The purpose of this paper is to examine the effects of the bundling of goods by an upstream, monopolist manufacturer who sells items to downstream retailers with differences in the demand functions they face when selling the items to final consumers. The retailers can then resell the goods to consumers. The model is kept parsimonious to best isolate these effects. To model legal realities, the manufacturer, M must offer the same terms to all retailers. There are two goods in the model, a and b. M may offer “packages” containing (qa, qb), which are quantities of the a and b goods respectively. These packages may be sold at transfer prices, T (qa, qb), to any retailer. In this setting, the manufacturer can not only adjust the types of goods included in a package but also the volume of each type. This gives the manufacturer additional flexibility to price discriminate, even though the same terms must be offered to all retailers. These packages can be sold at any price and the pricing format can be non-linear. In a world where bundling is illegal, packages may contain positive quantities of only one of the two goods.
Multiple items of the same good can be included in the packages. For example, in the non-bundling world, packages such as (0,152), (45,0), and (1,0) are allowed.
Packages such as (22, 33) or (1,1) are not allowed if bundling is illegal.
The demand functions faced by a retailer i are as follows:
pai(qai) = αai− qai (2.1)
pbi(qbi) = αbi− qbi (2.2)
where pai and pbi are the prices that a retailer i can sell a good for when they are sold in quantities qai or qbi, respectively. In general, the values αai and αbi can take on any non-negative value but will usually not be the same. For many of the ensuing examples, notation such as αh and αl will be used instead where ‘h’
indicates a relatively high value to a lower value denoted by l.
In this paper, these demand functions are kept simple since one of the main focuses of the paper is to see how the relative strength of the demand functions for the different goods facing the different retailers affects the terms which M will offer. Heterogeneity in retailer profits and revenues can be modeled by simply ad-justing the α terms. Allowing different slopes for the demand functions adds little to the model if the profits and revenues of the retailers relative to one another is the main concern. Accordingly, the above demand functions are chosen as they enable one to model sufficient heterogeneity in the demand functions for this pur-pose. To keep the focus on overall revenue and profits, the cost of manufacturing the goods is kept at zero. There are no shelf space or capacity issues for the retailer or manufacturer. The goods are kept independent. Whether substitutability or complementarity between the goods could affect the eventual terms offered by M is an open question, but one which might be difficult to find tractable answers to under this set-up.
To be clear, there are two types of prices here: the transfer prices T (qa, qb) for the packages which are sold from the manufacturer to the retailer and the final prices pai and pbi at which retailer i resells the goods to the final consumers. The manufacturer may sell the goods together in multiple quantities but the retailer is permitted to sell each good in individual units. Cournot pricing is assumed. The retailer is a territorial monopolist with market power in its own territory.
The order of events is assumed as follows: The manufacturer chooses the quantities of a and b in the packages and the prices of packages. He may effec-tively make certain packages unavailable by charging a price ∞ and can limit the retailers to only buying certain packages at certain prices. The monopolist man-ufacturer has most of the bargaining power here. Retailers, however, are free to buy any package which is available or buy nothing and accept a zero profit.
As a matter of semantics, it is worth emphasizing again that “packages” may include various numbers of one or both types of goods but may only have one type of good if bundling is per se illegal. “Bundled packages” or “bundles” are packages made available by M which include both types of goods. The “vertically-integrated” package is the revenue-maximizing amount. It is what the monopolists would sell if it were managing the territories rather than retailers. As the paper proceeds, it is good to keep in mind that the “vertically-integrated” quantities may actually be welfare-enhancing compared to the cases where less or even nothing is produced. One will see that the manufacturer often has an incentive to sell less than these vertically-integrated quantities to retailers in cases where bundling both is and is not allowed.
Manufacturer and retailers alike seek to maximize profit. For the
manufac-turer, M, this occurs by obtaining the most value for packages sold. For retailers, this occurs by maximizing the difference between product revenue and transfer prices paid to M. Retailers are allowed to dump any unsold quantity of any good at no cost. Consumer welfare is measured in the typical way which is by consid-ering the net excess of consumer valuation over price.