Part 1 - AL-Tax

This condition, jointly with the production function, gives the conditional factordemand functions for L(F, ϕ) and K(F, ϕ), where ϕ is a vector of prices, and theinstantaneous cost function net of depreciations is:CF ˆ ( , ϕ) w(1 τ ) LF ( , ϕ) pKF( , ϕ).Thus, the firm’s present value maximization problem becomes:max ρtqt , ˆ∫ ,0Le ( bFK ( L) CF ( ϕ))d t,Chapter 2where the first-order condition is simply:b C ˆ ( F , ϕ) ≡ MC( F , ϕ).tFMcKenzie et al. define the marginal effective tax rate on the cost of production(METRC) as the wedge between the gross of tax marginal cost and the net of taxmarginal cost, MC(F, ϕ) MC(F, ϕ 0 ), 14 divided by the net of tax marginal cost. Tokeep symmetry with the previous analysis, let us express the tax as a percentage ofthe gross of tax marginal cost. Under a Cobb–Douglas constant return-to-scale productionfunction, this is equal to the difference between geometric weighted averagesof input costs over gross of tax average costs:[ w(1 τ)]p w rMETRC [ w(1τ)] pL c d c dL c d,(2.24)where c and d are the shares of labor and capital respectively. The similaritybetween expressions (2.24) with expression (2.6) is obvious under the assumptionof no personal taxes.Considering a Leontief production function, 15 where inputs are used in a fixedproportion:[ w(1 τL)] pw rMETRC [ w(1 τ)] pL(2.25)Here the effective tax is simply the arithmetic weighted average of the marginaleffective tax rates on the inputs, which is higher than the geometric weighted average,reflecting the impossibility for the firm to change.In order to estimate the METRC it is necessary first to calculate the pre-tax rateof return on the various inputs.This latter case is equivalent to the marginal tax developed by Gérard et al.(1997), 16 who consider labor incremented by a marginal investment, implying that33