The effects of correlated demand on pricing, inventory, and production

Abstract

Existing explanations for price discrimination in products and services invoke reasons like customer segmentation, information rents, transactions costs, or inventory constraints. By contrast, we propose the sellers’ objective to smooth profits as a possible explanation. We show that when sellers carry multiple products, the spread in buying and selling prices of any product depends not only on its own profits and inventory position, but also on the correlations of these variables with the other products. Consequently, sellers may price the same product differently depending on the range of products that they carry.

Keywords:

• multi-product inventory
• price discrimination
• profit smoothing

JEL Codes:

• D21
• D40
• M21
• M41

View correction statement:

The effects of correlated demand on pricing, inventory, and production

Acknowledgements

We are grateful for helpful comments from the participants in the APJAE Conference (25–26 April 2011), Hawaii, Masako Darrough (discussant), Suresh Radhakrishnan (editor), Sharan Jagpal, Nitin Patel, and Ram Ramakrishnan.

This research was supported in part by a Faculty Research Grant from Rutgers Business School—Newark and New Brunswick.

Notes

1. Brent-WTI spread (http://www.econbrowser.com/archives/2011/02/brentwti_spread.html, 22 February 2011). I wanted today to try to make sense of another equally striking development in oil markets over the last 6 weeks – the disparity between the price of oil in the Midwest United States and that elsewhere in the world … has at times exceeded $15 a barrel. But that leaves lots of money on the table right now for physical arbitrage – … the Oil Drum notes that the most efficient way to do this would be to start running the Seaway pipeline, which is currently delivering oil from the Gulf of Mexico to Oklahoma, in reverse. But it seems ConocoPhillips … is not interested in that plan [because] transporting oil out of the Midwest might leave it vulnerable to political criticism as domestic oil prices rise in response that it perhaps avoids by maintaining the status quo.

2. This is similar in spirit to the objective in portfolio selection first introduced by Markowitz (1952). We note, however, that our model is different from the Markowitz model and we discuss this point later. Another approach documented in the operations literature to account for the volatility in profits is to consider the expected utility of the profits, which is equivalent to a linear mean-variance tradeoff in profits (Chen and Federgruen 2000, Sim et al. 2004).

3. Technically speaking, we should endow the seller with a cash position in order to purchase inventory. However, assuming that the seller can borrow at an interest rate of zero makes the initial asset position irrelevant. To understand Equation (2) assume that the seller has no assets to begin with and borrows the cost of inventory at an interest rate of 0. At the end of the period, they pay the debt and are left with the income and the value of end inventory less any other operating costs they may have incurred.