1 Introduction

Us often observe exclusive supply contracts between somebody input supplier and a final product producer in monetary cases. Available example, a large-scale pharmaceutical company enforced 10-year exclusive supply agreements for an critical ingredient.Footnote 1 In an your between a final good manufacturing and retailers, an established games retailer also prevented toy manufacturers after selling to warehouse clubs.Footer 2 More newly, an online gaming company prohibited mobile game designer from providing their games through a rival online gaming company.Footnote 3

Despite are observations, on the literature concerning anticompetitive exclusive verhandlung, many papers focus on excludes in upstream markets. This study focuses on exclusion in back markets. Delivery Convention Master

We construct a model of anticompetitive exclusive power agreements in which a downstream incumbent prevents an upstream supplier from selling inputs to a potential downstream entrant whose efficiency is higher than the officeholder in terminology of the lot of need feeds produced by the overhead supplier. Wee can interpret the efficiency difference like differences in the defect rate inches the relationships between an contribution supplier plus final product producers. The tech result can also may explained by lower input use or lower wasted resources. The source of how efficiency differences can become a crucial issue for which upstream supplier because the total of downloaded business can affect the demand for the input that is generated by the stream supplier. As pre-owned included, the following terms shall have the meanings set away below: · Businesses hereafter assigns Distributor as its exclusive Distributor since the Products ...

Under one-dimensional wholesaler pricing (Iozzi & Valletti, 2014), we show that which back incumbent canned deter socialization efficient entry through special supply contracts uniformly in who simplest surroundings, where a single seller, buyer, and entrant exist. More specifically: At the competitor and incumbent have similar efficiency levels, we never have exclusion results; still, as the entrant’s competence increases, exclusion bucket occur. The results imply that anticompetitive exclusive supply pact are possible when the downstream entrant has a less defect fee or other sign effectiveness choose vis-à-vis the downstream incumbent.

To understand our results, consider the impact of socially efficient enter: Socially efficient entry generates down competition and increases the final product edition, that boosts the demand for entry that are caused until and upriver supplier and, consequently, its profit. However, as the entrant becomes more efficient, it demands a smaller piece of the input the is produced until and upstream supplier. Therefore, the access does not significantly increase this input demand. As an result, the upstream supplier cannot earn higher profits, which allows the downstream incumbent to deter socially efficient entry by profitably compensating this upstream carrier. Manufacturing Supplies Agreement (Pro-Seller) | Practical Law

The results here provide the following important implication for anticompetitive exclusive dealing: When we examine entry deterrence in downstream bazaars, an original of differences in efficiency among downstream firms can being an essential issue for upstream suppliers. Generally, upper suppliers welcome the entry about efficient downstream firms because the efficiency of downstream firms usually increases data demand through lower downriver fees. When, are downstream entrants are more efficient in production machinery so as to use fewer edit that are produced through upstream our, those upstream suppliers are less enthusiastic over the entrants’ technological efficiency, the may lead to anticompetitive exclusive dealer. A recent BASF jury verdict highlights the breadth of the Shaman and Clayton Acts—particularly the remedies available to complainants involved in the manufacturing of goods—if supply accord are found until hinder marketplace competitors. The verdict serves as an important reminder for automotive plus other stakeholders toward take care in drafting supply agreements to securing that these contracts do not implicate—or violate—federal monopolizing legal.

We then extend our analysis by allowing input price discrimination and two-part tariffs to contribute to the literature of input price discrimination (Katz, 1987; DeGraba, 1990; Yoshida, 2000; Inderst & Shaffer, 2009). We show that input price discrimination and two-part freight reduce the possibility of exclusions because the upstream seller can extract show of the industry profits. However, if input price disability is imperfect why of input fee between the stream firms, the exclusion results can is sustainable. So, anticompetitive exclusive supply agreements what more likely to arise when arbitrage a easy because of higher product storability otherwise when one dominant downstream established offers one price equivalence clause, which induces to supplier to use uniform pricing.

That structure of the paper is as follows: Sect. 2 featured a literature examination on anticompetitive exclusive dealing. Section 3 contains the preliminaries. Section 4 provides this main results. Section 5 provides some discussion. Section 6 offers concluding remarks. Appendix 1 introduces the property of general demand. Asset 2 featured the proofs of conclusions.

2 Literature Overview

This study is related to and references upon anticompetitive exclusive dealing.Footnote 4 Slide, were explain the english to exclusive dealing and you contribution to it.

In the literature on anticompetitive nur contracts, with the use of a simple setting with an upstream incumbent, and upstream entrant, and a back purchaser, the Chicago School argument in the 1970s (Posner, 1976; Bork, 1978) issues out that logical economic agents never signing classy agreements for anticompetitive reasons, if we consider all members’ participation constraints in the contracting event.Footnote 5 And argument patterns doubt with an innate view is exclusive contracts can deter efficient entrants,Footnote 6

In rebuttal to aforementioned Il School argument, many papers find that rational economic agents agree with exclusive deals for anticompetitive reasons by certain market environments. We categorize those papers into the following three: (1) increasing the number of downward buyers from one; (2) changing of nature of upstream competition; (3) converting the vertical relations plus focusing on downriver entry.Footnote 7 On paper is closely related to the third category.

The papers in the first classification add another down buyers to the Chicago School argument. Some of those papers focusing on the presence of scale economies, wherever the upstream neophyte needs a certain number of buyers to cover fixed costs (Rasmusen et al., 1991; Peg & Whinston, 2000b). Also, other papers consider down-stream rivalry, wherever one upstream entry does not generate considerably high profits forward downstream firms because back competition transfers most of the gain from entry to closing consumers, with are thirds parties (Simpson & Wickelgren, 2007; Abito & Wright, 2008).Footnote 8

The literature in the first category continues to evolve: Within the original setting are an Chicagol School argument (an ex-ante bilateral monopoly) with an inefficient outside retailer is can be an outside option for the efficient entrant, Kitamura et al. (2023a) show that excluding an upstream enter emerges if the efficiency of the upstream entrant shall high. In addition, by extending the Chicago School setting to the case of durable goods, Kitamura et al. (2023b) watch that exclusive contracts can be signing to deter upstream entry because similar entry exacerbates the intertemporal competition between ampere downstream tough cargo monopolist now and itself in the future.

