Do higher tax rates spur more charity? I doubt it.

A few days ago I was talking with my mother about the state of the economy, income inequality, and social obligations... Typical evening conversation on any New Years, I'm sure. From life experience and observations on a (privileged) extended family, her opinion was that more charity occurred when tax rates were higher. I disagreed, and offered to present a mathematical demonstration on why that was the case. After that effort, I wanted to show the Internets the fruits of my labor.

Charitable giving is a very personal decision and the tax law surrounding it is complicated and arcane, so I start with some simplifying assumptions to make the problem more approachable. These are:

• Money given to charity is 100% tax-deductible.
• Each person lives for two periods, then dies, and their entire stock of wealth is donated after death.
• An individual's money earns 10% interest.
• To make the problem concrete, I'll imagine a person earning $100,000 in each period, and two different tax regimes: one with a 0% tax rate, and another with 50%. 

Now a quick exercise in arithmetic, starting with a tax rate of 50%. The individual earns $100,000 in the first period, $50,000 of which would go to the government. Instead that $50,000 is given to charity to avoid taxes. At the start of period two, they earn $5,000 in interest and another $50,000 in after-tax income, then die and donate all of it. Total charity given is $205,000.

Now imagine a tax rate of 0% (and if you're a libertarian, try not to faint with excitement). An individual earns $100,000 and keeps all of it, earns $10,000 in interest before the second period, makes another $100,000 then dies and gives all of it away. Total charity given is $210,000.

One could argue that this result emerges just from the assumptions made, which is partially true. However, as long as individuals can earn a higher return on investment than the government (which is not a controversial claim) and all money is transferred upon death (a de facto necessity) then the result, qualitatively, will still be the same. If you make the example more realistic, and envision a person making money then saving and investing it for more than just two years, the difference between the two tax rates becomes even more apparent.

Of course, someone might say there are distributional issues this exercise neglects. Maybe needy recipients of charity are more sympathetic than the undeserving heirs of some wealthy person. Aside from that, the general point still stands: when government takes money through taxes, the overall social "pie" becomes smaller. When individuals can invest it, they put money into productive activities which can generate more wealth, making the "pie" bigger. Even if higher tax rates drive some people to give more money to charity than they otherwise would, society in the aggregate is better off if that money can be productively invested by individuals instead. Charity is then a pleasant side-benefit of greater social wealth.