Recently, I made some pistachio gelato. The recipe called for shelled, unsalted pistachios. In the bulk section of the grocery store, there were two options for unsalted pistachios -- pistachios in the shell, and shelled pistachios. The obvious question is, is it more economical to purchase the unshelled pistachios, or the shelled pistachios?
My gut instinct, based on years of consumerism, is that the pistachios still in their shells would be less expensive overall than their shelled counterparts, so that is what I went with. But as I was spending the eternity it took to de-shell the pistachio, I wondered what is the price crossover point, where it would be less expensive to purchase shelled pistachios, and had I already crossed it?
Having unshelled pistachios in hand, it would be a cinch to figure this out, all I had to do was keep all the waste product and the pistachio meats, and weigh everything at the end. So I did.
The recipe called for 250 g of shelled, unsalted pistachios. I ended up with 250.5. From that 250.5 g of pistachio meats, I generated 274.8 g of waste -- shells, skins, and unopenable pistachios. In painfully explicit mathematics,
$$m_{s} = 250.5 g$$
$$m_{w} = 274.8 g$$
$$m_{t} = m_{s} + m_{w} = 205.5 g + 274.8 g = 525.3 g$$
The amount I paid for unshelled pistachios is
$$C_{u} = P_{u}m_{t}$$
Whereas, the amount I would have paid for shelled pistachios is
$$C_{s} = P_{s}m_{s}$$
And the point at which purchasing shelled pistachios becomes economically advantageous is
$$C_{u} \gt C_{s}$$
$$P_{u}m_{t} \gt P_{s}m_{s}$$
or,
$${P_{u} \over P_{s}} \gt {m_{s} \over m_{t}}$$
Unshelled pistachios were $6.99 / pound, whereas shelled pistachios were $15.99 / pound, so I came out ahead, but not by much. I will note that my thumbnail and my helper both disagree with this assessment.
The pistachio gelato recipe came from Liete's Culinaria, and it was delicious.
