorem sales tax. The last columns of 1A and 1B show inclusion of τ leads to more than a 10% improvement in Φ for γ = 1.3, but not for γ = 2.2. (In simulations not shown in Table 1, the profits tax alone is inferior to the sales tax alone, except at very low values of γ, such as 1.15.). Simulations 2A and B change the number of firms relative to the base (N = 3 or 27). Because pure profits fall as N rises (while the distortion in input choice does not change for a given τ), τ falls as N rises. Even with 27 firms, however, τ ranges from 9.0 to 13.4% depending on γ. With linear demand and no taxation, the pure profits of all N firms go to zero as N/(N + 1)2 or roughly inversely with N, but that is not true for τ which has fallen to just over 25% of its value as N has risen ninefold from 3 to 27. Simulations 3A and B change the deductible proportion of capital cost, δ, to either 0.25 or 0.75 from the base case of 0.5. Increases in δ decrease the distortion to input choices, and increase τ and Φ. In simulations 4A and B, a higher share of capital (2 in the Cobb– Douglas base case) decreases τ and Φ. In 5A and B, a higher elasticity of substitution rising from 0.5 (most realistic) through 2.0 has the same qualitative effect as an increase in the share of capital, 2. 4. Entry So far the number of firms has been exogenous. Alternatively, firms may pay a fixed cost to enter until there are no pure profits (after taxes). As a benchmark, I chose fixed costs, F, to equal the value necessary to produce zero profits when there are 9 firms, no taxes and parameters are as in simulation 1A. When profits are taxed, the
M. Gersovitz / Economics Letters 107 (2010) 145–147
proportion of fixed costs that is deductible is the same as for capital, δ, and profits are: Π = ð1−τÞð1−t ÞPM−½ð1−τÞwl + ð1−δτÞrkM−ð1−δτÞNF:
ð6Þ
Firms are Cournot oligopolists and maximize profits, but entry drives after-tax profits inclusive of fixed costs to zero, determining N. In simulation 6, N is not restricted to an integer (and equals 6.241 and 4.793 firms when γ = 1.30 and 2.20 respectively). Taxation decreases the number of firms, which lowers total fixed costs. The optimal number of firms is not an infinitesimal fraction of a firm (N ≈ 0), however, because the tax to achieve this outcome and thereby make fixed costs approximately zero (τ ≈ 1), is sub-optimal given the distortion to the use of capital.5 The tax rates in simulations 1A and 6 are not uniformly higher in one or the other of the simulations. Both taxes start higher in the case with zero-profit entry and then fall below the results in Table 1A as the social value of revenue rises; the switching value of γ (not shown) differs between the profits tax and the sales tax with the former switching between the two simulations at γ = 1.90 and the latter between γ = 1.45 and 1.60.
5 The values of Φ are incomparable between simulation 6 and the others because the former has fixed costs in all situations; the Ideal has only one firm that produces and pays a fixed cost and is regulated to price at constant unit cost plus a sales tax, while being reimbursed by the government for its fixed cost.
147
5. Conclusions Simulations suggest that even with relatively low pure profits, a moderately large number of firms and deadweight loss from imperfect deductibility of capital, there may still be a role for a profits tax. It is better to raise the deductibility of capital cost, δ, something many countries have managed (Mintz et al., 2005) than to abolish the profits tax, τ. Exploration seems warranted in realistic models, e.g. Perroni and Whalley (1998). References Atkinson, A.B., Stiglitz, J.E., 1980. Lectures on Public Economics. McGraw Hill, New York. Chirinko, R.S., 2002. Corporate taxation, capital formation, and the substitution elasticity between labor and capital. National Tax Journal 55, 339–355. Diamond, P.A, Mirrlees, J.A., 1971. “Optimal taxation and public production: I Production efficiency and II: tax rules”. American Economic Review 61 (8–27), 261–278. Guo, J.-T., Lansing, K.J., 1999. Optimal taxation of capital income with imperfectly competitive product markets. Journal of Economic Dynamics and Control 23, 967–995. Mintz, J., et al., 2005. The 2005 tax competitiveness report: unleashing the Canadian tiger. C.D. Howe Institute Commentary 216, 1–24. Perroni, C., Whalley, J., 1998. Rents and the cost and optimal design of commodity taxes. Review of Economics and Statistics 80, 357–364.
