Transactions Bundling in Monopsonistic Markets; Theory and Numerical Implications

Transactions Bundling in Monopsonistic Markets; Theory and Numerical Implications X. Dassiou City University London Dionysius Glycopantis 1 City University London Abstract. We show that for a price-setting monopsony, offering a mixed bundle in the transactions in goods of uncertain quality is profit enhancing and, contrary to conventional wisdom, is trade enhancing. The magnitude of the improvement in expected profits (volume of trade) relative to no bundling is greater the smaller (larger) the gap in the degree of quality uncertainty between the two goods. Also importantly, but on a smaller scale, if the degree of quality uncertainty between the two goods is equal, the expected profits (volume of trade) improvement is an increasing (decreasing) function of this common degree. JEL Classif cation: D4, D8. Keywords: Monopsony, Price discrimination, Mixed bundling, Quality uncertainty, Partner preference, Profit enhancing, Trade enhancing. 1. Introduction There are several contexts in which business to business exchange is buyer driven, as in the case of government or company-led procurement. The most prominent case of the former is defence procurement, while in the latter case we have the example of health care where an insurance company buys the services of a hospital using its monopsony power as in the USA health model. While this process is not new at the wholesale level, reverse auctions have gained in popularity with the advent of electronic commerce as this process was not possible at the retail level before it became electronic.2 For a price-setting buyer, price discrimination through the medium of bundling can be of two types: One is mixed bundling, which takes the form of offering either to trade separately in different goods at specific prices, or to trade in a package of goods at an aggregate price which includes a discount or a premium. Alternatively, there is pure bundling where a bundle of goods is offered at a package price alone and the individual goods are not traded separately by the price setting company. The intention of this paper is the theoretical analysis of price discrimination through the strategy of mixed bundling exercised by a buyer setting prices under conditions of monopsony power. We intend to analyse the practice of this type of bundling of one’s

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purchases in a package irrespective of whether this occurs electronically (business to- business online transactions), or offline. First we consider some evidence concerning bundling in general. As an example contract bundling by the US government agencies describes the practice of consolidating multiple purchases in an effort to reduce procurement paperwork. The result of this is that fewer and larger contracts are being won by fewer and larger companies, leaving small business with a smaller share of the federal spending pie (Worsham (1997), Weinstock (2002, 2003)). The figures in the table immediately below, produced by Eagle Eye Publishing Inc. are revealing of the extent that the practice of purchase bundling has taken in recent years. This is particularly so if one considers that these figures were compiled in accordance to the Eagle Eye’s definition. This expands the government’s definition of contract bundling, (this has been recently (2003) changed as discussed below), as ”two or more contracts that had previously gone to small businesses being combined into a larger award that is no longer suitable for a small company”, by also including ”accretive” bundling, the practice of adding dissimilar tasks to existing contracts. (Govexec.com, 2003). Fiscal Year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

% of government contract dollars bundled 41 43.9 42.4 41.4 42.8 41.6 45.3 47.5 45.8 51.2

Source: Eagle Eye Publishing, located at http://www.govexec.com/top200/03top/top03s1s1.htm It is telling that under Eagle Eye’s definition 54% of procurement dollars in fiscal 2002 were awarded on bundled contracts, while under the official classification less than 1% were considered as bundled! The fact that the government considers this as a worrying and undesirable trend is evident from the recent enactment of procurement laws in 2003. For example paragraph 801 of the DoD’s Defence Authorization Act prohibits bundling of procurements above $5,000,000 unless the Senior Procurement Executive can demonstrate ”that any alternative acquisition strategies have been identified, and that the benefits of the bundled acquisition strategy significantly exceed the benefits of the other possible alternatives identified”. This translates as a move to

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buyer mixed bundling. This is further reinforced by the Senate Bill 1375 which eliminates the requirement (necessary to find bundling) that prior contracts were previously awarded to small businesses, thus subjecting more acquisitions to the requirement of considering alternative strategies relative to purchase bundling. Our analysis supports the idea that the introduction of pieces of legislation such as the above, which do not disallow bundling, but rather argue for buyer flexibility by considering both bundled and unbundled purchasing arrangements (i.e. a move from pure to mixed bundling), is correct. Bundling is cost efficient and risk reducing, and in particular mixed bundling is relative to no bundling both profit (for the price setting firm) and trade enhancing. Consequently the US government is correct to resist the voices of lobbyists acting on the behalf of small companies which argue for more drastic measures that would lead to the elimination of procurement bundling. 3 Our paper is loosely related to the literature on bundling (Adams and Yellen (1976), McAffe et. al. (1989), and Whinston (1990)). However, all these articles deal with bundling as offered by the seller. In this paper we look at bundling options as offered by the monopsonistic buyer. While based on the Dassiou and Glycopantis (2008) mathematical model of monopsonistic bundling, we now look at both the trading opportunities and profit implications of such bundling offers under alternative specific conditions of quality certainty and adverse selection. Our paper, which, as said, focuses on mixed bundling is organized as follows: Section 1.1 discusses the cost efficiency of bundling, followed by Section 1.2 on the issue of adverse selection problems resulting from quality uncertainties in the goods purchased. Section 1.3 looks at the use of mixed bundling as a means of enhancing trade and profits which is also illustrated by a simple arithmetic example. Section 1.4 discusses the implications of the existence of complementarities resulting from the bundled purchasing of two or more goods. We then proceed to Section 2 on the use of mixed bundling purchasing as both profit enhancing for the price setting monopsonist and increasing the volume of trade in both goods. In order to support these conclusions, we look at illustrative figures in various tables and diagrams. Finally Section 3 summarises the conclusions and implications of our analysis. 1.1 Buyer bundling for cost efficiency While the setting of bundled transactions may facilitate the exercise of monopoly /monopsony power, it may also simultaneously reduce costs by increasing efficiency. In the example of insurance companies mentioned before, the insurance company bundles its purchasing of costs of care and the physicians’ fees in a single payment (bundled package). By bundling, the insurance company, through its buying power over hospitals, obtains the ability to control the physician fees despite the fact that it lacks monopsony power over the physicians themselves directly (Blackstone and Fuhr, 1996). Connected to this is the argument by DeGraba (2005) that risk averse sellers, (in this case the doctors), who can distinguish between large and small customers will

