Evolutionary Dynamics of Price Dispersion with Market-Dependent Costs

Abstract

The theoretical literature in economics has established causality from cost dispersion to price dispersion in a market for a homogeneous good in which buyers face search cost. In that literature, it is generally assumed that the cost distribution in the market is exogenous. In this paper we explore bidirectional causality between costs and prices, motivated by a long run perspective under which there are entry decisions on the sellers’ side on the basis of information about past prices. Moreover, we assume that decision makers do not have full information about former prices but they have access to a statistical estimate of past prices, typically provided by some external agency. We introduce a evolutionary discrete time model for the interaction of agents in the market which we analyze numerically. We show that, in this scenario of mutual influence between cost and prices, price dispersion (and cost dispersion) prevail in the stationary regime of the market. We provide evidence that features of the stationary price distribution are related with those of the initial distributions of price and costs and, in particular, we characterize initial conditions to deliver stationary leptokurtic price distributions, which have been recently reported to be prevalent in many markets.

Appendix: Sensitivity Analysis: Table and Figures

Table 2 collects the parameter values used for the figures in this appendix. Each row in Table 2 corresponds to the figure indicated in the last column of the table. Each figure has four panels. Since each of them has a clear counterpart in the main text mutatis mutandis, explanatory captions are omitted.

Table 2 Variations with respect to benchmark values

Fig. 10

Large value of $\mu _0$. a First and last period (cost, price), b time path $n_t$, c$\mu _t$ versus $n_t$, d$\sigma _t$ versus $n_t$

Fig. 11

Low value of $\mu _0$. a First and last period (cost, price), b time path $n_t$, c$\mu _t$ versus $n_t$, d$\sigma _t$ versus $n_t$

Fig. 12

Large value of $\alpha _0$. a First and last period (cost, price), b time path $n_t$, c$\mu _t$ versus $n_t$, d$\sigma _t$ versus $n_t$

Fig. 13

Low value of $\alpha _0$. a First and last period (cost, price), b time path $n_t$, c$\mu _t$ versus $n_t$, d$\sigma _t$ versus $n_t$

Fig. 14

Large value of $n_{0}$. a First and last period (cost, price), b time path $n_t$, c$\mu _t$ versus $n_t$, d$\sigma _t$ versus $n_t$

Fig. 15

Low value of $n_{0}$. a First and last period (cost, price), b time path $n_t$, c$\mu _t$ versus $n_t$, d$\sigma _t$ versus $n_t$

Fig. 16

Large value of $\tau$. a First and last period (cost, price), b time path $n_t$, c$\mu _t$ versus $n_t$, d$\sigma _t$ versus $n_t$

Fig. 17

Low value of $\tau$. a First and last period (cost, price), b time path $n_t$, c$\mu _t$ versus $n_t$, d$\sigma _t$ versus $n_t$

Fig. 18

Large value of $\eta$. a First and last period (cost, price), b time path $n_t$, c$\mu _t$ versus $n_t$, d$\sigma _t$ versus $n_t$

Fig. 19

Low value of $\eta$. a First and last period (cost, price), b time path $n_t$, c$\mu _t$ versus $n_t$, d$\sigma _t$ versus $n_t$