Why Hoarding is Bad

In the midst of this sudden pandemic, a recent phenomenon I’ve observed is people hoarding goods and foodstuff from grocery stores. It’s important to remember that empty shelves are not the byproduct of supply chain shortages but rather the effect of widespread hysteria and irrational forward thinking. In the midst of this madness, I thought it would be interesting to use economics to show how hoarding is bad for public welfare and why it may be in grocery stores’ best interest to institute quantity mandates on certain goods (e.g. frozen food, paper towels, toilet paper). Linked below is a very simple and drastically generalized problem which demonstrates the social disadvantages of hoarding. Please let me know if you have any feedback with regards to enriching the complexity of this problem.

https://docs.google.com/document/d/1_aJ-Rq47xDxGvqP1YHoFVXCHr-TqJXzZBQoECnuEAyk/edit?usp=sharing