Contents lists available at ScienceDirect
Economics Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o l e t
Taxation of profits when there are profits Mark Gersovitz ⁎ Department of Economics, Johns Hopkins University, Baltimore, MD 21218, United States
a r t i c l e
i n f o
Article history: Received 21 May 2009 Received in revised form 21 December 2009 Accepted 7 January 2010 Available online 14 January 2010
a b s t r a c t Profits taxes fall on both pure profits and the use of capital as an input. Simulations of a Cournot oligopoly suggest that gains from the former are not outweighed by losses from the latter. © 2010 Elsevier B.V. All rights reserved.
JEL classification: H21 Keywords: Profits taxation Cournot
1. Introduction Two rules for optimal taxation are: (1) tax any pure profits before anything else and (2) tax final consumption rather than inputs to production (Diamond and Mirrlees, 1971). Statutory profits taxes do not, however, allow the full deductibility of capital costs. If firms have market power, profits taxes combine taxation of pure profits with a distortion to the use of capital. Does deadweight loss from this distortion undermine the attraction of taxing pure profits? The question is inherently about magnitudes and so this paper simulates a Cournot oligopoly. The findings are broadly in accord with Guo and Lansing (1999) but derive from a very different specification. 2. The model
There are no fixed costs and unit cost, c, is independent of production but dependent on factor prices and input taxes. Firms use labor, l, and capital, k, costing w and r before taxes to produce a unit of output; w and r are exogenous to the industry. Firms pay a tax on final sales at rate t, receiving (1 − t)P per unit sold. Firms pay profits tax at rate τ. The profits tax allows deduction of a fraction, δ, of capital cost and the whole of labor cost; unit cost after taxes is c = (1 − τ) wl + (1 − δτ) rk.2 Firms' total after-tax profits, Π, are: Π = ð1−τÞð1−t ÞPM−½ð1−τÞwl + ð1−δτÞrkM:
ð2Þ
Firms choose capital and labor to minimize unit cost subject to the unit isoquant, F(k, l) = 1, and choose production scale, m, as standard Cournot oligopolists. Revenues from the sales and profits taxes are:
The model is partial equilibrium and demand is linear. Consumers demand quantity M at price P:
R = tPM + τ½ð1−t ÞP−ðwl + δrkÞM:
P ðM Þ = a−bM;
Government chooses taxes, t and τ, to maximize social welfare, V, the sum of consumer's surplus, S, after-tax profits, Π, and tax revenue, R, adjusted by the social value of revenue, γ:
ð1Þ
a, b N 0. N symmetric Cournot oligopolists each produce m units supplying total quantity M = Nm.1 ⁎ Tel.: + 1 410 516 7612. E-mail address: [email protected]. 1 Atkinson and Stiglitz (1980) assume a fixed markup on costs inclusive of taxes in a general equilibrium model of imperfect competition and taxation. A specific tax on unit cost that is passed forward raises the price of final goods by more than the tax because it is marked up. When Cournot oligopolists face linear demand, however, price rises only by the faction N/(N + 1) so the markup on the tax is negative, mitigating rather than exacerbating deadweight loss.
0165-1765/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2010.01.008
V = S + Π + γR:
ð3Þ
ð4Þ
Because w and r are exogenous, there are no inframarginal losses from taxes to factor owners. Taxes are shifted forward onto 2 For 36 countries, Mintz et al. (2005) estimate δs from negative (the marginal effective rate on capital exceeds the statutory rate primarily because capital goods are not exempt from sales taxes) to 0.79. If capital goods are subject to sales taxation, then the sales tax, t, should apply to capital as well as final goods, inducing further distortion.