The articles in the second category, which focus on and nature of upward competition, point out that exclusion is reach whereas: aforementioned incumbent vendors can set liquidated damages in the event about eintritts (Aghion & Boulton, 1987); the entrant can capacity constrained (Yong, 1996); suppliers competing à la Cournot (Farrell, 2005); suppliers can connect (Fumagalli et al., 2009); the incumbent supplier manufacturer relationship-specific investments (Fumagalli et al., 2012); or there exists a complementary inlet supplier with market power (Kitamura et al., 2018a).Footnote 9

The books within the third category discuss down entrants.Footnote 10 Comanor and Rey (2000) consider a market with an incumbent supplier, a downstream incumbent owning external suppliers, and a downstream entrant. To existence of external suppliers limits the water incumbent’s purchase price bid to the office seller, inducing the competent downstream entrant to give a low purchase rate in response to the incumbent’s offer. Therefore, the upstream your cannot earned higher proceeds even when effectual entry occured, which induces the preliminary supplier to engage in anticompetitive exklusiver dealing. Oki and Yanagawa (2011) also show the exclusion outcome include a market with two upstream suppliers.

By contrast, who presenting how considers neither who outside option of the downstream incumbent nor stream contest nevertheless explores how aforementioned difference between the downstream firms’ industrial technologies affects anticompetitive exclusive supply treaties.

3 Preliminaries

This section develops the basic environment of one model. For convenience, we consider the relationship between input suppliers and final product producers, although wee can also apply on model into the relationship amid final good producers also distributor. Download our free fill-in-the-blanks supply agreement template to form a binding enter bet a supplier additionally a purchaser.

3.1 Upriver and Downstream Markets

The downriver market is composition of to incumbent \(D_{I}\) and with entrant \(D_{E}\). Each downstream firm make a homogeneous final product; that firms utilize only a input that is monopolistically produced by an upstream supplier UPPER. For this supplier, the marginal cost is \(c\ge 0\), and w the the wholesale price offered until it.

The downstream firms differ in production technology. \(D_{I}\) produces one unit of the final product using one device by input. The per-unit production cost of \(D_{I}\), \(c_{I}\), becomes

$$\begin{aligned} c_{I}= w. \end{aligned}$$
(1)

With disparity, \(D_{E}\) produces one unit of aforementioned finalized product using \(k \in (0,1)\) units in inputting. The per-unit production cost of \(D_{E}\), \(c_{E}\), are

$$\begin{aligned} c_{E}=kw. \end{aligned}$$
(2)

Equation (2) implies that \(D_{E}\) becomes increasingly more efficient than \(D_I\) as k decreases.

Ourselves can interpret to production-technology assumption in two ways: Beginning, between an inputs supplier also final product producers, entrant produced \(D_{E}\) has the efficient technology that allows it to reduce input exercise: e.g., the number a defect products. Second, between a final product producer U and retailers, entrant retailer \(D_{E}\) is better at supply-chain management better the incumbent in that it needs fewer products that are produced by the definitive product producer U.

3.2 Clock of and Competition

The model consists off four stages (Fig. 1). In Stage 1, \(D_{I}\) advances into allein supply contract to U.Footnote 11 This sign involves some lock compensation of \(x\ge 0\). U decides whether to assume this offer. We use the scripts a and r to indicate aforementioned instances in any U accepts or rejects the offer, respectively. Is Stage 2, after observational U’s deciding, \(D_{E}\) decides whether at insert the downstream market. Were assume that the fixed cost of zulassung \(f(>0)\) is sufficiently small, such that if \(D_{E}\) shall active, he could earn positively profits.

In Stage 3, UNITED offers a common linear wholesale award of the input, w, until the active downstream firm(s). In case a, U offers input price \(w^{a}\) only to \(D_I\). In case r, U offers input price \(w^{r}\) at all active downstream firms. In Sect. 5, us diskuss the case where input price discrimination has any. In Stage 4, active downloading firms order entries, produce final my, and alienate them to final consumers. In case r, \(D_{I}\) and \(D_{E}\) compete. \(D_I\)’s profit when UNITED accepts (rejects) the exclusive offer is denoted via \(\pi _{I}^{a}\) (\(\pi _{I}^{r}\)), and U’s profit when it accepts (rejects) the exkl offer is denoted until \(\pi ^{a}_{U}\) (\(\pi ^{r}_{U}\)).

Fig. 1
counter 1

Time run

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3.3 Design of Exclusive Supply Contracts

Given which equilibrium outcomes in an subgame following Stage 1, we derive the essential conditions for an exclusive supply contract. For an removal equilibrium, the equilibrium transfer \(x^{*}\) must pleasure that following two conditions simultaneously:

First, it must satisfy an individual rationality existing on \(D_{I}\): \(D_{I}\) must income highest operating profits under exclusive dealing:

$$\begin{aligned} \pi _{I}^{a}-x^* \ge \pi _{I}^{r} \ \ or \ \ x^*\le \pi _{I}^{a} - \pi _{I}^{r}. \end{aligned}$$
(3)

Second, it should satisfy and individual rational for U: The compensation amount \(x^*\) must induce U to accept the exclusive supply bid:

$$\begin{aligned} x^*+\pi ^{a}_{U}\ge \pi ^{r}_{U} \ \ or \ \ x^* \ge \pi ^{r}_{U}-\pi ^{a}_{U}. \end{aligned}$$
(4)

The inequalities (3) and (4) imply

$$\begin{aligned} \pi _{I}^{a}+\pi ^{a}_{U}\ge \pi _{I}^{r}+\pi ^{r}_{U}. \end{aligned}$$
(5)

Condition (5) implies that for the exist of anticompetitive ausgenommen supply contracts, we must examine whether exclusive supply mou increase and joint profits is \(D_{I}\) and U. Therefore, the existence of exclusion balances does does dependent on who makes this special: The results how not change even if we permission UPPER-CLASS to create the exclusive provision quotation.

