Fall 2010 Seminar Series

DATE: October 7th
LOCATION: E62-550
TIME: 4:15pm
Reception immediately following in same room

SPEAKER:
Awi Federgruen

TITLE
How Much is a Reduction of Your Customers' Wait Worth?
Estimating industry wide demand functions on the basis of equilibrium conditions  in an  underlying competition model

ABSTRACT
In many service industries, companies compete with each other on the basis of the waiting time their customers' experience, along with other strategic instruments such as the price they charge for their service. We develop a methodology to estimate to what extent waiting time performance measures impact different firms' market shares and price decisions. We report on a large scale empirical industrial organization study in which the demand equations for fast-food drive-thru restaurants are estimated based on so-called structural estimation methods, anchored on the Nash equilibrium conditions of a price competition model.. Our results confirm the belief expressed by industry experts, that in the fast-food drive-thru industry customers trade off price and waiting time and that, on average, a seven second waiting time reduction results in a 1%.increase in market share. Correspondingly, our estimates indicate that consumers attribute a very high cost to the time they spend waiting.

The above competition model belongs to a general class of price competition models with Mixed Multi Nomial Logit demand functions under affine cost functions. We characterize the equilibrium behavior of this class of models starting with the case where each product in the market is sold by a separate, independent firm. Here we identify a natural upper bound for the price levels. Assuming the prices are restricted by these bounds, we show that a pure Nash equilibrium exists in the interior of this feasible price region and that the set of equilibria is given by the solutions of the system of First Order Condition equations. This provides a justification for the many reported structural estimation methods which require that equilibria correspond with the solutions to this system of FOC equations. We provide an example that shows that a condition like ours is necessary for the existence of a Nash equilibrium. We show that the upper bound for the prices can be assumed, without loss of generality, under an intuitive, widely applicable and easily verified condition. We also provide conditions when the Nash equilibrium is unique and computable with a simple computational scheme. The above results are generalized to the general multi-product case where several products may be sold by the same firm.

 

Joint work with G. Allon, Kellogg School and M. Pierson, HBS