Part 1 - AL-Tax

Chapter 211. Note that the firm will invest when:In the absence of taxes and economic depreciations, we can write p˜ r and the fundamentalquadratic φ(ξ) satisfied by γ as:where after some rearranging we have:which states that when returns are uncertain, the return must exceed the cost of capital (thisresult is equivalent to the one developed by Dixit and Pindyck, 1994, p. 145).12. The ‘real’ interest rate in the case of technological growth is r g, resulting in:while13. A cash-flow tax estimates the tax burden on a cash-in/cash-out basis. If a company buys a machineusing equity in year 0 for $10 and it generates a cash inflow of $15 in year 1, the taxable incomewould be $10 in year 0 and $15 in year 1. This is equivalent to full immediate expensing. Inother words, a cash flow tax is CFT τ(F(K) I), which, under similar assumptions as equation(2.22), simplifies to CFT τ(p r)K, equal to E.14. φ 0 is the vector of user prices for inputs that existed prior to the imposition of taxes, i.e. w and qr.15. The general form for the effective tax in a CES production function is:where ε 1/(1 ρ) is the elasticity of substitution.16. Without personal taxes expression (2.27) in Gérard et al. (1997) reduces to p* p w(1 τ L ).17. Or more generally for the case of n inputs:where w i w i /w i (1 t i ).( )( ) ( )AETRB τ A r δ τ pr,p( )( ) ( )AETRF τ A r δ g τpr g.p⎛ɶpi1AETRC p⎝⎜1γ1pɶɶ pσγ 2(1 γ),γ 2n∑n∑i1⎞⎛n ⎞wjɶp∑ wji1METRC 1,w1 γpɶɶ p.γpɶɶ p pɶ1( α ) γ σγ 2(1 γ) 0,2j⎠⎟1⎡[ w(1 τ )]ρεcε pρεdε ⎤ ρε ⎡wρεLcεMETRC ⎣⎢⎦⎥ ⎣⎢ r1⎡ w τρεcεpρεdε⎣⎢ [ (1 L )]⎤ρε⎦ ⎥⎝⎜pn∑i1w1ρε ε⎤ρεj⎠⎟d⎦⎥,37