Matched Charitable Contributions: Comparative Statics and Equilibrium

Daniel K. Biederman

Department of Economics, University of North Dakota, Grand Forks, USA.

DOI: 10.4236/tel.[phone]                

Abstract

A small optimizing agent maximizes his utility by allocating his income to private consumption and to a contribution to a particular charity. The agent’s contribution may be matched, at a particular rate, by a large agent. We provide a comprehensive comparative-statics analysis of the agent’s problem, allowing for changes in the agent’s income, the agent’s conjecture about other agents’ contributions, and the match rate. A Nash equilibrium among n such agents is shown to exist if private consumption is a normal good for all agents. The equilibrium is unique if private consumption and charitable giving are normal goods for all agents.

Keywords

Charitable Contributions; Match Rate; Monotonic Transformation; Nash Equilibrium

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. Karlan and J. A. List, “Does Price Matter in Charitable Giving? Evidence from a Large-Scale Natural Field Experiment,” American Economic Review, Vol. 97, No. 5, 2007, pp. 1774-1793. http://dx.doi.org/10.1257/aer.97.5.1774
[2]	J. Andreoni, “Leadership Giving in Charitable Fund-Raising,” Journal of Public Economic Theory, Vol. 8, No. 1, 2006, pp. 1-22. http://dx.doi.org/10.1111/j.1467-9779.2006.00250.x
[3]	C. C. Eckel and P. J. Grossman, “Subsidizing Charitable Contributions: A Natural Field Experiment Comparing Matching and Rebate Subsidies,” Experimental Economics, Vol. 11, No. 3, 2008, pp. 234-252. http://dx.doi.org/10.1007/s10683-008-9198-0
[4]	N. Gong and B. D. Grundy, “Charitable Fund Raising: Matching Grants or Seed Money,” Unpublished Manuscript, 2011.
[5]	S. Huck and I. Rasul, “Matched Fundraising: Evidence from a Natural Field Experiment,” Journal of Public Economics, Vol. 95, No. 5-6, 2011, pp. 351-362. http://dx.doi.org/10.1016/j.jpubeco.2010.10.005
[6]	D. Karlan, J. A. List and E. Shafir, “Small Matches and Charitable Giving: Evidence from a Natural Field Experiment,” Journal of Public Economics, Vol. 95, No. 5-6, 2011, pp. 344-350. http://dx.doi.org/10.1016/j.jpubeco.2010.11.024
[7]	S. Meier, “Do Subsidies Increase Charitable Giving in the Long Run? Matching Contributions in a Field Experiment,” Journal of the European Economic Association, Vol. 5, No. 6, 2007, pp. 1203-1222. http://dx.doi.org/10.1162/JEEA.2007.5.6.1203
[8]	D. Rondeau and J. A. List, “Matching and Challenge Gifts to Charity: Evidence from Laboratory and Natural Field Experiments,” Experimental Economics, Vol. 11, No. 3, 2008, pp. 253-257. http://dx.doi.org/10.1007/s10683-007-9190-0
[9]	T. Bergstrom, L. Blume and H. Varian, “On the Private Provision of Public Goods,” Journal of Public Economics, Vol. 29, 1986, pp. 25-49. http://dx.doi.org/10.1016/0047-2727(86)90024-1
[10]	A. Apinunmahakul and V. Barham, “Strategic Interaction and Charitable Fundraising,” Modern Economy, Vol. 3, 2012, pp. 338-345. http://dx.doi.org/10.4236/me.2012.33044
[11]	J. Andreoni, “Giving with Impure Altruism: Applications to Charity and Ricardian Equivalence,” Journal of Political Economy, Vol. 97, No. 6, 1989, pp. 1447-1458. http://dx.doi.org/10.1086/261662
[12]	J. Andreoni, “Toward a Theory of Charitable Fund-Raising,” Journal of Political Economy, Vol. 106, No. 6, 1998, pp. 1186-1213. http://dx.doi.org/10.1086/250044
[13]	R. Auspitz and R. Lieben, “Untersuchungen über die Theorie des Preises,” Duncker & Humblot, Leipzig, 1889.
[14]	J. S. Chipman, “An Empirical Implication of Auspitz-Lieben-Edgeworth-Pareto Complementarity,” Journal of Economic Theory, Vol. 14, No. 1, 1977, pp. 228-231. http://dx.doi.org/10.1016/0022-0531(77)90096-5
[15]	C. E. Weber, “Two Further Implications of Auspitz-Lie-ben-Edgeworth-Pareto Complementarity,” Economics Letters, Vol. 67, No. 3, 2000, pp. 289-295. http://dx.doi.org/10.1016/S0165-1765(99)00277-3
[16]	X. Vives, “Oligopoly Pricing: Old Ideas and New Tools,” MIT Press, Cambridge, 1999.