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Evaluating
Equilibrium Outcomes of a Joint Production Monopoly: A Simple Pedagogical Model |
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| Paper Id :
19494 Submission Date :
2024-11-11 Acceptance Date :
2024-11-22 Publication Date :
2024-11-25
This is an open-access research paper/article distributed under the terms of the Creative Commons Attribution 4.0 International, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. DOI:10.5281/zenodo.14512002 For verification of this paper, please visit on
http://www.socialresearchfoundation.com/innovation.php#8
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| Abstract |
The paper attempts to model a simple case of
joint production monopoly by incorporating a parameter in the cost function
implicating the direct cost advantage of joint production. This framework
computes all the equilibrium outcomes, namely prices, outputs, and profits. The
effect of the cost advantage parameter on all these outcomes is also evaluated. |
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| Keywords | Joint Production, Substitutes, Monopoly, Oligopoly. | ||||||
| Introduction | In today’s world, a pure monopoly supplying a single product hardly exists. Most commonly, it is observed that a single firm supplies numerous variants of the same product, which makes them gross substitutes (Snyder et al., 2015) of one another. Now that different variants are produced and supplied, they are naturally sold at different prices in the market according to their existing market demands. However, one interesting fact remains that the basic line of production is the same for all these variants, which have a significant scope reduction in the cost of production, especially for the variants sold at relatively higher prices. In reality, most of these firms are a part of some oligopolistic market structure (Varian, 2015) who interact among themselves strategically with a significant amount of rivalry. |
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| Objective of study | Since studying the impact of cost advantage on equilibrium outcomes for a firm in such a market structure is quite complicated, especially for a beginner, the paper intends to focus on the same questions with a simple pedagogical model of a simple market structure that is a monopoly, which is producing two substitute goods and enjoys a cost advantage due to joint production. To carry forward this objective, the paper has followed the following outline: firstly, the concept of monopoly and joint production monopoly with a brief literature review on various aspects of joint production in monopolistic and oligopolistic market structure (Varian, 2015) has been introduced, along with relevant gaps in the literature. The following section briefly explains the methodology used for building the model. It is followed by a presentation of a simple pedagogical model in alignment with the study's objectives and, finally, the concluding remarks regarding the model's findings and the further scope of enriching the model. |
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| Review of Literature | Monopoly: A pure monopoly exists when only one producer (seller) exists in a market. There are no competitors or rivals. However, the policies of a monopolist may be constrained by the indirect competition of all commodities for the consumers’ money and of reasonably adequate substitute goods and by the threat of potential competition if market entry is possible (Gould & Lazear, 1989). Joint production Monopoly: A joint production monopoly (Koutsoyiannis, 1975) is a type of anticompetitive behaviour where firms, usually an oligopoly, collude to gain monopoly profits as a group. This is similar to tacit collusion but is not a formal cartel. Numerous studies have been conducted at various levels to gather meaningful insights regarding the anti-competitive behaviours of firms (especially large ones) that lead to the concentration of market power since it seems counter to the welfare interests of most governments. Among a few, one such anti-competitive behaviour was observed to be significantly common: joint production by large firms, either on their own, creating economies of scale and scope, or by collaborating with other firms by horizontal and or vertical joint production arrangements. (Tirole, 1988) through merger (Kwoka, 2012) and other forms of tacit collusion (Shapiro, 1989) such as joint venture (Harrigan, 1988) for example. Now, all of these directly imply a significant cost advantage, which consequently leads to creating barriers to entry (Bain, 1956) and hence reduces competitiveness in the market. Studies have taken place on various industries like the airline industry, banking sector (Degryse et al., 2004) etc. In short, all the studies on joint production monopolies reveal that while joint production agreements can lead to significant efficiency gain, they also have the potential to reduce competition (Bresnahan & Reiss, 1991) and create a monopolistic market structure. Horizontal and vertical joint production arrangements can consolidate market power, raise barriers to entry and facilitate tacit or explicit collusion. Regulatory authorities are crucial in monitoring such arrangements to ensure they do not lead to anti-competitive outcomes that harm consumer' behaviour and hinder market innovation. Moreover, these studies emphasise the need for careful antitrust analysis, especially in industries with high concentration of substantial barriers to entry, where joint production may have the most significant impact on competition. In view of the above-mentioned discourse, any student of economics would be interested in the direct or indirect consequences of changing any cost advantage parameter present in the cost function of a firm producing multiple outputs that are substitutes for one another on its equilibrium outcomes. Since the studies considered here mainly deal with significantly complex market structures, it becomes quite difficult to model them. Mathematically, hence, the basic objective is to study the impact of cost advantage due to joint production on the equilibrium outcomes of an imperfectly competitive firm. A joint production monopoly firm could be a good starting point for a mathematical model. Therefore, a simple pedagogical model that banks primarily on mathematics is built to evaluate the equilibrium outcomes of joint production to verify the impact of the cost advantage of joint production and its relationship with the equilibrium outcomes. |
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| Methodology | The methodology used is the universal
optimisation technique (individual profit maximisation). A monopoly for
producing two goods, which are substitutes, is considered. The inverse demand
functions of those goods take the price of a good being inversely related to
the output of the same good (since the law of demand must hold) and directly
related to the output of the other good (since they are gross substitutes)
Along with them, a simple cost function involving outputs of both the goods and
introduced a parameter representing the cost advantage due to joint production
is considered. Only the first-order condition(Sydsaeter et al., 2016)
(necessary) of optimisation has been considered. After computing
equilibrium outcomes, the impact of a change in the cost advantage parameters
on all those outcomes is computed. |
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| Analysis |
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| Conclusion |
The results obtained here do not contain many elements of surprise. With
cost advantage due to the joint production of substitute goods, it makes sense
to have a direct relationship between the cost advantage parameter and the
equilibrium outputs and profit. The key observation that comes out from this
simple pedagogical model is the relationship between the same parameter with
the equilibrium prices. On the one hand, we get increased outputs with an
increased cost advantage, but on the other hand, we see that the equilibrium
prices may or may not decline with the same advantage. The pecuniary response
with an increased cost advantage is rather complicated since it depends on a lot
of other factors, like the responsiveness of outputs for a change in the cost
advantage parameter and also the nature of the market demand of the two
substitute goods and their interrelationship between them: reflected by values
of the coefficients of the output terms in the inverse market demand
functions. Finally, we can conclude that this is perhaps the simplest way to
reach the paper's objective. There is ample scope for refinements by introducing
more relevant market structures like oligopoly and maybe all producing more
than two substitute goods (as is a reality in today’s world) and carrying on
the same exercise to study their outcomes. |
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| References |
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