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# AT9283 br Free entry equilibrium At stage of

Free entry equilibrium
At stage 2 of the game, n ≥ 2 firms simultaneously decide whether or not to enter the industry. Market entry involves a sunk fixed cost f > 0, which we assume cannot be subtracted from the tax base. Our assumption reflects that deductions of market entry costs are often incomplete. One reason is that some firms will incur market research costs, but decide not to enter. Such firms cannot deduct these costs against future taxation, or they AT9283 must deduct them at a different tax rate if the parent company decides not to enter the foreign market. Furthermore, entrants in markets are often unprofitable during the first years, and market entry costs are often carried forward as losses. These losses cannot be carried forward with interest. To simplify, we therefore ignore, without loss of generality, that parts of market entry costs can be subtracted from the tax base. Firm i’s expected (after-tax) profits from entry is given by where and is given by Eq. (8) and .
In an industry with free entry, the equilibrium number of firms, denoted by n*, is determined by the zero-profit condition, i.e., firms enter the market until Π=0 (up to the integer problem). Inserting Eq. (8) into Eq. (14), the equilibrium number of firms in the industry is (implicitly) defined by the following condition
Given that market entry is determined by the zero-profit condition, the impact of corporate taxation on the equilibrium number of firms follows straightforwardly from Proposition 2. Since firms' equilibrium profits are strictly decreasing in the corporate tax rate, a higher corporate tax rate reduces market entry. Applying the implicit function theorem on Eq. (15), we get the following comparative statics with respect to the corporate tax rate which is strictly negative by the equilibrium conditions in Eqs. (6) and (7).
In a similar way, we can derive the effect of the tax deduction scheme on market entry. From Proposition 2, we know that the impact of allowing for capital cost deduction on equilibrium profits is ambiguous. Thus, the impact on market entry is also ambiguous. Applying the implicit function theorem on Eq. (15), we get the following comparative statics with respect to the deduction share of capital costs where the sign depends on the production technology. If the industry is characterized by CRS technology, then capital cost deduction does not affect market entry, as the positive direct effect (capital cost savings) is exactly cancelled out by the negative strategic effect (intensified price competition). However, if the industry is characterized by DRS technology, then a larger deduction of capital costs (higher α) reduces the equilibrium number of firms, as the profit loss due to intensified price competition (triggered by reduced marginal costs) dominates the profit gain of capital cost deduction. In this case, disallowing capital cost deduction, as under CBIT, will stimulate market entry. The reverse is true if the industry is characterized by IRS technology. We can summarize our findings in the following Proposition.

Proofs are provided in Appendix A.
What are the effects of corporate taxation and deduction scheme for capital costs on equilibrium prices in industries with free market entry? Taking the partial derivative of Eq. (8) with respect to t and α, and imposing the equilibrium level of firms n* given by Eq. (15), we get the following (implicit) comparative statics where the first term is the direct effect (when keeping the number of firms in the industry fixed) and the second term is the strategic effect due to a change in market entry and thus the equilibrium number of firms. By analyzing these expressions, we get the following results:

Proofs are provided in Appendix A.
When accounting for entry, corporate taxation always leads to higher prices in the product market, even under ACE with complete deduction of capital costs from the tax base (α=1). The reason is that corporate taxation has both a direct effect on prices and an indirect effect through the change in entry and thus competition intensity. In Eq. (18), these two effects are captured by the first and second term, respectively. While ACE eliminates the direct distortionary effect on firms' pricing, the indirect effect through competition prevails. Since firms' after-tax profits are inevitably affected by corporate taxation, intensity of competition will be reduced. Thus, corporate taxation has distortionary effects on product prices irrespective of whether ACE or CBIT is introduced.