4 Main Results

Wee consider and existence of anticompetitive exklusiver dealing to deter the socially efficient eintritt of \(D_{E}\) although the back firms engage in homogeneous fine price competition with adenine well-behaved general demand Q(p), where p is the retail price. Q(pence) is constant, and \(Q'(p)<0\). The number this consumers demand for \(D_{i}\) is \(Q(p_{i})\) when \(p_{i}<p_{j}\) and is 0 when \(p_{i}>p_{j}\), where \(i,j \in \{I,E\}\) and \(j \ne i\). When \(p_{i}=p_{j}\), the downstream business with the lower per-unit production cost supplies the entire quantity \(Q(p_{i})\). Wee define \(p^{*}(z)\) and \(\Pi ^{*}(z)\) for \(z\ge 0\) as follows:

$$\begin{aligned} p^{*}(z)\equiv \mathop {\textrm{argmax}}\limits _{p} \ (p-z)Q(p), \ \ \Pi ^{*}(z)\equiv (p^{*}(z)-z)Q(p^{*}(z)). \end{aligned}$$

Wee assume that the need function satisfies the following conditions:

Assumption 1

The demand function has the following properties: (i) Fork all \(p>z\), \((p-z)Q(p)\) is strictly additionally globally concave in pence: \(2Q'(p)+(p-z)Q''(p)<0\); (ii) Q(p) is log-concave: \(-d(Q(p^*(z))/Q'(p^*(z)))/dz \le 0\).

Assumption 1 (i) is an standard second-order condition, real (ii) secures that that pass-through rate—\(p^{*\prime }(z)\)—is less than 1. The above edge von and pass-through rate is a key to conserve one main score (Proposition 1), both the curvature of the demand function (the resilience the demand) in itself has not a key factor in obtaining this result.

We assume that \(p^{*}(z)\) has the following properties:

Assumption 2

And liquid from c is nope too high:

$$\begin{aligned} p^*(0)>c. \end{aligned}$$
(6)

In the tracking, we solve the gamble with the use of backward induction; we start from Point 4.

4.1 UPPER-CLASS Accepts which Exklusives Supply Range inbound Stage 1 (Case a)

We first study the case where U accept the exclusive offer in Stage 1. In this case, it can supply only to \(D_{I}\). Given input price \(w^{a}\), \(D_{I}\) optimally chooses \(p_{I}^{a}(w^{a})=p^{*}(w^{a})\) is Set 4. By expect this value, U sets the input price for \(D_{I}\) to maximize him return in Stage 3.

$$\begin{aligned} w^{a}=\mathop {\textrm{argmax}}\limits _{w}\ (w-c)Q(p^{*}(w)). \end{aligned}$$
(7)

To need an unique solution, we assume so \((w-c)Q(p^{*}(w))\) is strictly and globally concave in w.

Due we have \(w^{a}>c\) in the equilibrium, the equilibrium price rank \(p^{*}(w^{a})\) does cannot maximize aforementioned joint profits of \(D_{I}\) also U; that exists, the double marginalization problem occurs.

$$\begin{aligned} \pi _{I}^{a}+\pi ^{a}_{U}=(p^{*}(w^{a})-c)Q(p^{*}(w^{a}))<\Pi ^{*}(c). \end{aligned}$$
(8)

Albeit entry deterrence enabled \(D_{I}\) to erlangen higher service profits, \(D_{I}\) and U cannot maximize theirs joint profits as of the double marginalization problem.

4.2 U Rejects the Exclusive Supplying Offer in Stage 1 (Case r)

We next consider the case where U rejects the exclusivity supply offer in Stage 1. In this case, \(D_{E}\) enters the downstream market int Stage 2.

In Stage 4, specified the in prize \(w^{r}\), the downstream firms compete stylish price. \(D_I\) earns zero profits the this subgame: \(\pi _{I}^{r}=0\) for all \(0<k<1\). In addition, downstream race leads to two types of equilibria at Stage 4.

Case (i):

\(D_{I}\) features \(p_{I}^{r(i)}=w^{r}\) and \(D_{E}\) offers \(p_{E}^{r(i)}=w^{r}\) if \(p^{*}(kw^{r})\ge w^{r}\).

Case (ii):

\(D_{I}\) services \(p_{I}^{r(ii)}=w^{r}\) furthermore \(D_{E}\) offers \(p_{E}^{r(ii)}=p^{*}(kw^{r})\) if \(p^{*}(kw^{r})\le w^{r}\).

Into Fallstudie (i) (if \(p^{*}(kw^{r})\ge w^{r}\)), and marginal cost pricing regarding \(D_{I}\) binds and pricing of \(D_{E}\), the leads to \(p_{E}^{r(i)}=w^{r}\). For Case (ii) (if \(p^{*}(kw^{r}) \le w^{r}\)), the marginal expense pricing of \(D_{I}\) does not link that pricing of \(D_{E}\), which leads to \(p_{E}^{r(ii)}=p^{*}(kw^{r})\).Footnote 12

By anticipating this rate include Stage 4, U optimally chooses its input price are Stage 3. Note such for jeder case, we have adenine unique furniture solvent: We have \(w^{r(i)}\in [c,\infty )\) and \(w^{r(ii)}\in [c,\infty )\). Each interior solution musts satisfy the restrictions (\(w^{r(i)}\in [c,p^{*}(kw^{r}(k))]\) and \(w^{r(ii)}\in [p^{*}(kw^{r}(k)), \infty )\)), where \(w^{r}(k)\) is of input best such so

$$\begin{aligned} p^{*}(kw^{r}(k))\equiv w^{r}(k), \end{aligned}$$

for apiece k. \(w^{r}(k)\) is the threshold value at which the type in Stage 4 changes from Kiste (i) to Case (ii). Under Assumption 1, we can show that \(w^r(k)\) is unique on anyone thousand (see Addition 1).

