On Price versus Quality

Abstract

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.