Residual income elasticity

The residual income elasticity indicates by how much the income remaining after tax deduction (residual income) increases if the taxable income increases by 1%.

The residual income R is the difference between the taxable income Y and the tax amount T (Y) :

${\displaystyle R=Y-T(Y)}$

The mathematical definition for residual income elasticity is: ${\displaystyle \rho }$

${\displaystyle \rho (Y)={\frac {dR}{dY}}\cdot {\frac {Y}{R}}={\frac {d(Y-T(Y))}{dY}}\cdot {\frac {Y}{Y-T(Y)}}}$

A progressive tariff is residual inelastic because is. ${\displaystyle \rho (Y)<1}$

The residual income elasticity can also be expressed in terms of marginal tax rate and average tax rate .

${\displaystyle \rho (Y)=(1-{\frac {dT(Y)}{dY}})\cdot {\frac {1}{1-{\frac {T(Y)}{Y}}}}={\frac {1-{\frac {dT(Y)}{dY}}}{1-{\frac {T(Y)}{Y}}}}={\frac {1-{\text{Grenzsteuersatz}}}{1-{\text{Durchschnittssteuersatz}}}}}$

With

• ${\displaystyle Y}$: Taxable income
• ${\displaystyle T}$: Income tax
• ${\displaystyle R=Y-T(Y)}$: Residual income

See also

• Tax amount elasticity
• Income elasticity
• Income effect

literature

• J. Hanns Pichler, Hubert Verhonig, Norbert Hentschel: Inflation and indexing: theoretical analysis, instruments, empirical findings and criticism, Issue 290, Volkswirtschaftliche Schriften (1979), ISBN 3428044878

Individual evidence

1. ^ Fundamentals of Taxation, Silke Übelmesser, LMU Munich, SS 2010, slide 28