linear income tax system with zero tax on contributions (s=0), we ask whether levying
a small tax (possibly negative) on charitable contributions would increase welfare.9
Denote the Lagrangean expression for the optimal income tax problem, given
a tax s on contributions, by:
(12)
wr
L(s) = W[V NS (w )]dF (w ) + μ1 1 t ∙
wc wc
∫ w [1 - Ins (w)]dF(w ) + (1 + s) ∙ ∫ zNS (w)dF(w) - g - T >
w w
K
∫ zNS ( w ) dF ( w )k
w
where μ1 and μ2 denote the Lagrange multipliers associated with the constraints in
equations (10) and (11). Employing the envelope theorem and omitting the NS
superscript for brevity of notation, we seek to sign the following derivative:
where t*,T* and g* denote the optimal tax parameters and λ(w) denotes the Lagrange
multiplier associated with the individual optimization.
(13)
∂L
_ ж л ж
∂s s=0,t*,T*,g*
[W ' [V ( w )] ∙ λ( w ) ∙ z ( w )]dF ( w ) - μ1 ∙ t ∙

dF ( w )
+ μ1 ∙
w
w
ʃ[z ( w )]dF ( w ) + ( μ1 - μ2) ∙

dF ( w ),
There are two conflicting considerations in the design of the optimal
tax/subsidy on charitable contributions. On the one hand, there is a Pigouvian motive
to subsidize contributions, because they generate a positive externality. This is due to
9 Assuming that second order conditions are satisfied, this would imply that the optimal tax on
contributions should be positive (negative), if a small tax (subsidy, respectively) is shown to be
desirable.
13
More intriguing information
1. Innovation in commercialization of pelagic fish: the example of "Srdela Snack" Franchise2. Olive Tree Farming in Jaen: Situation With the New Cap and Comparison With the Province Income Per Capita.
3. AGRIBUSINESS EXECUTIVE EDUCATION AND KNOWLEDGE EXCHANGE: NEW MECHANISMS OF KNOWLEDGE MANAGEMENT INVOLVING THE UNIVERSITY, PRIVATE FIRM STAKEHOLDERS AND PUBLIC SECTOR
4. The name is absent
5. An Economic Analysis of Fresh Fruit and Vegetable Consumption: Implications for Overweight and Obesity among Higher- and Lower-Income Consumers
6. Are class size differences related to pupils’ educational progress and classroom processes? Findings from the Institute of Education Class Size Study of children aged 5-7 Years
7. Impact of Ethanol Production on U.S. and Regional Gasoline Prices and On the Profitability of U.S. Oil Refinery Industry
8. Herman Melville and the Problem of Evil
9. The name is absent
10. THE WELFARE EFFECTS OF CONSUMING A CANCER PREVENTION DIET