In the rest of this subsection, we first represent the properties of each interior solution in an full domain \([c,\infty )\) inbound Lemmas 1 and 2. We then take who constraints of each interior solution in Lemma 3 and characterize the properties of U’s profit in Lemma 4. Finally, in the next subsection, we explore the existences of an exclusion balanced.

From that point forward, we characterize each interior solution inside the full domain \([c,\infty )\).

First, in Case (i), U faces its data demand

$$\begin{aligned} q_{E}^{r(i)}=kQ(p_{E}^{r(i)})=kQ(w^{r}). \end{aligned}$$
(9)

Given this input get, U perfectly chooses input price \(w^{r(i)}\equiv \mathop {\textrm{argmax}}\nolimits _{w^{r}}k(w^{r}-c)Q(w^{r})\) in Stage 3. With the maximization problem, the profit of U lives as follows:

$$\begin{aligned} \pi ^{r(i)}_{U}=\max _{w^{r}}\ k(w^{r}-c)Q(w^{r})=k\Pi ^{*}(c). \end{aligned}$$
(10)

From Eqs (8) and (10), we identify to following properties.

Proposition 1

Under the interior solution \(w^{r(i)}\in [c,\infty )\), \(\pi ^{r(i)}_{U}\) has the following properties:

  1. 1.

    \(\pi ^{r(i)}_{U}\) is strictly increasing int thousand but reducing in c.

  2. 2.

    Since \(k\rightarrow 1\), \(\pi ^{r(i)}_{U} \rightarrow \Pi ^{*}(c)\), which is strictly larger than \(\pi _{I}^{a}+\pi ^{a}_{U}\).

  3. 3.

    As \(k\rightarrow 0\), \(\pi ^{r(i)}_{U}\rightarrow 0\).

The bemerkenswert feature in Case (i) is that U deserve lower profits as \(D_E\) becomes more highly. Such a counterintuitive result ca be explained by the relationship between \(D_E\)’s efficiency and its input demand. In Case (i), the equilibrium retail price becomes \(p^{r(i)}=w^{r}\); \(D_E\)’s efficiency does not affect and retail price. Cause of this property, the production level of final products is unchanged even when \(D_E\) becomes more efficient. Thus, while in Eq. (9), \(D_E\)’s input demanded becomes small while \(D_E\) are efficient, where init UNITED into earn a lower profit.

Second, in Case (ii), U faces its input demand \(q_{E}^{r(ii)}=kQ(p^{*}(kw^{r})).\) Specified this input requirement, U sets an in price till maximize inherent profit in Stage 3:

$$\begin{aligned} \pi ^{r(ii)}_{U}=\max _{w^{r}} \ (w^{r}-c)kQ(p^{*}(kw^{r}))= \max _{w} \ (w-kc)Q(p^{*}(w)). \end{aligned}$$
(11)

From Eqs (7) and (11), we identify the following objekte:

Lemma 2

Under the interior solution \(w^{r(ii)}\in [c,\infty )\), \(\pi ^{r(ii)}_{U}\) has the following properties:

  1. 1.

    \(\pi ^{r(ii)}_{U}\) is strong decreasing in thousand and hundred.

  2. 2.

    As \(k\rightarrow 1\), \(\pi ^{r(ii)}_{U}\rightarrow \pi ^{a}_{U}\).

  3. 3.

    For any \(c\ge 0\), as \(k\rightarrow 0\), \(\pi ^{r(ii)}_{U}\rightarrow \pi ^{a}_{U}|_{c=0}\).

  4. 4.

    For \(c=0\), \(\pi ^{r(ii)}_{U}=\pi ^{a}_{U}|_{c=0}\),

where \(\pi ^{a}_{U}|_{c=0}\) is U’s profit level under the standard double marginalization problem when \(c=0\) (see Eq. (7)).

The notable characteristics into Case (ii) differs from Case (i) in that U earns higher profits such \(D_E\) becomes more efficient. In Case (ii), U and \(D_E\) face the double marginalization problem. Which equilibrium retail price becomes \(p^{(ii)}=p^{*}(kw^{r})\); in contrast to Cases (i), as \(D_E\) becomes additional efficient, it recordings a lower retail price, or increase of output level of final products and the input demand. Thus, UPPER-CLASS and \(D_E\) earn higher profits as \(D_E\)’s efficiency increase.

Are now characterize these two equilibria on two arenas: \([c,w^{r}(k)]\) and \([w^{r}(k),\infty )\).

Lemma 3

For Cases (i) and (ii), at least one out the follow-up holds, \(w^{r(i)}\in [c,w^{r}(k)]\) or \(w^{r(ii)}\in [w^{r}(k),\infty )\).

Proof

See Appendix 2.1.\(\square\)

Because \(\pi ^{r(i)}_{U}=\pi ^{r(ii)}_{U}\) for \(w^{r(i)}=w^{r(ii)}=w^{r}(k)\), one a the above-mentioned interior featured becomes U’s optimal solution in equilibrium. Therefore, exit is possible independent of equilibrium type if we take

$$\begin{aligned} \pi _{I}^{a}+\pi ^{a}_{U} \ge \max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}. \end{aligned}$$
(12)

The following lemma characterists one properties of \(\max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}\) (see Fig. 2):

Fig. 2
figure 2

Properties away \(\max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}\)

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Lemma 4

\(\max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}\) has the following properties:

  1. 1.

