The Economics of Charity Drives

There's a recent trend among charity organisers to donate rice to charities based on fun activities, and these could range from online games which promises to donate X no. of grains of rice for every correct answer, to physical activities which pegs the no. of bowls of rice to a measurable output of some sporting events like running or skipping.

At the end of the day, every participant and organiser is happy to have contributed something worthwhile to charity, as the results are tallied, but does anyone pause to calculate the dollar value of such an act of charity?

As a mathematical exercise, let's assume that:

(1) a sponsor offers to pay for a bowl of uncooked rice for persons for every 10 units of output achieved by each participant. Remember, these could be anything from running 10 metres to climbing 10 steps to skipping 10 times.

(2) a total of 10,000 bowls was earned for charity at the end of the day.

I've looked up various websites that gives the relevant measurements and here are some estimates that 1 cup of uncooked rice (for 2 pax) weighs about 7 oz or 0.2kg.

==> Therefore, 1 bowl for 4 pax is approximately 2 cups or 14 oz or 0.4kg (i.e. double).

==> 10,000 bowls = 10,000 x 0.4kg = 4,000kg = 800 bags of rice @ 5kg


Now, the price of rice varies from supermart to supermart, so let's take 3 price labels and compute the dollar equivalent of "10,000 bowls of rice":

Brand A, 5kg @ $6.60 = $6.60 x 800 bags = $5,280

Brand B, 5kg @ $9.10 = $9.10 x 800 bags = $7,280

Brand C, 5kg @ $13.20 = $13.20 x 800 bags = $10,560


Assuming if the output achieved at the charity event is doubled, the figures above will also be doubled accordingly.


But what about the average dollar equivalent raised by each participant in the charity event?

Let's assume that we got 800 bags of Brand B rice @ $9.10 totalling $7,280.

If there were 100 participants, each person would have generated $72.80 or 8 bags of rice.
If there were 150 participants, each person would have generated $48.53 or 5.3 bags of rice.
If there were 200 participants, each person would have generated $36.40 or 4 bags of rice.


Once again, if we double the amount of rice earned for charity to 20,000 bowls, the figures above will also double, ceteris paribus.

Isn't that amazing?