Firms are subject to corporate taxation and

Firms are subject to corporate taxation, and face either an ACE or a CBIT tax scheme. The two tax regimes achieve financing neutrality by treating debt and equity equally, but differ according to whether deduction of capital costs from the corporate tax novel isoform identification is allowed or not. While ACE allows for complete tax deduction of both debt and equity costs, CBIT does not allow for any capital cost deductions. Firm i’s after-tax profits can therefore be specified as follows where r is the interest rate of capital, t is the corporate tax rate, and α is the share of the capital costs that are tax deductible by the firms. A pure CBIT scheme is captured by α=0, whereas a pure ACE system is captured by α=1. If 0 < α < 1, the tax system is a hybrid between CBIT and ACE where a fraction of the firm's capital costs are tax deductible. This can be interpreted as a conventional tax scheme, where firms are required to have a certain amount of non-tax deductible equity and excessive amounts of interest deductions from debt are restricted by thin capitalization rules.
Oligopoly equilibrium At stage 3 of the game, each firm sets the price in order to maximize profits taking the other firms' prices as given. Assuming that n ≥ 2 firms have entered the market, the profit-maximizing price of firm i is given by the following first-order condition:where ∂D/∂p=−1/τ from Eq. (3). In order to ensure equilibrium existence and uniqueness, we assume that product differentiation is sufficiently large, i.e., where and The first condition ensures that the second-order condition, which is reported in footnote 6, is always satisfied, whereas the second condition ensures that equilibrium (after-tax) profits are non-negative. Notice that these conditions are always fulfilled for CRS and DRS technologies, and thus may only bind for IRS technology. Imposing symmetry, i.e., p=p=p for all i=1,…,n, and solving Eq. (5) for p, we get the following symmetric Nash price equilibrium where each firm's equilibrium demand is . The first term in Eq. (8) is the standard mark-up related to the intensity of competition, which is measured both in terms of the number of firms and the degree of product differentiation. The second term is the effective marginal capital costs, which consist of the true marginal costs adjusted for the tax wedge, defined by the ratio of capital tax deductions relative to the corporate tax rate. It is straightforward to verify from Eq. (8) that industries with less differentiated (more homogeneous) products have lower prices. The reason is simply that a lower τ makes demand more price elastic and thus triggers price competition among the firms. Moreover, we can also show that industries with a higher number of firms have lower prices in equilibrium, but the effect is less obvious, as can be seen from the following comparative statics where the inequality holds for all production technologies, including an IRS technology (G<0), by the equilibrium condition in Eq. (6). An increase in the number of firms has two effects on prices. First, there is a business-stealing effect that triggers price competition, where the magnitude is measured by the degree of product differentiation. Second, there is also a marginal cost effect unless technology is CRS (G=0). With DRS technology (G>0), an increased number of firms in the market implies that each firm has lower marginal costs (due to lower production), which reinforces the negative price effect due to harder competition. With IRS technology (G<0), more firms in the market implies that each firm has higher marginal costs, which counteracts the negative price effect due to more competition. However, the cost effect never offsets the competition effect, such that equilibrium prices are always decreasing in the number of firms in the market. The effect of corporate taxation on equilibrium prices is given by the following comparative statics Thus, equilibrium prices are (weakly) increasing in the corporate tax rate. Interestingly, under an ACE scheme (α=1), corporate taxation involves no distortion of equilibrium prices. The reason is that corporate taxation becomes a de facto lump-sum profit tax when firms are allowed to deduct all capital costs from the tax base. However, if capital cost deductions are disallowed (α=0), as under CBIT, or only partial (0<α<1), as under a conventional tax scheme, we have the standard result that corporate taxation induces an upward distortion of equilibrium prices. In this case, a higher corporate tax rate increases the effective marginal costs, which makes the firms' less aggressive and results in higher prices. The price distortion is the strongest under CBIT, which is equivalent to a unit tax on sales when capital costs are not allowed to be deducted from the tax base.