We present a model that generates empirically plausible price distributions in directed search equilibrium. There are many identical buyers and many identical capacity-constrained sellers who post prices. These prices can be renegotiated to some degree and the outcome depends on the number of buyers who want to purchase the good. In equilibrium all sellers post the same price, demand is randomly distributed, and there is sale price dispersion. Prices and distributions depend on market tightness and on the properties of renegotiation outcomes. In a labor market context, the model generates a strong empirical prediction. If workers can renegotiate the posted wage, then the model predicts a positively skewed and realistic-looking density function of realized wages when the mean number of job-seekers per vacancy is large.
Camera, G., and C. Selcuk (2009). Price dispersion with directed search. Journal of the European Economic Association 7(6), 1193–1224. doi: 10.1162/JEEA.2009.7.6.1193