Mixed pricing in monopoly and oligopoly: theory and implications for merger analysis

ABSTRACT

Mixed pricing is when firms supplying an input to other firms charge some customers a fixed, take-it-or-leave-it (ToL) price, whilst other customers are allowed to bargain for a special (lower) price. The practice appears to be almost ubiquitous in business-to-business markets. The paper analyses how monopoly or non-cooperative oligopoly sellers will optimally choose which customers to bargain with, and will choose the ToL price to be paid by other customers. In the model, average revenues and thus profits increase as the number of competitors gets smaller, but this is achieved without the restriction of output predicted by standard price theory. Implications for merger analysis and policy are drawn out.

KEYWORDS:

• Mixed pricing
• oligopoly
• merger analysis

Acknowledgments

The author thanks two referees and Steffen Lippert for excellent comments and advice, as well as participants at the 2nd ATE Symposium, Sydney, 15–16 December 2014.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. Budzinski and Ruhmer (2010) survey merger simulation models in practice.

2. Depending on whether competing firms sell a differentiated or homogeneous product.

3. Mixed pricing is an example of what could be termed ‘pricing discrimination’, rather than price discrimination – that is, applying different pricing regimes to different customers. The quite extensive literature on price discrimination in oligopoly is surveyed in Hazledine (2015).

4. Chen (2003) has a dominant firm + competitive fringe downstream industry. The dominant firm negotiates with the monopoly upstream supplier, with exogenous bargaining power. The supplier also sets a ToL price paid by all the fringe firms. Issues of countervailing power are dealt with.

5. It is also empirically likely that many or most customers with high outside-option costs will be relatively small, but customer size will not be a formal element of the mixed pricing model developed below. I follows King (2013) – and, of course, the entire textbook price theory literature – in assuming that upstream suppliers have the power to impose ToL pricing on any customer – that is, that these customers will not throw down the gauntlet of refusing to deal at all with the supplier if negotiation on price and quantity is not permitted.

6. Sunday Star Times, ‘Insurers go quiet on “discretionary discounts”’, 12 October 2014.

7. Of course, airfares (date of purchase) and book prices (hardcover/paperback) are discriminated by other means.

8. Auckland's second largest taxi company, Discount Taxis, offers, for the asking, a $40 cash fare from the university to the airport. If you don't ask, you could pay a metered fare of up to twice as much, depending on traffic conditions. So ask!

9. Such discounts will normally be offered to overseas (especially Chinese) agents, who can deliver blocks of fee-paying students.

10. Excepting large one-off projects, such as the construction of a road or a building.

11. The input–output tables reveal that the parent four-digit industry ‘Services to Buildings & Dwellings’ accounts, on average, for exactly 1% of total customers’ intermediate input costs.

12. For an essential input, the intrinsic value would be the loss in profits to the firm if it has to cease production, for lack of the input.

13. In general, the customer's best outside option could include sourcing the input from outside the market (e.g. importing it) or producing in-house (upward vertical integration).

14. If there are a maximum of N similar-sized potential customer firms (i.e. firms with higher self-cleaning costs than the professionals), a unit of cleaning will be of size 1/N. However, we will not be using the number of customers in the model. Of course, all firms who can self-clean at lower cost than the professionals will do so.

15. In practice, and especially in commercial retail situations such as building supplies, what will be negotiated will be a discount rate, or set of rates, off the ToL price(s), to be applied to all purchases over some future period.