146
M. Gersovitz / Economics Letters 107 (2010) 145–147
Table 1 Simulation results. Social value of taxes
Profit tax rate
Sales tax rate
Taxes per unit output
Output
After-tax profits
Fraction of max Δ V
Profit tax rate
Sales tax rate
Taxes per unit output
Output
After-tax profits
Fraction of max Δ V
γ
τ
t
T/M
M
Π/(PM)
Φ
τ
t
T/M
M
Π/(PM)
Φ
0.157 0.348
1.558 1.222
0.051 0.028
0.491 0.841
0.151 0.347
1.548 1.205
0.061 0.036
0.435 0.817
1.601 1.267
0.019 0.011
0.793 0.940
1.571 1.238
0.040 0.021
0.572 0.871
1.613 1.264
0.056 0.031
0.483 0.839
1.554 1.216
0.055 0.031
0.468 0.832
1B. Sales tax only: τ = 0
1A. Base case 1.30 2.20
0.207 0.276
0.091 0.210
2A. Number of firms: N = 3 1.30 2.20
0.349 0.462
1.30 2.20
0.113 0.163
0.000 0.128
0.138 0.342
0.154 0.347
1.408 1.119
0.118 0.061
0.220 0.647
1.553 1.214
0.056 0.032
0.461 0.829
0.316 0.398
0.103 0.231
0.170 0.365
1.639 1.290
0.047 0.025
0.537 0.861
0.304 0.381
0.070 0.186
0.160 0.348
0.135 0.242
0.176 0.351
0.403 0.476
0.078 0.198
0.164 0.348
4B. Share of capital: 2 = 0.375
5A. Elasticity of substitution: σ = 0.5 1.30 2.20
0.090 0.134
3B. Deductibility of capital cost: δ = 0.75
4 Share of capital: 2 = 0.125 1.30 2.20
0.123 0.249
2B. Number of firms: N = 27
3A. Deductibility of capital cost: δ = 0.25 0.101 0.220
0 0
0.175 0.237
0.095 0.217
0.163 0.361
5B. Elasticity of substitution: σ = 2.0 1.564 1.229
0.046 0.025
0.523 0.853
1.438 1.161
0 0
0.295 0.670
0.129 0.184
0.105 0.226
0.155 0.348
6. Fixed costs and free entry 1.30 2.20
0.274 0.263
0.105 0.198
0.192 0.334
consumers. If, instead, factor supplies were fixed, taxes would be shifted onto factors without inducing any deadweight loss, a bias in favor of the profits tax I want to avoid. 3. Simulations Table 1 reports the simulations. The base simulation (1A) assumes: a = 2, b = 0.5, N = 9, δ = 0.5, w = 0.75, and r = 0.25. The unit isoquant −1 is CES, ½2 k−ρ + ð1− 2Þl−ρ ρ = 1 with σ = 1 / (1 + ρ), the elasticity of substitution. In the base simulation, σ = 1, which biases in favor of deadweight loss,3 and 2 = 0.25. The social value of revenue is controversial and simulations are done for a low and high γ. In the absence of taxes, the share of profits in the value of output (Π/PM) is 9.1%, but the optimal taxes lower it sharply. I have juggled N, a, b, w and r to produce moderate after-tax pure profits to avoid a bias in favor of the profits tax.4 Maximization of Eq. (4) was by grid search over t and τ from 0.0000 to 0.9995 in steps of 0.0005. Taxes are thereby non-negative, consistent with statutes. The non-negativity constraint could bind for the sales tax because subsidies may be optimal for low γ, certainly for γ=1. Optimal taxes in Table 1 are, however, strictly positive except when market power is highest (N=3) and the social value of revenue is lowest (γ=1.30). Table 1 reports: the social-welfare maximizing tax rates, total taxes paid per unit output, output, the share of after-tax profits in the value of sales, and a welfare indicator for each policy package: Φ=
ðV of a Tax PackageÞ−ðV without any TaxesÞ : ðV of the Ideal PackageÞ−ðV without any TaxesÞ
ð5Þ
3 Chirinko's (2002) survey supports σ = 0.5, but the range is wide including lower estimates producing even less deadweight loss. The values of w and r are chosen so that absent taxes the unit isoquants of all CES production functions share a common point for the wage rental ratio tangency when 2 = 0.25, a starting point for the simulations that change the elasticity of substitution. 4 Industries with lower rates of pure profits due to easier entry and hence a lower optimal rate of profits taxation other things equal also likely have a lower capital intensity (2) so that other things are not equal and the distortion from any level of profits taxation is less (Table 1, 4A and B).
