Time- and State-Dependent Pricing: A Unified Framework

47 Pages Posted: 19 Sep 2011

See all articles by Marco Bonomo

Marco Bonomo

Insper Institute of Education and Research

Carlos Carvalho

Asset 1 Investment Company; Pontifical Catholic University of Rio de Janeiro (PUC-Rio) - Department of Economics

René Garcia

Université de Montréal - CIREQ - Département de sciences économiques; University of Montreal

Date Written: September 19, 2011

Abstract

We develop a tractable unified framework for solving optimal time- and state-dependent price-setting problems. We use it to study models with adjustment costs and infrequent information, entertaining various alternatives for the source and nature of infrequent information. In particular, we consider both models where information is infrequent for exogenous reasons and models where firms face a lump-sum cost to gather and process information. Our choice of state variables is key to make the problems tractable. Specifically, we replace the usual state variable in state-dependent pricing problems – the discrepancy between the firm's price and its frictionless optimal level – with its expectation conditional on the firm's information set, and augment the state space with the time elapsed since the last date when information was fully factored into the pricing decision ("information date"). This allows us to formulate all price-setting problems as two-dimensional optimal stopping problems. Our analysis uncovers new insights about price setting. Despite the presence of menu costs, firms may choose to change prices in the absence of new information. Time dependency in pricing rules arises as a consequence of the build up of unobserved information. In these circumstances, the inaction region changes as a function of the time elapsed since the last information date. When the next information date is known, the presence of menu costs produces an extreme form of inaction: irrespective of the size of the expected price discrepancy, it is never optimal to adjust just prior to the information date.

Keywords: menu costs, information costs, infrequent information, sticky information, inattentiveness, optimal price setting, state-dependent pricing, time-dependent pricing

JEL Classification: E00, E31

Suggested Citation

Bonomo, Marco and Carvalho, Carlos and Garcia, René, Time- and State-Dependent Pricing: A Unified Framework (September 19, 2011). Available at SSRN: https://ssrn.com/abstract=1930633 or http://dx.doi.org/10.2139/ssrn.1930633

Marco Bonomo

Insper Institute of Education and Research ( email )

R Quata 300
Sao Paulo, 04542-030
Brazil

Carlos Carvalho (Contact Author)

Asset 1 Investment Company ( email )

Avenida Juscelino Kubitschek, 1600/Conj 52
São Paulo, São Paulo
Brazil

HOME PAGE: http://www.asset1.com.br

Pontifical Catholic University of Rio de Janeiro (PUC-Rio) - Department of Economics ( email )

Rua Marques de Sao Vicente, 225/206F
Rio de Janeiro, RJ 22453
Brazil

HOME PAGE: http://https://sites.google.com/site/cvianac2/carloscarvalho

René Garcia

Université de Montréal - CIREQ - Département de sciences économiques ( email )

C.P. 6128, succursale Centre-Ville
3150, rue Jean-Brillant, bureau C-6027
Montreal, Quebec H3C 3J7
Canada
514-985-4014 (Phone)

University of Montreal ( email )

United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
138
Abstract Views
803
rank
230,780
PlumX Metrics