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offer lower prices to the former. Monopsony power is the ”buying side” equivalent of the monopoly power and normally results in fewer units of goods or services purchased at a lower price. So, in the example of bundling physician services and hospital charges, this creates an incentive for hospitals to limit unnecessary tests and consultations as ordered by physicians, and provides a gain to the insurance company through cost containment. 1.2. Buyer bundling under adverse selection Cost containment should not be considered as the only force behind bundled purchasing. It can also be used to deal with information asymmetries that arise in markets with monopoly and/or monopsony power. If the firm is unable to determine the quality of the goods provided by a potential trading partner, the former may find it profitable to bundle its purchases. This feature introduces what we refer to in our model as partner preference (e.g. adverse selection) facing the price-setting firm. We show that by bundling its purchases and offering a premium for doing so, the firm can reduce adverse selection problems by enhancing its ability to successfully identify trading partners and increase profits. Offsets4 are an example of the way the buyer may try to manipulate the price of the total package purchases in the case of government procurement (these are discussed in length in Taylor (2000, 2002, 2003)). Offsets may take the form of purchase bundling by including an offset service in the purchase by a government of a good of service. If the government is assumed to have some degree of oligopsony power, it may use contracts that shift the risk from the buyer to the seller. An offset example is a ”turnkey” contract in which the seller is legally responsible for the initial feasibility study, the design, engineering and completion of the good or service, and does not receive full payment until all obligations concerning the product and the accompaniment services are complete. Alternatively, a ”product-in-hand” contract may be used. This is even more restrictive as in addition to the previous obligations, the seller also has the obligation to teach local employees how to maintain and troubleshoot (i.e. quality check) the product, and only after this has been completed does the seller receive full payment by the buyer. Both of the above offset contracts5 are used to deal with ”exchange hazards”. In Taylor’s terminology the term ”exchange hazards” refers to the existence of transaction costs, bounded rationality and asymmetric information faced by a buying government and it can be seen as the equivalent to the term of partner preference employed in our model below. With risk transferred almost entirely to the seller the output price will rise drastically; however our model demonstrates that such bundling, as opposed to no bundling, of the purchase of a product with a service(s) (the latter taking the form of training and education, or market services, or management services) can still be profit enhancing for the buyer. 1.3 Buyer mixed bundling as a means to enhance profits and trade

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As Taylor (2002) argues, it is better to make these offsets optional rather than mandatory (i.e. mixed bundling) as such an arrangement will enable the identification of more potential partners: Taylor gives an example of this from the housing market: If you could purchase either a completely furnished house that boasts extras (a bundle) like a swimming pool and a deck for a given price, or another house that is unfurnished with no amenities at a lower price, you may find that the cost differential is far greater than the total cost of purchasing the extras as components. However if you announce to the housing market that you will only consider bids that include bundled extras (pure bundling), real estate agents will act accordingly and this will reduce the size of the market. In other words, if buyers are so inflexible that they insist on specific package offers only, their behaviour undermines their own best interests by restricting their options (at least in the short run). In order to illustrate how mixed bundling works through a simple example, we consider a purchasing monopsonist company, P, who tries to maximise its profit and as a side-effect may increase trade. P runs a shoe factory that uses two types of machines G1 and G2 to produce alternative pairs of shoes. There are seven companies M1 - M7 producing the machines, and each machine carries a label with its cost of production; the higher this cost is, the more productive the machine is. We assume that these seven producers have the following costs of production:

M1 M2 M3 M4 M5 M6 M7

G1 0.15 0.15 0.25 0.35 0.45 0.55 0.75

G2 0.75 0.55 0.45 0.35 0.25 0.15 0.15

The monopsonist P buys machines, and the more expensively produced these machines are, the higher his productivity. Consequently, in our paper we assume that the valuations of P for the two goods are linear functions of the costs of production, as the latter reflect the quality of the goods produced. In the above example we assume that P’s valuations of Goods G1 and G2 are respectively v1 = 0.4 + 0.6c1 and v2 = 0.4 + 0.6c2 where c1 and c2 are the costs of producing the two goods. The numbers chosen above ensure that an Adams and Yellen (1976, p. 481) type of exclusion condition is always satisfied. The exclusion condition states that “no individual consumes a good if the cost of that good exceeds his reservation price”. In the case of monopsony such a condition would require that under bundling no company sells in the package a good whose cost exceeds P’s valuation of the good. This means that for the firms that sell the package u i  ci , for i = 1, 2. In this specific example

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there are obviously no companies whose cost of producing a machine exceeds P’s valuation for that machine. Consequently, there are no firms to be excluded on these grounds. However, as we have shown in Dassiou and Glycopantis (2008) even if such firms are present in our model, this condition is always satisfied by companies selling both goods bundled. Historically the prices for the two machines are identical, and are the outcome of some kind of bounded rationality calculation by the monopsonist P. First we consider the case of no bundling, where the price offered by P for each of the two goods is 0.25. As a result producers M1-M3 only sell G1, producers M5-M7 only sell G2 and M4 sells neither good. The corresponding surpluses for the seven producers are (0.1, 0.1, 0, 0, 0, 0.1, 0.1) amounting to a total surplus of 0.4, while P’s surplus is 4(0.4 + 0.6 ∗ 0.15 − 0.25)+ 2(0.4 + 0.6 ∗ 0.25 − 0.25) = 1.56. We then assume that the monopsonist decides to adopt mixed bundling. P offers a price of 0.15 for each good sold separately and a bundle price of 0.7 (involving a premium of 0.4). As a result M1 only sells G1, M7 only G2, and M2-M6 will offer to trade with P in the package of both goods. The sellers’ surpluses are all zero, while P’s surplus from the transactions is 2(0.4 + 0.6 ∗ 0.15 − 0.15) + 5(0.4 ∗ 2 + 0.6 ∗ 0.7 − 0.7) = 0.68 + 2.6 = 3.28. Finally if there was pure bundling offered by P, only 5 producers M2-M6 would trade with P in the packaged transaction (each with a 0 surplus). P’s corresponding surplus is 5(0.4 ∗ 2 + 0.6 ∗ 0.7 − 0.7) = 2.6. Hence we see that mixed bundling as compared to no bundling is profit enhancing for the price-setting P. The increase in P’s profits of 1.72 more than exceeds the eliminated surplus of the seven producers which was equal to 0.4. In other words, there is both more inclusion which leads to an increase in trade in the Goods G1 and G2, as well as more extraction of the trading partners’ surplus. Similarly mixed bundling, compared to pure bundling, is both profit and trade enhancing and hence Pareto efficient. Note that in the case of mixed bundling, each company will wish to sell the bundle if 0.70 − c1 − c2  0.15 − ci. This gives that what is required for G j to be bundled with G i is that c j  0.55, which is satisfied in the case of companies M2-M6, but not in the case of G2 of M1 and G1 of M7. As a result these two companies only trade in one good. On the other hand, for P to wish to trade in both goods, rather than say only G i, u 1 + u 2 − 0.70  u i − 0.15 ⇐⇒ u j  0.55. Combining these two gives u j  0.55  c j ,which gets us back to the exclusion condition and the fact that it is satisfied for all trading partners of P who trade in the package rather than the individual goods. Hence companies for which u i  ci, for either G1 or G2 will not bundle in the package but only in one or neither good. We will return to this in Section 2. Our paper demonstrates that mixed purchase bundling by the buyer has the advan-

