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# ap4 mg There is also a literature on the impact

There is also a literature on the impact of commodity (consumption) taxation under imperfect competition. Besley (1989) applies a Cournot model, in which production takes place under IRS and in which free entry leads to an excessive number of firms in the market. Introducing a distortive specific commodity tax increases market surplus (i.e., welfare) by reducing the number of firms, fostering production per firm, and triggering a tax shifting of less than 100% into the consumer price if the indirect demand function is concave. Delipalla and Keen (1992) rely on a free-entry conjectural model (hosting Cournot as a special case), also characterized by excessive entry and IRS, and focus on the comparison of ad-valorem vs. specific commodity taxation. Delipalla and Keen (1992, p. 366) conclude that “The results of Besley, 1989, Konishi et al., 1990, for instance, and the intuition behind some of these here, suggest that discriminatory taxes on fixed and marginal costs may be particularly well-targeted for effective tax design.” Finally, Hamilton (1999) extends the approach by Delipalla and Keen (1992) for non-linear ad-valorem taxes and shows that there always exists a tax schedule that can correct the welfare loss triggered by imperfect ap4 mg (i.e., a schedule that induces firms to behave as if they were price takers).
Compared to this literature, the corporate tax in our model can be interpreted as an imperfect tax on market entry costs that achieves many of the effects of the franchise tax in Konishi, 1990, Konishi et al., 1990. Limiting tax deductibility of capital costs, furthermore, drives a wedge between the tax on fixed costs and the tax burden on marginal costs, and it allows to install a factor tax. In light of the discussion above and taking into account the strategic price effects, an ACE system could be seen as a subsidy on marginal costs. From our model, however, follows that taxes and subsidies on marginal costs depend on the exact production structure. Previous literature assumed CRS in production and achieved IRS by adding fixed production (or entry) costs. Our set-up combines fixed entry costs with a fully flexible production structure (including IRS, CRS, and DRS).

Model
To study the effects of the two corporate tax schemes, ACE and CBIT, under imperfect competition, we apply the standard oligopoly model by Salop (1979). This model is particularly suited for analyzing industries where firms sell differentiated products, compete in prices and market entry is endogenous, which are key features of most real-world industries. We consider an industry with n ≥ 2 firms symmetrically located on a (Salop) circle with circumference equal to 1. Each firm i offers a product at price p, where i=1,…,n. There is a continuum of consumers uniformly located on the circle with total mass normalized to one. Each consumer demands one (or zero) unit of the product, and ϕ units of a numeraire good. The (quasi-linear) utility to an arbitrary consumer located at x ∈ [0,1] of buying product i is given by where v is the gross utility of consuming the product (i.e., the reservation price), τ is the transport cost per unit of distance, and d= z−x is the distance to firm i’s location z ∈ [0,1]. Note that the demand for the numeraire good ϕ absorbs all income effects. Distance is, as usual, interpreted either in physical or product space.
Each consumer has income m. Normalizing the price of the numeraire good to unity, and inserting the budget constraint into Eq. (1), we can write the net utility of consumer x as follows We assume that v is sufficiently large, so that all consumers buy one unit of the product from the most preferred firm (full market coverage). The consumer that is indifferent between buying from firm i and firm i+1 is located at whereas the consumer indifferent between buying from firm i and firm i−1 is located at
Firm i’s demand is then given by
As usual, each firm produces the quantity that is demanded. We allow for a fairly general production technology that accommodates different scale properties, but assume, for simplicity, that capital is the only input in production. For each firm i, the relationship between capital and production is defined by the inverse production function k=G (D), which is assumed to be continuous and twice differentiable with G(0)=0 and G′(.) > 0. Constant returns to scale (CRS) imply constant marginal productivity of capital, i.e., G″=0, and marginal capital costs equal to average capital costs, i.e., G′=G/D. Decreasing returns to scale (DRS) yield decreasing marginal productivity of capital, i.e., G > 0, and marginal capital costs exceeding average capital costs, i.e., G′ > G/D, whereas the opposite is true for an increasing returns to scale (IRS) technology.