V is the relevant value of social welfare, Eq. (4). Linear transforms of V do not change Φ. In the Ideal Package, firms price at constant average cost plus a socially-optimal ad valorem sales tax because government revenue cannot be raised in a non-distortionary way. The index measures how much of the gap between an Ideal without market power and doing nothing is closed by any simulated policy package. In the base simulation, 1A, the profits tax, τ, is significant (20.7% to 27.6%), rising with γ but well below the 100% implied by δ = 1. Simulation 1B sets τ = 0, so the government only has the ad valorem sales tax. The last columns of 1A and 1B show inclusion of τ leads to more than a 10% improvement in Φ for γ = 1.3, but not for γ = 2.2. (In simulations not shown in Table 1, the profits tax alone is inferior to the sales tax alone, except at very low values of γ, such as 1.15.). Simulations 2A and B change the number of firms relative to the base (N = 3 or 27). Because pure profits fall as N rises (while the distortion in input choice does not change for a given τ), τ falls as N rises. Even with 27 firms, however, τ ranges from 9.0 to 13.4% depending on γ. With linear demand and no taxation, the pure profits of all N firms go to zero as N/(N + 1)2 or roughly inversely with N, but that is not true for τ which has fallen to just over 25% of its value as N has risen ninefold from 3 to 27. Simulations 3A and B change the deductible proportion of capital cost, δ, to either 0.25 or 0.75 from the base case of 0.5. Increases in δ decrease the distortion to input choices, and increase τ and Φ. In simulations 4A and B, a higher share of capital (2 in the Cobb– Douglas base case) decreases τ and Φ. In 5A and B, a higher elasticity of substitution rising from 0.5 (most realistic) through 2.0 has the same qualitative effect as an increase in the share of capital, 2. 4. Entry So far the number of firms has been exogenous. Alternatively, firms may pay a fixed cost to enter until there are no pure profits (after taxes). As a benchmark, I chose fixed costs, F, to equal the value necessary to produce zero profits when there are 9 firms, no taxes and parameters are as in simulation 1A. When profits are taxed, the
M. Gersovitz / Economics Letters 107 (2010) 145–147
proportion of fixed costs that is deductible is the same as for capital, δ, and profits are: Π = ð1−τÞð1−t ÞPM−½ð1−τÞwl + ð1−δτÞrkM−ð1−δτÞNF:
ð6Þ
Firms are Cournot oligopolists and maximize profits, but entry drives after-tax profits inclusive of fixed costs to zero, determining N. In simulation 6, N is not restricted to an integer (and equals 6.241 and 4.793 firms when γ = 1.30 and 2.20 respectively). Taxation decreases the number of firms, which lowers total fixed costs. The optimal number of firms is not an infinitesimal fraction of a firm (N ≈ 0), however, because the tax to achieve this outcome and thereby make fixed costs approximately zero (τ ≈ 1), is sub-optimal given the distortion to the use of capital.5 The tax rates in simulations 1A and 6 are not uniformly higher in one or the other of the simulations. Both taxes start higher in the case with zero-profit entry and then fall below the results in Table 1A as the social value of revenue rises; the switching value of γ (not shown) differs between the profits tax and the sales tax with the former switching between the two simulations at γ = 1.90 and the latter between γ = 1.45 and 1.60.
5 The values of Φ are incomparable between simulation 6 and the others because the former has fixed costs in all situations; the Ideal has only one firm that produces and pays a fixed cost and is regulated to price at constant unit cost plus a sales tax, while being reimbursed by the government for its fixed cost.
147
5. Conclusions Simulations suggest that even with relatively low pure profits, a moderately large number of firms and deadweight loss from imperfect deductibility of capital, there may still be a role for a profits tax. It is better to raise the deductibility of capital cost, δ, something many countries have managed (Mintz et al., 2005) than to abolish the profits tax, τ. Exploration seems warranted in realistic models, e.g. Perroni and Whalley (1998). References Atkinson, A.B., Stiglitz, J.E., 1980. Lectures on Public Economics. McGraw Hill, New York. Chirinko, R.S., 2002. Corporate taxation, capital formation, and the substitution elasticity between labor and capital. National Tax Journal 55, 339–355. Diamond, P.A, Mirrlees, J.A., 1971. “Optimal taxation and public production: I Production efficiency and II: tax rules”. American Economic Review 61 (8–27), 261–278. Guo, J.-T., Lansing, K.J., 1999. Optimal taxation of capital income with imperfectly competitive product markets. Journal of Economic Dynamics and Control 23, 967–995. Mintz, J., et al., 2005. The 2005 tax competitiveness report: unleashing the Canadian tiger. C.D. Howe Institute Commentary 216, 1–24. Perroni, C., Whalley, J., 1998. Rents and the cost and optimal design of commodity taxes. Review of Economics and Statistics 80, 357–364.