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tage of attracting sellers with low costs in either or both goods, hence increasing the volume of trade in each good relative to what it would have been without bundling. As a result, trade in the goods will increase, rather than decrease as it is argued by small companies as mentioned in the section on U.S. government procurement practices discussed in the introduction. More specifically under transaction bundling the price-setting buyer firm will be willing to offer a bundled price which is higher than the sum of the two separate prices, as the option of a bundled purchase will increase his profit. The uncertainty associated with the unobservable heterogeneity in the sellers’ valuation of the two goods which are equal to the unobserved - by the price-setting firm - costs of production is reduced by taking the seller’s average willingness to sell, i.e. package purchasing reduces the dispersion of the valuations by the seller for the individual goods. This is both what the buyer is willing to pay a premium for, and also what leads to more trade occurring in both goods. Hence, by offering the opportunity of bundling its purchases the firm profitably enhances its ability to successfully identify trading partners and in doing so both enhances its profits and increases trade volume. This reason behind purchase bundling is (to the best of our knowledge) minimally, if at all, discussed in the literature. 1.4 Issues of complementarity It should be noted that this result as proved in our paper, is independent of the existence - if any - of complementarities between the two goods in the bundle. Package bidding in spectrum, (radio frequencies, etc.) auctions conducted by the Federal Communications Commission (FCC) resulted in higher prices being offered for packages as compared to individual licence bidding in the presence of strong complementarities (CRA (1998); also see Ausubel & Milgrom (2002) for a theoretical exposition of package bidding involving substitute or complement goods.) This also applies to the retail market: Lucking-Reiley (2000) gives the example of the Winebid online auction of wines, where the high bid for a collection of wines could exceed the sum of the high bids for the individual bottles in the package as wine collectors have super-additive preferences. In our model the demand for the individual goods is independent and there are no complementarities between the goods in the bundle. The argument is that just as it is profitable for a monopolist to offer mixed bundling at a bundle price which is lower than the sum of the individual prices (hence exploiting the average willingness to pay), it is equally profitable for a monopsonist to offer a bundled purchase price which is higher that the sum of the individual prices on offer (hence exploiting the average willingness to sell). This argument clearly does not rely on the existence of complementarity between the goods traded. If anything we expect that the presence of these would reinforce the desire to bundle by adding an additional, this time strategic (Nalebuff (2004), incentive for the monopsonist to bundle, especially if his position is contested by potential entrants.

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2. The Monopsony Case Model Our theoretical model is loosely related to the bundling models of Adams and Yellen (1976) and the tying model by Whinston (1990). On the other hand it is closely related to the model by McAfee et. al. (1989, henceforth MMW), that deals with mixed bundling offered by a price setting monopolist. It is based on the Dassiou and Glycopantis (2008) mathematical model on transactions bundling. For comparison purposes we follow the notation in Dassiou and Glycopantis (2008) as the present paper analyses numerical evidence that follows from that investigation. There are two goods for potential trade, G1 and G2, between a monopsonist firm P, and a firm M who can be one of a number of types as examined, in detail, below. The odd number tables in this paper are the same as the tables in Dassiou and Glycopantis (2008). They are supplemented however with corresponding tables, each considering the special case of zero adverse selection. The comparison allows us to understand the significance of the presence of randomness in determining bundling outcomes. Furthermore, we only borrowed Figures 2 and 3 from the earlier paper and our analysis is based also on another four figures. This allows us to consider in various cases the existence of local maxima of the surplus function of the monopsonist. Firm M attaches valuations q i to G i and can decide whether to sell neither of the two goods, just one good, or both goods. The vector q = (q 1 , q 2 ) defines the type of firm M and this is known to P only as probability distributions. It is assumed that q 1 and q 2 have independent uniform distributions over [0, 1].6 Firm M has a single unit supply for the goods it is selling, and P has a single unit demand for the good(s) it is buying. At every single period a single unit of each good can become available. Prices p = (p1 , p2 ), where because the good is bought by P then conventionally we take pi ≤ 0 with p = (p1 , p2 ) ≥ (−1, −1), and a possible premium e are announced by firm P. If good G i is sold by a firm in M, then q i is the cost of production to that firm. Firm P buys the good, pays −pi for it and values the good according to the type of firm he transacted with. The assumption is that P obtains utility which depends on the cost of the good, SiP = a i + b i q i where a i , b i ≥ 0. This is the valuation of the good bought (we shall return to this below); for symmetry to the values’ range of the valuations by firm M we will set that (a i + b i q i ) ∈ [0, 1]. The net surplus to P is SiP = a i + b i q i + pi . The goods sold by M are of uncertain quality. In this case we say that P has a partner preference, as its surplus function depends on the quality type of the firm with which it transacts. The term b i can be thought of as a measure of the intensity (degree) of P’s partner preference, i.e., the importance it assigns to, or the extent of his inability to uncover the features determining, the quality characteristics of the good. The uncovering of the valuation (cost) of the good by its seller is now of double importance for P. It is both relevant for assigning a price as close to that valuation as possible, thus extracting the maximum possible of the seller’s surplus, but also for determining P’s own valuation. We shall return to this point below. In the extreme case of b i = 0, there