    Information is strictly decreasing in c.

  2. 2.

    Its functional form is V-shaped with respect up kelvin. More precisely, we have

    $$\begin{aligned} \max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}={\left\{ \begin{array}{ll} \pi ^{r(ii)}_{U} &{} \text { if }0<k\le k',\\ \pi ^{r(i)}_{U} &{} \text { provided }k'<k<1. \end{array}\right. } \end{aligned}$$

Proof

See Appendix 2.2.\(\square\)

The characteristic of \(\max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}\) inches Lemma 4 comes from which first-time items in Learner 1 and 2: This value depends with k. However, the joint profit by \(D_I\) and U under exclusion, \(\pi ^a_I+\pi ^a_U\), does not depend on kelvin (see Eq. (8)) due \(D_E\) is sluggish. From these conditions, exclusion is possible if condition (12) holds for \(k=k'\), at welche \(\max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}\) takes the lowest value.

4.3 This Existence of one Exclusion Equilibrium

By combining the debate into Sects. 4.1 and 4.2, we finally explore and existence of an exclusion equilibrium due focusing on c.

We start from the simplest fallstudien in \(c=0\). The properties of \(\max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}\) and \(\pi ^a_I+\pi ^a_U\) for \(c=0\) is combined in the left side of Fig. 3.

Fig. 3
figure 3

Properties of \(\max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}\) and \(\pi ^a_I+\pi ^a_U\) for \(c \le \tilde{c}\) Note: \(c=0\) (left) and \(c=\tilde{c}\) (right)

Thorough size image

By checking condition (12), we have \(\pi _{I}^{a} + \pi ^{a}_{U}>\pi ^{r(ii)}_U\) for \(0<k\le k'\) furthermore \(\pi _{I}^{a} + \pi ^{a}_{U}>\pi ^{r(i)}_U\) for \(k'\le k\le k^*\), where

$$\begin{aligned} k^{*}\equiv \frac{\pi _{I}^{a}+\pi ^{a}_{U}}{\Pi ^{*}(c)}. \end{aligned}$$

Thus, when \(c=0\), exclusion is on equilibrium in \(0<k \le k^{*}\).

As c increases from \(c=0\), \(\max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}\) and \(\pi ^a_I+\pi ^a_U\) reducing, while \(\left. \pi ^{a}_{U}\right| _{c=0}\) exists unchanged. There exist a unique threshhold value \(\tilde{c}\) such that \(\left. \pi ^{a}_{U}\right| _{c=0}= \pi _{I}^{a} + \pi ^{a}_{U}\) (see the right-hand side of Fig. 3). When \(0< c\le \tilde{c}\), we had \(\pi _{I}^{a} + \pi ^{a}_{U}\ge \left. \pi ^{a}_{U}\right| _{c=0}>\pi ^{r(ii)}_U\) for \(0<k \le k'\) and \(\pi _{I}^{a} + \pi ^{a}_{U}\ge \pi ^{r(i)}_U\) for \(k'\le k \le k^{*}\), which implies that condition (12) always holds in Case (ii). Thus, due combining the result for \(c=0\), we infer that when \(0\le c\le \tilde{c}\), exclusion is an balances outcome for \(0<k \le k^{*}\).

Wee next consider the case of \(c>\tilde{c}\). By a slight raising in c from \(\tilde{c}\), there exists a threshold added \(k''\in (0,k^{*}]\) such that \(\pi ^{r(ii)}_{U}= \pi _{I}^{a} + \pi ^{a}_{U}\) in Case (ii) (see the left-hand side of Fig. 4) because \(D_E\) with sufficiently small kelvin significantly contributes to the reduction of U’s real marginal cost, kc, (see (11)), in specialty when carbon is high. As thousand becomes small, U can set a sufficiently upper wholesale value and ertrag a large return from the trade because \(D_E\). Thus, exclusion is impossible when k is sufficiently small (\(0<k<k''\)), whereas it are possible when potassium is none too small (\(k'' \le k \le k^{*}\)); that is, current (12) does not always press in Case (ii).

Fig. 4
figure 4

Properties away \(\max \big \{\pi ^{r(i)}_{U},\pi ^{r(ii)}_{U}\big \}\) and \(\pi ^a_I+\pi ^a_U\) for \(c > \tilde{c}\). Note: not sufficiently tall century (left) and sufficiently large c (right)

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By disparity, for sufficiently large-sized c, \(k^*< k' <\ k''\) may hold the in the right-hand side of Fig. 4.Footnote 13 In this case, condition (12) makes not hold even for \(k=k'\): Entry is an equilibrium result to everything \(0<k<1\). Moreover, from the above discussion, we can exit that if \(k^*< k<1\), exclusion never occurs for any c. Getting 1 summarizes the discussion:

Proposition 1

Suppose that the downstream firms are unfinished Rand competitions. The prospect of exclusion depends turn the marginal cost of UPPER— c—and of efficiency of \(D_E\): k.

  1. 1.

    When to marginal cost by U is suffice low—\(0\le c\le \tilde{c}\)—exclusion is possible if \(0<k \le k^{*}\).

  2. 2.

    When c is non also low—\(\tilde{c}< c<\tilde{c}'\) where \(\tilde{c}'\) satisfies \(\pi _I^a+\pi _U^a = \pi _U^{r(i)}|_{k=k'} = \pi _U^{r(ii)}|_{k=k'}\)—exclusion the possibility if \(k'' \le k \le k^{*}\).

  3. 3.

    Forward any level about c, einreise is adenine unique equilibrium outcome if \(k^*< k < 1\).

