N° 2024-4 - A COMPREHENSIVE ANALYSIS OF PRODUCTION EFFICIENCY:

It is equal to the percentage difference between the marginal product and the price of the production factor, regardless of the type of market friction. [...] (24a) Pi ∂Xj We denote Γ the matrix of factor supply elasticities, where the term Γi,j in the ith row and jth columns corresponds to the elasticity of the aggregate supply of the ith production factor with respect to the price of the jth production factor, ∣∣∣∣ ∫def ∂logXi pj ∂Xi(w)Γi,j ≡ = dF (w). [...] Therefore, the incidence of a tax reform at the GE can be broken down into the incidence of the same reform at the PE level, augmented by the cumulative impact of this reform on each aggregate income at the PE, times the respective GE multiplier, 20The right-hand side of (31) is obtained from (30) by using tax reforms in the direction R(y) = −1, which implies Ryj (Y(w)) = 0. [...] In Figure 1, this implies that the effects of reforms in the direction RN (·) cease after the first demand-driven responses.22 Following Proposition 2, a reform in the direction RN (·) at the GE and a reform in the direction R(·) at the PE have the same impact on taxp∑ayers’ utility levels, factor supplies and consumption. [...] Rewriting taxpayers’ liabilities as T (Y(w)) = nj=1 pj Xj(w) − C(w), the effects on the government’s La- grangian of reforms in the direction RN (·) at the GE differ from the effects of reforms in the direction R(·) at the PE only due to price changes in the former and not the latter.