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is no partner preference and the cost of the good is no longer used by P as a proxy to its value. On the other hand, a i can be thought as the extent of P’s ability to ascertain some of the features of the goods which he considers buying, i.e. a certain component. This comes from prior information about the good if it is of standardized format. Note that because SiP ≤ 1, in the extreme case where a i = 1, it follows that b i = 0. More generally, high values in the certain component restrict the intensity in partner preference. If a i = 1 P’s net surplus function of the good it purchases will definitely be non-negative, as it will be equal to 1 + pi. The announced prices p1 , p2 are those for the single transactions in each good , and pb = p1 + p2 − e is the price offered by P for the two purchases bundled together after applying a premium of size e . In other words, this is a model of mixed bundling in which P offers to either purchase each good separately or both goods bundled together. Given the uncertainty of the type of firm he transacts with, the objective of P is to maximise his expected surplus. The relation pb = p1 + p2 − e holds throughout and given that P is a buyer, p1 and p2 are both negative. P says I pay for the two goods −p1 and −p2 and to induce you (the seller) even further, I offer a premium of e if you sell them to me as a package. Therefore −pb = −(p1 + p2 − e ) denotes what P is prepared to pay for the package. As mentioned before, in any transaction there are four possibilities for M. Depending on its type, either it will choose to sell neither good at the set of prices p = (p1 , p2 , pb ) announced by P, and we denote by R0 (p) the area (q 1 , q 2 ) for which this is true; or it will sell G 1 only, R1 (p); or it will sell G 2 only, R2 (p); or it will sell both goods, R12 (p). Firm P is trying to induce possible transactions which will maximise his expected surplus. In a general formulation the three variables p1 , p2 and e must be chosen by P with the objective of maximising its expected surplus (p1 , p2 , e ). The maximisation of (p1 , p2 , e ) is sought in the first instance with respect to p1 , p2 under the assumption of a fixed e > 0, and then we will also look for a local maximum of (p1 , p2 , e ) with respect to all three variables and point out some of its properties. Now if e > 0, then this implies that P is offering more favourable money terms for the packaged transaction to its trading partners relative to the prices on offer for the two separate purchases. The assumption that e > 0 is a natural one to make as otherwise a seller would never sell both goods as a bundle to the monopsonist, but always offer the goods separately, since she has the option to do so within a mixed bundling framework. However, the surprising part is that choosing to offer a premium is surplus enhancing for the monopsonist as this paper proves, without the need to assume any complementarities in the monopsonist’s preferences. We will refer to the case we are considering as transaction bundling. (We have al-

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1 θ2

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O′

R1U

−p∗2 U R12

O

R2U

−p∗1

θ1

1

Unbundled monopsony

Figure 1

ready discussed transaction bundling in its benchmark format of a monopolist bundling the goods it sells in Dassiou and Glycopantis (2005), and in its linked exchange (countertrade) form in Dassiou et. al. (2004) when a buying transaction is linked to a selling transaction.) The four groups mentioned earlier are defined as: R0 (p) = {q ∈ [0, 1]2 : 0 = max(0, −q 1 − p1 , −q 2 − p2, −q 1 − q 2 − (p1 + p2 − e ))} (1) R1 (p) = {q ∈ [0, 1]2 : −q 1 − p1 = max(0, −q 1 − p1 , −q 2 − p2 , −q 1 −q 2 −(p1 + p2 −e ))}; (2) R2 (p) = {q ∈ [0, 1]2 : −q 2 − p2 = max(0, −q 1 − p1 , −q 2 − p2 , −q 1 −q 2 −(p1 + p2 −e ))}; (3) R12 (p) = {q ∈ [0, 1]2 : −q 1 −q 2 −(p1 + p2 −e ) = max(0, −q 1 − p1 , −q 2 − p2 , −q 1 −q 2 −(p1 + p2 −e ))} (4) where p = (p1 , p2 ). These four sets partition the unit square. An illustration of the trade areas in an unbundled monopsony is given in Figure 1.

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θ2

1

−p1 D

H

115

O′

F

R1B (p) W′ −p2 + ǫ

R0B (p) R1U (p)

J

W

R0U (p) M

B (p) R12

−p∗2 L

U R12 (p)

O

U

N A

B R12 (p)

E

R0B (p) R2U (p)

C

−p2

R2B (p) G 1 θ1

I K −p∗1 A′ −p1 + ǫ Mixed bundling monopsony

Unbundled prices: p∗1, p∗2; Bundled prices: p1, p2 A′W′: part of θ1 + θ2 = −p1 − p2 AW: part of θ1 + θ2 = −p1 − p2 + ǫ The superscript U denotes unbundled and B bundled regions

Figure 2

The increase in trade volume in the case of the mixed bundling monopsony relative to the case of no bundling is shown in Figure 2 and is discussed below. The expected net surplus for P can now be written down. It is equal to:

=

(p1 , p2 , e ) =

Z R1 (p)

Z

(a 1 + b 1q 1 + p1) dF(q ) +

Z

(a 2 + b 2 q 2 + p2) dF(q )+

R2 (p)

(a 1 + b 1 q 1 + a 2 + b 2 q 2 + p1 + p2 − e ) dF(q )

(5)

R12 (p)

As the expected surplus of P depends on whom it transacts with, i.e. there is partner preference; both q 1 and q 2 are dual role variables as participation constraints for both M as well as P. In the case of no bundling for example M will not sell good G i to P unless −pi ≥ q i , and P in turn will not purchase the good unless −pi ≤ a i + b i q i .

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This implies an expected net surplus of p2 )dq 2 , which is maximized for −p∗1 =

−p Z 1

(a 1 + b 1 q 2 + p1 )dq 1 +

0 a1 2−b 1

and −p∗2 =

a2 2−b 2 .