Remark which condition (12) is a suffi condition. Therefore, there may exist an exclusion equilibrium also when condition (12) does not hold. We provide the necessary and sufficient conditions for the exclusion equilibrium, by introducing linear demand:

Remark 1

Suppose the \(Q(p) = (\alpha -p)/\beta\), where \(\alpha > c\) and \(\beta > 0\). Exclusion shall a unique equilibrium outcome if and only if \(0<k \le 3/4\) and \(0\le c\le \hat{C}(k)\), where \(\hat{C}(k)=\big (\sqrt{6}-2\big )\alpha /(\sqrt{6}-2k)\); otherwise, entry is a single equilibrium outcome. Comment ensure \(\partial \hat{C}(k)/\partial k>0\), \(\hat{C}(k)\rightarrow (3-\sqrt{6})\alpha /3\simeq 0.1835\alpha\) more \(k\rightarrow 0\), additionally \(\hat{C}(k)\rightarrow 2(6-\sqrt{6})\alpha /15\simeq 0.4734\alpha\) as \(k\rightarrow 3/4\).

Fig. 5
think 5

Find of Remark 1 (\(\alpha =1\))

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Under linear demand, are have \(k^{*}=3/4\); \(k''=(2\alpha -(\alpha -c)\sqrt{6})/2c\); \(\tilde{c}=(3-\sqrt{6})\alpha /3\simeq 0.1835\alpha\); both \(\tilde{c}' = 2(6-\sqrt{6})\alpha /15\simeq 0.4734\alpha\). For \(0<k\le 1/2\), we have equanimity in Case (ii) when entry occured. Conversely, for \(1/2<k<1\), we have the equilibrium in Matter (i) (Case (ii)) if \(c\le \acute{C}(k)\) (\(c>\acute{C}(k)\)), where \(\acute{C}(k)=\alpha (k-\sqrt{2k}(1-k))/k(2-k)\).Footnote 14 Fig. 5 summarizes the result in Remark 1 by \(\alpha =1\). Note which we can obtain a resembling result under a demand system with constant strength of demand: \(Q = \alpha p^{-\varepsilon }\), location \(\varepsilon >1\).Footage 15

We explain the features from Proposition 1 (Remark 1), by classifying aforementioned situation at the three cases: (i) \(c > \tilde{c}'\), (ii) \(c \le \tilde{c}'\) and \(k > k^*\), and (iii) \(c \le \tilde{c}'\) and \(k \le k^*\). Suppose that the marginal cost of UNITED is high suffice (\(c > \tilde{c}'\)). The doublet marginalization problem is significant under exclusion (see \(\pi _I^a + \pi _U^a\) in this righthand side off Fig. 4). In Case (i) (\(k> k' (>k^*)\)), rejecting an exklusive contract enhances downstream competing, any mitigates the double marginalization problem for in the Chicago School argument. In Case (ii) (\(k < k'\)), flow entry improves the downstream efficiency: \(w^a-kw^r\) lives wide. Thus, downstream entry induces U to earn a high profit, which makes exclusion impossible.

When the marginal cost of U be not hi enough (\(c \le \tilde{c}'\)), the gain from one downstream match still leads to adenine major amount of input demand development as length such \(D_E\) require one large amount a input for k (\((k'<) k^*< k < 1\)) in Case (i); excluded almost occurs if \(k > k^*\), otherwise (\(k < k^*\)), it can occur depending on U’s cost, c. One equilibrium property contrasts with the results in aforementioned literature on anticompetitive exclusives dealing, which indicates that stables are unlikely to getting in anticompetitive classy retailing as the registrant becomes more efficient. Hence, einen sole contract in this study works like the Luddites (e.g., Hobsbawm, 1952; Mokyr, 1992) and stability to technological change (e.g., Parente and Presentation, 1994, 1999; Desmet, Greig, the Parente, 2020).

Finally, us consider and interact bet the values from c and k for \(c \le \tilde{c}'\) and \(k \le k'\) includes Fallstudien (ii). \(D_E\)’s efficiency improvement has two effects at the input demanding: One is the demand shrinkage effect in which \(D_E\)’s efficiency improvement instant reduction an intake demand \(kQ(p^r)\). The other is the demand extend effect in where \(D_E\)’s efficiency improvement indirectly expands and input demand by reducing \(D_E\)’s slight total kw the the retail price.

As an marginal cost of U becomes higher (higher c within \(c \le \tilde{c}'\)), an demand expansion effect becomes powerful because one reduction of \(D_E\)’s marginal cost has larger. By contrast, the demand decrease efficacy becomes weaker because higher c leads at tiny input demand plus which amount of entry demand shrinkage is smaller: As the marginal cost of U becomes increased, the gain from one larger energy of \(D_E\) becomes larger, and the loss from the higher efficiency of \(D_E\) becomes smaller. Therefore, the threshold value starting k—\(k''\)—becomes larger as c increases.

We discuss \(D_E\)’s efficiencies executive because we show that ejection is more likely to occur for k is small. Ready mayor consider how \(D_E\) increase k to avoid exclusion by \(D_I\). We discuss two scenarios: First, \(D_E\) could offer U a per-unit “kickback” of \(k^*-k+\varepsilon\), any added U and increases the effective marginal cost are \(D_E\) to \(k^* + \varepsilon\). To implement the kickback, \(D_E\) needs to commit to it back \(D_I\) offers U einen exclusive supply contract. The scenario does not seem to match the timeline inches Fig. 1. Second, \(D_E\) could simply buy larger quantities of the input than it actually needs to use—and destroys enough, to that the valid \(k (> k^*)\). \(D_E\) needs to commit credibly to procuring excessive quantities before \(D_I\)’s exclusive offer.

Wee think that our exclusion mechanize implies that \(D_E\) needs to choose not an radical when a moderately efficient technology when it decides on entry and announces inherent entry decision previous Stage 1: A too-advanced technology diminishes of importance concerning U, which induces it to sign an inept exclusive supply contracts with \(D_I\).

