Identity’s Shadow Prices: The Case of Charity

Abstract

ABSTRACTThis paper develops a rational action model of charitable giving based on an expanded utility function that includes “identity utility”. The model is used to develop a procedure that can identify, from changes in individual donations over time, whether they are simply reactions to changes in the “prices” of charity--determined by changes in marginal tax rates--or due to changes in donor attitudes towards the charitable causes they support. An approach to using this procedure for market research is proposed.KEYWORDS: charityidentity utilityrational choice Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1. The concept of the “personal identity narrative” in this paper was inspired by the positive critiques of the concept of “identity utility” by Davis (Citation2007) and Boulu-Rashef (Citation2015)2. This assertion is proved in the section, “The Donor’s Optimal Spend”, below.3. This restriction will be relaxed later in this paper.4. If a suitable narrative could be found for making the y-intercept of this function different from (greater than or less than) F, the function O(s) would represent the northeast quadrant of an ellipse centered at (0,0) rather than the northeast quadrant of a circle. The x-axis intercept would still have length F, because when all the agent’s residual wealth is spent, it cannot be a source of additional utility to him. The y-axis intercept could be some multiple of F. This would imply that the agent, A, would have a greater or lesser value for his money than for the “other economic goods” he could buy with it. While this is conceivable, in this paper the simple solution, in which the x- and y-axis intercepts are equal, is used. Transforming a symmetrical circle into an ellipse would complicate the algebra, but it would not affect the thrust of the arguments developed in what follows.5. Applying the decomposition of Hicks or Slutsky, the income effect of a tax reduction is an increase of spendable income. To determine the substitution effect of a price change, the income effect must be factored out.6. The derivation is as follows: Substituting x for (1+ε1)/P1 in (14) gives s1 = xF1/1+x2. If (1+ε1)/P1 ≥0, as it must be if ε1 ≥ −1, then x ≥0, and the derivative of s1 with respect to x is positive. Since s1 is an increasing function of x, and x is an increasing function of ε1, s1 is an increasing function of ε1.7. Since s1 is strictly increasing for ε1 > −1, ε1 is also a function of s1, by the Inverse Function Theorem.8. If A gives to three charities, B1, B2, and B3, then D = ∑13Di, s = ∑13si, and F = ∑13Fi. Here, si/s is the proportion of A’s total spend on charity allocated to charity Bi. Fi/F is the proportion of A’s residual wealth fund allocated to charity Bi. Going forward, each charity will be considered individually.9. Assuming that the income elasticity of F is 1.