Modeling Charity Through Public Goods Models

In November, Millions of supporters from almost 20 countries participate in Movember, a month-long process of raising money for men’s health issues such as Prostate Cancer, Testicular Cancer, and Mental Health. People like Myself shave off all of their facial hair and then grow a “Mo,” a mustache, for the entire month of November while raising funds for this charity. As Movember is very important to me, I have participated in this month of charitable giving since 2021 and intend to do so for the rest of my life.

As an Econ student, charitable giving from NGOs, like Movember, classified by the IRS as 501(c) organizations, has always fascinated me. In the U.S., Charitable Giving totaled 557.16 Billion Dollars. This amount consists of donations from individuals, corporations, foundations, and bequeathments to various Non-governmental organizations, including religious institutions, charities, education, and grants (National Philanthropic Trust). As charitable giving to NGOs is an integral part of life in America, it would be worthwhile to explore how Economists model this odd behavior of altruism, guilt, and tax cuts.

One Way Economists model donations is through public goods models. A public good is a non-excludable, non-rivalrous market, meaning that no one can prevent you from using this good or service and that one’s use of it does not diminish its availability to others. charities are often thought of as a form of public goods called imperfect public goods. This is because one’s contribution to a charity is non-rivalrous, but the service you donate to is often excludable, helping only a targeted portion of the population. Using Movember as an example, anyone can donate to this charity, but the END and its services target men with health needs. As a result of the excludability, the public good model can be helpful but not perfect for modeling NGO’s. 

The beauty of public goods models is that they are simple but can be built out through various variables to make them more complex and accurate. Think of a possible donation function for an individual donor to an NGO: 

Maxd = 𝛔1UR(d) – 𝛔2G(d) – d

In this Model, a total donation ( Maxd) is comprised of a donation (d), the Guilt of that individual (G(d)), and the altruism of the donator (UR(d)) Measured by the utility generated by a recipient (The NGO) from the donation. This model is made more complex by the added Importance weights at the beginning of each variable denoted by 𝛔i, where i is a different number between 1 and the number of variables in the person’s decision-making process for donating (excluding the initial donation). This added variable considers the complexity of donations from suppliers of donations, as every person adds different weight to parts of the decision-making process (one person might feel more guilty than altruistic or vice versa). This individual’s total donation considers the costs (Variables in which the sign is negative) and the benefits (just altruism in this simple model) of a donation to an NGO. It is also of note that the elasticity of the maximum donation is close to zero. This phenomenon is often called a ‘drop in the bucket.’ The close-to-perfect inelasticity captures the fact that an increase in a single dollar donation from a donator does little for the cause, and thus, more money is needed to push the button along for the NGO to make a profit. The NGO’s total profit would then be the total of all donations made by individual donors minus the total costs of running the NGO (paying employees, paying for capital, etc). 

While simple on the surface, public goods models can be built out to be more complex, helping economists model individual donation behavior through Maxd functions and NGO’s total contribution to causes through a profit function. While guilt and altruism are two crucial factors in decision-making for donations, tax cuts, increased status, and other variables can be added to the model to make it more accurate. While modeling something often private to many individuals can be ethically dubious, economists must understand the decision-making that goes into both donations and profit for NGOs. With that being said, regardless of why you donate, the causes are often life-changing and impactful for various communities in the U.S. and around the world. 

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