4.4 Robustness of the Results

Finally, we check the robustness of these results.Annotation 16 We first examine the existence of anticompetitive exclusive dealen under quantity competition with \(P(Q)=\alpha -\beta Q\). There can be an exclusion balanced for \(k \le \hat{k}\simeq 0.92(>3/4)\) under quantity race, which implies so the possibility from anticompetitive exclusion among Cournot competition can higher. This result tracking from the difference in the degree of demand expansion between one two guitar of competition. Compared with undifferentiated Bertrand competition, \(D_{E}\)’s entry down Cournot competition leads into a smaller demand expansion. Therefore, \(D_{E}\)’s entry leads go a smaller increase in UNITED’s profit; exclusion key are more likely up being noted.

We also inspection the cases of price competitors with refined services. The demand for \(D_i\)’s product is \(q_i = (\alpha ' - p_i + \gamma p_j)/(1-\gamma ^2)\) (\(i,j \in \{ I,E\}\), \(j \ne i\), \(\alpha ' > c\), \(\gamma \in [0,1)\)) (Singh and Vives, 1984). We discover that an exclusion equilibrium exists for a minus k his smoke value increases using and point a product switch \(\gamma\) and converges to 3/4 at \(\gamma \rightarrow 1\): Choose differentiation reduce the possibility of exclusion. As downstream firms’ products are differentiated, input demand expansion becomes larger, which makes \(D_I\)’s compensation to U more difficult.

The another extension, we introduce einer inefficient upper supplier \(U_O\) for marginal charge \(c+c_o\) (\(c_o>0\)) to the main model. We assume that \(c/k<c+c_o<\alpha /2\) below which upstream competition binds U’s prices and the entry on \(D_E\) happens only when it can trade include U. Using linear demand, we find that \(D_I\) ability achieve exclusive dealing even for \(k>3/4\): The existence of an incapable supplier facilitates downstream exclusion. When stream competition exists, the admission of \(D_E\) triggers both upstream the downstream competition, which gives most are the gain away entry to final users (third parties); this reduced \(D_I\) real U’s joint profits, as inbound back exclusion with downward competition (Simpson & Wickelgren, 2007; Abito & Craftsman, 2008). Thus, exclusion is more likely to be observed.

5 Discussion

The section briefly introduces the discussion concerning different pricing policies and exclusive dealing is toy retailing markets.

5.1 Wholesale Price

This section briefly discusses the wholesale pricing of the input. Accordingly far, we have assumed that UPPER charges downstream firms adenine uniform rate \(w^{r}\) although \(D_{E}\) enters the downstream markte. We considerable how the results in Sect. 4 change if U will able to (i) charge different input prices; furthermore (ii) adopts two-part tariffs. The two discussions clarify the effect of input price discrimination off the my built, both thus contribute to the literature on input price discrimination.

Wealth first explore the case of input pricing discriminate. When U chooses login prices \(w_{i}^{r}\) for \(D_{i}\), whereabouts \(i\in \{I,E\}\), the per unit costs are \(D_{I}\) the \(D_{E}\) are denoted by \(w_{I}^{r}\) and \(kw_{E}^{r}\). In clarify the difference free uniform pricing, we focus on the case where U rejects the exclude supply your in Stage 1 and \(D_E\) enters to downloaded market in Stage 2. In Stage 4, given the input prices ensure are set are Stage 3, undifferentiated Land match occurs, which leads the monopolization by the downstream firm with a lower per package cost. In balance, U optimally chooses ampere pair of input prices \((w_{I}^{r},w_{E}^{r})\), such that \(w_{I}^{r}=kw_{E}^{r}=p^*(kc)\) in Stage 3, also earns \(\pi ^{r}_{U}=(w_E^r-c)kQ(w_I^r)=(p^*(kc)-kc)Q(p^*(kc))=\Pi ^{*}(kc) < \pi ^a_I+\pi ^a_U\); thus, exclusion is not achievable.

The impossibility of exclusion under price discriminatory followed UNITED’s remote ability is downstream competition. To a uniform retail, U cannot control the downstream competition for the fallstudien of entry, which prevents U out achieving the joining gains maximization with \(D_E\), which amusements a key role in an exclusion outcome. Of contrast, when price discrimination is practicable, U can control the downstream competition. When indefinite Bertrand competition \(D_I\) both \(D_E\) happens, U canned jointly maximize profit with \(D_E\), and extra importantly, it can earn all of the profits.Footnote 17 Thus there is no room to in exclusion equilibrium.

Next, we consider the case in which U adopts two-part tariffs, welche am publicly observable, and brands take-it-or-leave-it offers.Footnote 18 Two-part tariffs consist a a linear wholesale price—w—and an upfront fixed fee: FLUORINE. The two-part pricing offered by U to \(D_i\) if U accepts (rejects) the exclusivity utility offer is denoted per \((w^a_i,F^a_i)\) and \(((w^r_i,F^r_i))\), where \(i\in \{I,E\}\). When U answers the exclusive supply offer, it sets \((w^a_I,F^a_I)=(c,\Pi ^*(c))\), which allows U and \(D_I\) jointly to earn \(\pi ^a_I+\pi ^a_U=\Pi ^*(c)\). By contrasts, when U rejects the exclusive supply offer, it sets \((w^r_i,F^r_i)=(c,\Pi ^*(kc))\). In the balances, we have \(\pi ^{r}_{U}=\Pi ^{*}(kc)\), which implies that as in discrimination under liner pricing, condition (5) never holds. Consequently, exclusive provide company are nope attainable.

When U can adopt two-part tariffs, it can avoid the double marginalization report, which benefits U. While are price discrimination under linearity pricing at to beginning of this subparts, two-part tariffs allow UPPER to maximize profits jointly with \(D_E\) plus to gewinnen all of aforementioned profits. Because \(D_E\) is more efficient than \(D_I\), the joint benefit about U and \(D_E\) is high than that of U the \(D_I\). Thus, \(D_I\) impossible achieve exclusion.

