Part 1 - AL-Tax

International Taxation Handbookinput factors are used in a particular proportion. A similar formula was also usedby Daly and Jung (1987).2.4.2 Average ETRCAs a natural extension to the model, following the same reasoning as in Gérard(1993) and Devereux and Griffith (1998), we propose an average effective tax rateon the cost of production (AETRC), where factors receive a return other than theirmarginal product.Ex-ante, a firm has a production project with a net present value before taxes:NPV * ( e( ) pw tp w∫ )ρδπd t ,0 ρδπ where w is the gross of tax return to labor (i.e. w w(1 τ L )). Similarly as in section2.2.4, the net present value of taxes is:∫NPVT τ( δ)e( ρδπ ) tp dt Aτ we0τ( p δ)1 τA Lw.ρδπ ρδπ Defining the average effective tax rate as the ratio of the two former expressions,we obtain:( τ )( ) ( )AETRC Aρ δ π τ p ρ π τLw.pwWe can show that if a marginal product requires a fixed proportion of capital andlabor the AETRC is equal to the METRC. Given that for a marginal product we needit to pay the cost of capital plus the incremental labor costs per euro of capital:( ρδπ ) t∫0∫ d. t0NPV* NPVT 1 δe( ρδπ ) tdt we( ρδπ ) tFrom there we obtain expression (2.16), which is the pre-tax rate of return usedin equation (2.25).Similar propositions as before may be derived knowing that the AETRC can be∫0Ldtrewritten as: 17 AETRC METRC 1⎛ pɶ w ⎞⎝⎜pw⎠⎟⎛ pɶ w ⎞⎝⎜pw⎠⎟ τ,34