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−p Z 2

(a 2 + b 2 q 2 +

0

Theorem 1 Suppose that the premium is set exogenously. Then in the case of monopsony: Calculated at e = 0, the maximum expected net surplus of P of expression (5) increases with e , and it is also an increasing function of both the degree of partner preference and the certainty component in the value of goods purchased. The impact of the latter dominates that of the former when both change by the same amount but in opposite directions. Unless P’s ability to ascertain the quality of the goods it considers buying equals zero, bundling the purchases is surplus superior to no bundling. Proof. See the proof of Theorem 1 in Dassiou and Glycopantis (2008). We now turn our attention to the case in which e is also one of the endogenous variables to be chosen by the firm. Theorem 2 Suppose that e is set endogenously. Then in the case of monopsony: Mixed bundling is optimal (e > 0) for a 1 , a 2 > 0. The expected net surplus function (5) attains a local maximum in p1 , p2 and e . Both P’s net surplus as well as the surplus premium e are increasing functions of the certain components (a 1 , a 2 ) of the two goods as well as their degrees of partner preference (b 1 , b 2 ). For a 1 = 0 or a 2 = 0 no bundling is an optimal solution (e = 0). Proof. See the proof of Theorem 2 in Dassiou and Glycopantis (2008). Note that the values for e which allow for an interior maximum are as follows: for b 1 = b 2 = 0 ⇒ e < 0.67, for b i = 1, b j = 0 =⇒ e < 0.7071, and for b 1 = b 2 = 1 =⇒ e < 1. We have calculated the surplus maximising values of p1, p2 , e , for the full range of the value combinations of the a ’s and b ’s for which there is a local maximum. It can be seen that the net surplus reaches a peak value of = 0.5492 for a 1 = a 2 = 1, by setting a bundling premium of e = 0.4714 and optimal prices p1 = p2 = − 13 . This case is illustrated in Figure 3. If b 1 = b 2 = 0, this means the second order conditions for a local maximum combined with the fact that e is positive mean that e < 32 as mentioned above. A sufficient, though not necessary, condition for a local maximum to exist was that both a i + b i ≤ 1 and a j + b j ≤ 1.7 Figures 4 and 5 illustrate two such cases where both pairs of the parameters add up to a + b = 0.8 and a + b = 0.9 respectively. On the other hand, Figure 6 illustrates a case where a 1 + b 1 = 1, a 2 + b 2 = 1.1 and there is singularity of at e = 0.67. The numerical values also confirm that P’s expected optimal net surplus as well as

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0.8 0.6 0.4

0.2

-0.5

0

0.5

1

1.5

2 ǫ

-0.2 α1 = α2 = 1, β1 = β2 = 0 ǫ = 0.47, Σ = 0.55 p1 = p2 = −0.33

Figure 3

0.3 0.2

0.1

0.1

0

0.1

0.2

0.3

0.4

0.5

-0.1 α1 = 0.3, α2 = 0.5, β1 = 0.5, β = 0.3 ǫ = 0.18887,

P

= 0.109, p1 = −0.163, p2 = −0.264

Figure 4

0.6

0.8

1 ǫ

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0.2 0.15 0.1

0.05

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

1

0.8

-0.05 α1 = 0.3, α2 = 0.5, β1 = 0.6, β2 = 0.4, ǫ = 0.2355 P

= 0.118360, p1 = −0.167, p2 = −0.2728

Figure 5

1.2 1 0.8 0.6 0.4

0.2

-0.2

0

0.2

0.4

0.6

0.8

-0.2 α1 = α2 = 1, β1 = 0, β2 = 0.1

Figure 6

1

1.2

ǫ

ǫ

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its corresponding bundling premium e are both increasing functions of the certainty components (a 1 , a 2 ) of the two goods, as well as their degrees of partner preference (b 1 , b 2 ). However as before, if a i is increased (decreased) and b i is decreased (increased) by the same amount, P’s optimal premium, e , and the net surplus will increase (decrease), as it is shown in Tables 1 and 5 (see the Appendix). Also in the case of zero quality uncertainty for both goods e , and the net surplus are increasing functions of the a ’s, as shown in Tables 2 and 6. The absolute values of the optimum price p1 (p2 ) offered by the monopsonist is increasing (decreasing) in a 1 and b 1 and decreasing (increasing) in a 2 and b 2 . As shown in Table 3, the effect of a i dominates over that of b i when these two parameters both change by the same amount in opposite directions. Table 4 gives the corresponding figures for b 1 = b 2 = 0 and again we see that the absolute values of the optimum prices are an increasing function of the good’s own certainty parameter and a decreasing function of the other good’s a . Moreover, we confirm that for given values of a 1 and a 2 , the absolute values of the prices in Table 4 are generally smaller than the corresponding ones in Table 3. This is as expected as the effect of the certainty parameter on the price is reinforced by the effect of the uncertainty parameter, especially if the latter is large in value, relative to the case when there is zero partner preference in both goods as in Table 4. However for rather large values of a , a value of b greater than zero does not seem to contribute much to the prices offered by the monopsonist to its trading partners. In fact for a 1 = a 2 = 0.8, the absolute value of the prices when b 1 = b 2 = 0.2 is slightly less than when b 1 = b 2 = 0. Following this, it is easy to check that the net surplus is an increasing function of both p1, and p2 , and therefore this dominating effect of the certainty over the uncertainty parameter also carries over to P’s net surplus as seen in Table 5. Comparing Table 6 to Table 5 confirms that the uncertainty parameters reinforce the effect of the certainty parameters on the net surplus by increasing it. In Table 7 we calculated the percentage improvement in P’s net surplus from purchase bundling relative to no bundling for the case b 1 = 1 − a 1 and b 2 = 1 − a 2. This takes maximum values for equal values in the certain components and the degrees of partner preference between the two goods, while it decreases for diverging values between the a ’s and the b ′ s. For example, if z = a 1 = a 2 = 1 − b 2 = 1 − b 1 , the percentage improvement ranges from a maximum of 12.12% for z = 0.2, to a minimum of 9.84% for z = 1 (hence the improvement is decreasing in the degree quality certainty component z, with an obvious discontinuity for z = 0, as no bundling is optimal in this case). In other words, when the degrees of adverse selection of the two goods are identical, then it is more profitable to bundle purchase the higher this common degree, i.e. the smaller z, is. On the other hand, this surplus improvement from mixed purchase bundling becomes smaller the larger the divergence between the values of the certain

