Profit maximization in a multi-product firm with impatient customers

Abstract

In this paper, the standard model of profit maximization is extended to include multi-product production in a market characterized by impatient customers. A formal model is presented that includes price, delivery frequency, production run length per set-up and product range as endogenous variables. The model facilitates the analysis of the complex interactions between these variables and highlights the inherent problems relating to profit maximization. For example, offering a broader range of products and/or more rapid delivery may seem to be a sensible response for a multi-product firm with impatient customers in a scenario of depressed demand. However, the analysis shows that such strategies could be counterproductive.

Keywords:

• economics
• manufacturing
• multi-product
• pricing
• delivery lags
• inventory

Acknowledgements

The comments of two anonymous referees were most helpful. A larger version of the paper with a technical appendix is available in pdf form at: http://www.econ.stir.ac.uk/staff/levin/index.htm