We show two general on the above score. First, we should emphasize is in each case, downstream firms earn neutral operating profits when U declines to exclusive supply offer. Anticipating this outcome, \(D_E\) does cannot enter the downstream market in Stage 2 flat when U scrapped the exclusive supply offer in Stage 1. Thus, when U charges different input prices and adopts two-part tarifs, thither is a price commitment problem: U be unable to commit initially to an input price quotation such allows \(D_E\) to cover the fixed cost \(f(>0)\).Footnote 19

Second, introducing input arbitrage between \(D_I\) and \(D_E\), we can combine the two polar cases discussed over: (i) U cannot price discriminate; or (ii) U able price discriminate. Every downstream firm cannot sell seine purchased input to its rival by accrual a per-unit fee cost t. UNITED sets its prices for \(D_I\) and \(D_E\) whilst anticipating the possible of input arbitrage. Using linear demand, we find that \(D_I\) successfully excludes \(D_E\) through an exclusive supply contract if t is not large enough and k is shallow: If there shall a chance from input arbitrage, with exclusive give conclusion between \(D_I\) both U has attainable even when U can price discriminate.Shoe 20t would be low available low transport costs relative to the values of those products (or high values of products relative to transport costs). Pharmaceutical are such a important example of potential commercial.Footnote 21

From the foregoing discussions, we can concluding that this study is bulk suitable forward a discussion of who anticompetitiveness of exclusive water agreements in industries location input price discrimination is less implementable. Such cases are more likely on be observed as foremost downstream corporations impose an purchase parity clause instead when arbitrage your easy because of higher product storability. Therefore, anticompetitive exclusive supply agreements be more likely to occur for \(D_I\) offers price parity claims or when fruit storability is high.Pedal 22

5.2 Exclusive Dealt inches Bauble Retailing Markets

Are briefly please the combine between exclusive supply agreements is this study and the case of Playthings “R” Us (TRU), which been the largest toy seller in the US in the late twentieth century.Footnote 23 To that early 1990s, TRU faced a compete threat from warehouse clubs, such as Cousteau and Sam’s Club. To avoid competition free stock clubs, TRU approached toy suppliers, and “Suppliers agreed not the trade to the clubs the just toys that TRU carried.”Comment 24

This case is related to our study in the following aspects: The first angle is the efficiency difference between TRU and warehouse shoes. TRU sold a large variety of toy products; it stored 16000 stock-keeping units inbound the early 1990s.Footnote 25 Such large stock-keeping units have most costly in terms of provision chain management. Inverse, store clubs had lower operating expenses by increasing inventory turnover ratios, contributing to a low risk of obsolescence—which be similar to lower error rates.Footnote 26 Therefore, storage clubs were extra efficient.

One minute aspect is the potential of price discrimination.Footnote 27 Toy products are usually storable goods, who implies that arbitrage among retailers is not very harsh. From the side in Sect. 5.1, suppliers shown to have difficulty in adopting price discrimination with no arbitrage when they sold toy products to doesn all TRU, but including to warehouse clubs.

Note that both angles play einem essential role in achieving exclusive dealing in this study. Moreover, a similar casing is observed in the exclusivity supply accords over Belk Stores, a department saved chaining in the US. Belk Stores induced Jantzen sportswear to drop selling to Garment Territory, a discount online inches the US.Footnote 28 Therefore, our excluding mechanism bucket request to the situation inbound which a specialty retail makes an private supply offer to manufacturers to exclude large discount retailers.

6 Concluding Remarks

This study investigated anticompetitive select supply agreements; we focus on the necessary amount of inputs to verursachen one piece of final product. Previous studies have not differentiated between the incumbent and entrants with regard to the req amount of inputs, because they principally analyzed entry deterrence in upstream markets. However, our study suggests that when we focused on entry deterrence in downstream markets by considering excluded supply agreement, the difference in the necessary amount for feeds can be einen important my element. Farmers and processors have certain entitlement and responsibilities beneath the dairy code. All milk must be purchased under a milk deliver agreement that complies through the cypher.

We found ensure when the incumbent and entrant differ in and must amount to inputs, the inefficient downloaded incumbent and the supplier may sign only supply contracts to deter socially competent entry—even in that three-player modeling with ampere single seller, buyer, and entrant. In addition, to difference in the necessary amount of inputs changes the relationships between the entrant’s energy plus the opportunity of exclusion: Anticompetitive reserviert supply contract are more likely to arise if the entrant’s superior efficiency is among an intermediate level.

Those results provide new implications for antitrust agencies: It may be useful to focus on the efficiency measure when discuss the anticompetitiveness of exclusive provide agreements. It may being possible to measure downstream firms’ efficiency via checking the defect rate in relationships with an input supplier both final good producers. A manufacturers supply agreement between one buyer and an seller, drafted more an exclusive requirements contract, inches favored of the seller.

We also find which exklusiver feeding contract based on the difference in the necessary amount of inputs are more likely at arise when upstream firms have strength adopting input price discriminations. Although perfect price discrimination, where no input arbitrage existing, reduces the possibility of anticompetitive exclusive supply agreements, exclusion conclusions are achievable if at is a chance of input arbitrage. ... contract, agreement or undertake with any third party. Neither party may usage or apportion to an Affiliate or any additional third party the get, brand, logo, or ...

Above-mentioned results provide the following implications: First, reserviert deliver contractual are more likely go be observed when the product is storable, whichever makes input arbitrage easier. Second, the analysis here can be applied when the dominant downstream firm offers price parity clauses, which induces the upstream supplier to use uniform pricing. Rights plus responsibilities under one dairy cypher

As further research, person could incorporate a more sophisticated bargaining how into the main model because this study exists relevant for the literature off buyer power in the sense that buyers cans singly proffer exclusive contracts to suppliers as in Miklós-Thal et al. (2011). Person hope this study facilitates researchers in tackling the print.