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component parameters between the two goods is. For example the improvement is only 4.5% for a i = 1 − b i = 0 and a j = 1 − b j = 1. Both of these findings are illustrated in Table 7, and they are of additional interest because they are in stark contrast to the findings in the tables below concerning the impact of bundling on the volume of trade. Finally, in Table 8 we have the corresponding relative profit increases when there is zero partner preference in both goods. The profit enhancement is again an increasing function of the values of both certainty parameters although the figures are considerably smaller than the ones observed in the previous table. To re-iterate mixed bundling is profit enhancing, and even more so if in the presence of quality uncertainty. The distinguishing characteristics of our work relative to other papers on bundling are twofold: First it considers bundling as offered by the buyer rather than the seller and second it investigates the trade implications of bundling activities as they affect the monopsonist’s trading partners. The trade volume increases in the monopsony case relative to the case of no bundling. P reduces in absolute value both of the separate prices it offers to its trading partner (|p1 | , |p2 | , Figure 2) relative to their unbundled values (|p∗1 | , |p∗2 | , Figure 1), thus reducing the incentive for a firm M to participate in R1 and R2 , while offering a premium e for the bundled transaction substantial enough to increase trade in both G 1 (RB1 + RB12 ) and G 2 (RB2 + RB12 ), relative to their unbundled sizes. It is easy to numerically check that there is always an increase in the size of trade in both goods relative to its unbundled size by substituting for the bundled and unbundled surplus maximising prices and the corresponding optimal value of e and calculating for these values8 RB1 + RB12 − RU1 − RU12 = p∗1 − p1 − e p2 +

e2 , 2

(6)

RB2 + RB12 − RU2 − RU12 = p∗2 − p2 − e p1 +

e2 , 2

(7)

and9 .

both of which were found to be always positive for the full range of possible values for a 1 and a 2 . More specifically, relations (6) and (7) imply that the improvement in the trade for G 1 is more (less) substantial the larger (smaller) a 2 , and the smaller (larger) a 1 is, while the reverse is true for G 2. The intuition behind this is obvious. Through bundling, there is more room for a dramatic improvement in the volume of trade in a good with low degree of quality certainty if its purchase is combined with a good of substantially higher quality certainty. For example, compared to no bundling the percentage increase in the trade volume of G 1 (G 2) is equal to 58.13% (4.44%) for a 1 = 1 − b 1 = 0.2, a 2 = 1 − b 2 = 1 and, symmetrically, equal to 4.44% (58.13%) for a 1 = 1 − b 1 = 1, a 2 = 1 − b 2 = 0.2. Table 9 in the Appendix shows an illustration of

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the improvement in the trade volume for G 1 for different values of a Table 10 measures the quality uncertainty in both goods.

1

121

and a 2 . Also

The findings in Table 9 (Table 10) contrast to the findings in Table 7 (Table 8), regarding P’s percentage improvement in its maximum expected surplus relative to no bundling, in two important respects: First, the size of the improvement in profits increases (decreases) as a result of a movement along the diagonal of Table 7 (Table 8) from the bottom right-hand side corner towards the top left-hand side corner, i.e. the size of the surplus improvement is an increasing function of the degree of quality uncertainty (certainty in case b 1 , b 2 = 0), when the latter is equal between the two goods purchased. In contrast Tables 9 and 10 indicate that while the improvement in the trade volume of either good is also an increasing function of the degree of quality certainty if a i = a j and b i = b j = 0, it is also a decreasing function of the degree of adverse selection when the latter is identical for the two goods and varies inversely in relation to the a ′ s. More importantly, in terms of the magnitude of the change, Table 7 indicates that the larger the difference in the degrees of quality uncertainty between two goods is, the smaller the size of the profit enhancement that the price setting firm experiences relative to no bundling. This is in stark contrast to the findings regarding the improvement in the volume of trade in a good low quality certainty, relative to the volume of trade in that same good in the case of no bundling. As predicted by relations (6) and (7), Table 9 illustrates that this is larger, the larger is the gap in the degree of quality certainty between the two bundled goods. 3. Conclusions Our paper examines the issue of the superiority of mixed bundling relative to no bundling under monopsony conditions. It is found that mixed purchase bundling in a two product market is locally optimal (profit maximising) for the price-setting monopsonistic company, unless the degree of quality certainty in the goods sold by its trading partners is extremely low. This happens because mixed purchase bundling allows the monopsonist to profitably exploit the average willingness to sell by offering the option of a purchase premium for a package sale. This is shown to be profitable without the need for the existence of any complementarities between the goods in the bundle, as the unobserved heterogeneity in the sellers’ valuations (costs) of the two goods is reduced. The paper also has important policy implications. According to conventional theory, monopsony power on the ”buying side” will normally result in fewer goods or services being purchased (as mentioned in the introduction by means of the example of the bundling of physician services and hospital charges by the buying insurance companies). However, our model argues that if it is feared that pure bundling is trade restricting as in the case of US government procurement, then the right move is a shift towards the use of mixed bundling, rather than banishing bundling altogether, as the

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former will lead to an expansion of trade through the mixed bundling of purchases as compared to the latter. More specifically, the volume of trade in goods with high quality uncertainty is significantly increased if the transactions for such goods are packaged rather than performed separately, especially if a high quality uncertainty good is packaged with one with a substantially lower degree of quality uncertainty. While this leads to a smaller improvement in the surplus of the offering the option monopsonist, purchase bundling is still profit enhancing relative to no bundling and hence will be offered by the monopsonist as an option to the selling companies. Hence the policy maker needs to worry neither about the practice of bundle purchasing (it is trade enhancing rather than restricting as long as it is of a mixed type), nor about regulating to encourage the practice relative to no bundling. Mixed bundling will be offered by a monopsonistic price setting profit maximising company as it is more profitable relative to no bundling. In the case of government procurement the legislation should simply seek to ensure that this is preferred to pure bundling as the chosen practice.

