On Price versus Quality

In this work we propose a model where the value of a buyer for some product (like a slice of pizza) is a combination of their personal desire for the product (how hungry they are for pizza) and the quality of the product (how good the pizza is). Sellers in this setting have a two-dimensional optimization problem of determining both the quality level at which to make their product (how expensive ingredients to use) and the price at which to sell it. We analyze optimal seller strategies as well as analogs of Walrasian equilibria in this setting. A key question we are interested in is: to what extent will the price of a good be a reliable indicator of the good's quality? One result we show is that indeed in this model, price will be a surprisingly robust signal for quality under optimal seller behavior. In particular, while the specific quality and price that a seller should choose will depend highly on the specific distribution of buyers, for optimal sellers, price and quality will be linearly related, independent of that distribution. We also show that for the case of multiple buyers and sellers, an analog of Walrasian equilibrium exists in this setting, and can be found via a natural tatonnement process. Finally, we analyze markets with a combination of "locals" (who know the quality of each good) and "tourists" (who do not) and analyze under what conditions the market will become a tourist trap, setting quality to zero while keeping prices high.