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1 Notes 1. Xeni Dasiou is a Reader in the Department of Economics, City University, Northampton Square, London ECIV OHB, UK (e-mail: [email protected]), Dionysius Glycopantis is Professor of Economics, in the Department of Economics, City University, Northampton Square, London ECIV OHB, UK (e-mail: [email protected]). All comments received on an earlier draft, especially those of Allan Muir, are greatly appreciated 2. This retail level equivalent is referred to as the ”name your price” model, as patented by Priceline.com which enables consumers to provide price requests to participating sellers, who can fill as much of the demand as they wish at price points determined by the consumers (Saloner & Spence, (2002)). 3. For a more extensive discussion on this, see Dassiou and Glycopantis (2006). 4. Offsets are non-standard contracts that governments use to extract rents from multinational corporations. Studies on the rationale for offsets suggest among other things transaction costs, price and quality. 5. Normally offsets are an instrument of reciprocal (countertrade) exchange, where the offsetting arrangements include elements of barter countertrade. In that respect they are more relevant to the earlier sister paper to this one by Dassiou et. al. (2004) on the bundling of reciprocal transactions. However, many commercial transactions involve packages of goods and services in which a given purchase is contingent on the tied purchase of other products (Hall and Markowski, 1996). 6. The case presented can be considered as the limiting case of the following situations. The unit square is divided into squares of equal area and at every corner there is a firm, with valuations given by the coordinates of that point. All valuations are taken to be equally probable. The limiting case occurs as the area of each square becomes smaller and smaller. 7. Numerical calculations looking at the value combinations of the parameters, revealed that a local maximum did not exist if after fixing the parameter values for the one good, say G i, such that a i + b i = 1, the parameter values for G j were such that a j + b j > 1.4. 8. Can be located in Figure 2 as consisting of the reduction in trade for Good 1 (relative to the area of trading for Good 1 in Figure 1) equal to the area of the rectangle with base length −p∗1 + p1 and height one, and the gains in trade given by the areas of the triangle with base −p1 + e − (−p1 ) = e and height −p2 + e − (−p2 ) = e , plus the area of the rectangle with height −p2 and base −p1 + e − (−p1) = e . 9. Can be located in Figure 2 as consisting of the reduction in trade for Good 2 (relative to the area of trading for Good 2 in Figure 1) equal to the area of the rectangle with height −p∗2 + p2 and a base length of one, and the gains in trade for Good 2 given by the

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areas of the triangle with base −p1 + e − (−p1) = e and height −p2 + e − (−p2) = e , plus the area of the rectangle with height −p2 + e − (−p2) = e and base −p1 .

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4. Appendix

Table 1: Monopsonist bundling premium values, b 1 = 1 − a 1 and b 2 = 1 − a 2 ↓ a 2 /a 1 −→ 0 0.2 0.4 0.6 0.8 1

0 0 0 0 0 0 0

0.2 0 0.20 0.25 0.27 0.28 0.29

0.4 0 0.25 0.31 0.35 0.36 0.37

0.6 0 0.27 0.35 0.39 0.41 0.42

0.8 0 0.28 0.36 0.41 0.44 0.45

(e ),

for

1 0 0.29 0.37 0.42 0.45 0.47

Table 2: Monopsonist optimal bundling premium values, ↓ a 2 /a 1 −→ 0 0.2 0.4 0.6 0.8 1

0 0 0 0 0 0 0

b 1=b 2=0 0.2 0.4 0 0 0.04 0.06 0.06 0.1 0.09 0.13 0.09 0.16 0.15 0.19

0.6 0 0.09 0.13 0.17 0.21 0.27

0.8 0 0.09 0.16 0.21 0.28 0.36

1 0 0.15 0.19 0.27 0.36 0.47

(e ),

for

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Table 3: Prices ↓ a 2 /a 1→

0 .2 .4 .6 .8 1

(p1 , p2 ) charged by the monopsonist for b 1 = 1 − a 1 and b 2 = 1 − a 2 0 .2 .4 .6 .8 (0, 0) (−.17, 0) (−.29, 0) (−.38, 0) (−.44, 0) (0, −.17) (−.14, −.14) (−.25, −.13) (−.33, −.11) (−.40, −.10) (0, −.29) (−.13, −.25) (−.22, −.22) (−.30, −.20) (−.36, −.18) (0, −.38) (−.11, −.33) (−.20, −.30) (−.27, −.27) (−.33, −.25) (0, −.44) (−.10, −.40) (−.18, −.36) (−.25, −.33) (−.31, −.31) (0, −.50) (−.09, −.45) (−.17, −.42) (−.23, −.38) (−.29, −.36)

1 (−.50, 0) (−.45, −.09) (−.42, −.17) (−.38, −.23) (−.36, −.29) (−.33, −.33)

Table 4: Prices ↓ a 2 /a 1→

0 .2 .4 .6 .8 .1

(p1 , p2 )

0 (0, 0) (0, −.1) (0, −.2) (0, −.3) (0, −.4) (0, −.5)

charged by the monopsonist for

b 1=b 2=0 .2 .4 (−.1, 0) (−.2, 0) (−.1, −.1) (−.19, −.09) (−.09, −.19) (−.19, −.19) (−.08, −.29) (−.17, −.28) (−.08, −.39) (−.16, −.38) (−.05, −.49) (−.13, −.47)

.6 (−.3, 0) (−.29, −.08) (−.28, −.17) (−.26, −.26) (−.24, −.35) (−.20, −.45)

.8 (−.4, 0) (−.39, −.08) (−.38, −.16) (−.35, −.24) (−.32, −.32) (−.27, −.40)

1 (−.5, 0) (−.49, −.05) (−.47, −.13) (−.45, −.20) (−.40, −.27) (−.33, −.33)

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Table 5: Monopsonist’s maximum net surplus for b 1 = 1 − a 1 and b 2 = 1 − a 2 a j /a i 0 0.2 0.4 0.6 0.8 1

0 0 0.02 0.06 0.11 0.18 0.25

0.2 0.02 0.04 0.08 0.14 0.20 0.28

0.4 0.06 0.08 0.13 0.19 0.26 0.33

0.6 0.11 0.14 0.19 0.25 0.32 0.40

0.8 0.18 0.20 0.26 0.32 0.39 0.47

1 0.25 0.28 0.33 0.40 0.47 0.55

Table 6: Monopsonist’s maximum net surplus for b 1 = b 2 = 0 a j /a i 0 0.2 0.4 0.6 0.8 1

0 0 0.01 0.04 0.09 0.16 0.25

0.2 0.01 0.02 0.05 0.10 0.17 0.26

0.4 0.04 0.05 0.08 0.13 0.21 0.30

0.6 0.09 0.10 0.13 0.19 0.26 0.36

0.8 0.16 0.17 0.21 0.26 0.34 0.44

1 0.25 0.26 0.30 0.36 0.44 0.55

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Table 7: Monopsonist’s % improvement of maximum net surplus relative to no bundling for b 1 = 1 − a 1 and b 2 = 1 − a 2 a j /a i 0.2 0.4 0.6 0.8 1

0.2 12.12 8.11 7.00 5.67 4.49

0.4 8.11 11.40 10.60 9.40 8.10

0.6 7.00 10.60 11.11 10.70 9.40

0.8 5.67 9.40 10.70 10.40 10.05

1 4.49 8.10 9.40 10.05 9.84

Table 8: Monopsonist’s % improvement of maximum net surplus relative to no bundling for b 1 = b 2 = 0 a j /a 0.2 0.4 0.6 0.8 1

i

0.2 1.01 1.20 1.20 1.06 0.85

0.4 1.20 2.50 3.00 3.13 3.17

0.6 1.20 3.00 4.28 5.04 5.56

0.8 1.06 3.13 5.04 6.56 7.78

1 0.85 3.17 5.56 7.78 9.84

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Table 9: % improvement in trade volume for G1 relative to no bundling for b 1 = 1 − a 1 and b 2 = 1 − a 2 ↓ a 2 /a 1 −→ 0.2 0.4 0.6 0.8 1

0.2 15.14 31.25 43.03 51.46 58.13

0.4 9.38 19.27 27.62 32.79 36.79

0.6 6.78 14.61 20.82 25.27 28.35

0.8 5.31 11.46 16.78 20.86 23.47

1 4.44 9.58 14.08 17.59 20.26

Table 10: % improvement in trade volume for G1 relative to no bundling for b 1 = b 2 = 0 ↓ a 2 /a 1 −→ 0.2 0.4 0.6 0.8 1

0.2 1.66 5.24 11.84 16.31 32.83

0.4 1.17 4.13 8.29 13.77 20.52

0.6 1.10 3.54 7.16 11.91 18.88

0.8 0.88 3.31 6.71 11.93 18.73

1 1.15 3.26 7.16 12.79 20.26

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5. References Adams W. J. and Yellen, J. L., (1976). “Commodity bundling and the burden of monopoly’, Quarterly Journal of Economics, Vol. 90, pp. 475-498. Ausubel, L. M. and Milgrom, P. R., (2002). “Ascending auctions with package bidding”, Frontiers of Theoretical Economics, Vol. 1, pp. 1-42. Blackstone, E. A. and Fuhr J. P., Jr., (1996), “Monopsony power, bundling and cost containment”, Widener Law Symposium, J. 375. Charles Rivers Associates Incorporated & Market Design, Inc., (1998). “Report 2: Simultaneous ascending auctions with package bidding”, submitted to Federal Communications Commission, CRA No. 1351-00. Dassiou, X. and Glycopantis, D., (2005), ‘E-Commerce and the role of price discrimination using transactions bundling”, Essays in honour of Professor S.A. Sarantides, Vol. B, The University of Piraeus, Greece. Dassiou, X. and Glycopantis, D., (2006), “The economic theory of price discrimination via transactions bundling: An assessment of the policy implications”, Review of Law and Economics, Vol. 2: No. 2, Article 5. http://www.bepress.com/rle/vol2/iss2/art5). Dassiou, X. and Glycopantis, D., (2008). “Price discrimination through transactions bundling: The case of monopsonist“, Journal of Mathematical Economics, Vol. 44, 672-681. Dassiou, X., Chong, C. J., and Maldoom, D., (2004), “Trade and linked exchange; Price discrimination through transaction bundling”, Topics in Theoretical Economics, vol. 4: No.1, Article 3.(http://www.bepress.com/bejte/topics/vol4/iss1/art3). Hall, P. and Markowski, S., (1996), “Some lessons from the Australian defence offsets experience”, Defence Analysis, Vol. 12, No. 3, pp.289-314. DeGraba, P. J., (2005), “Quantity discounts from risk averse sellers”, Working paper No. 276, Bureau of Economics, Federal Trade Commision, Washington, DC 20580. Lucking-Reiley, D., (2000), “Auctions on the internet: What’s being auctioned, and how?”, Journal of Industrial Economics, Vol. 48, pp.227-252. McAfee, R. P., McMillan, J. and Whinston, M. D., (1989), “Multiproduct monopoly, commodity bundling, and correlation of values”, Quarterly Journal of Economics, Vol. 114, pp. 371-383. Nalebuff, B., (2004), “Bundling as an entry barrier”, Quarterly Journal of Economics, Vol. 119, pp. 159-187. Saloner G. and Spence A. M., (2002), Creating and capturing value: perspectives and cases on electronic commerce, Jon Wiley & Sons, Inc. Taylor, T. K., (2000), “A transaction cost approach to offsets in government procurement”, mimeo, Department of Economics, University of Richmond, Virginia, USA. Taylor, T. K., (September 2002), “Using offsets in procurement as an economic development strategy”, Working Paper, Alfred University, New York.

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Taylor, T. K., (2003), “Modeling offset policy in government procurement”, Journal of Policy Modeling, Vol. 25, pp. 985-998. Weinstock, M., (30th October 2002), “OMB orders agencies to reduce contract bundling”, Government Executive Magazine. (http://www.govexec.com/dailyfed/1002/103002w1.htm). Weinstock, M., (2003), “Breaking up bundled contracts”, Government Executive, Vol. 35, Issue 6. Whinston, M., (1990), “Tying, foreclosure and exclusion”, American Economic Review, Vol. 80, 837-857. Worsham, J., (1997), “Bundles too big for small firms’, Nation’s Buiness, Vol. 85, Issue 12.