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Review of Industrial Organization

Erschienen in:

08.06.2017

Product Similarity and Cross-Price Elasticity

verfasst von: Sreya Kolay, Rajeev K. Tyagi

Erschienen in: Review of Industrial Organization | Ausgabe 1/2018

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Abstract

We use a spatial competition model to show how an increasing similarity between two products can monotonically increase, monotonically decrease, or have a non-monotonic effect on cross-price elasticity. We relate these results to prior research that links cross-price elasticity to product similarity, and the literature on market structure, merger analysis, and price discrimination.

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Nächster Artikel Analyzing the Impact of Electricity Market Structure Changes and Mergers: The Importance of Forward Commitments

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Stegemann (1974), Werden (1992), and Sethuraman et al. (1999) highlight the scaling effect in cross-price elasticity, making it sensitive to the market share of firms.

Using the equilibrium expressions, the \(y\le y_{\max }\) condition for ruling out local monopoly situation (i.e., \(s_{2}>s_{1}\) in Fig. 1) becomes \(y\le \frac{3(\alpha +1)}{14t}\), and the \(y>y_{\min }\) condition to ensure that the weaker firm survives and sells positive quantity profitably becomes \(y>\frac{3-17\alpha }{14t}\). Since \(y>0\) for the demand functions (5) and (6) to hold, overall we need \(\max \{0,\frac{3-17\alpha }{14t} \}<y\le \frac{3(\alpha +1)}{14t}.\)

Comparative statics with respect to t yield qualitatively the same results as with respect to y since decreasing t, the strength of disutility of buying a product away from ideal point, is functionally equivalent to bringing the two products closer horizontally.

The \(y\le y_{\max }\) condition for ruling out local monopoly situation is now \(y\le \frac{3(1+\alpha -c\left( \alpha \right) -c\left( 1\right) )}{14t} \), and the \(y>y_{\min }\) condition to ensure that the weaker firm survives and sells a positive quantity profitably becomes \(y>\frac{3-17\alpha -3c\left( 1\right) +17c\left( a\right) }{14t}.\) Since \(y>0\) for the demand functions (5) and (6) to hold, overall we need \(\max \{0,\frac{3-17\alpha -3c\left( 1\right) +17c\left( a\right) }{14t}\}<y\le \frac{3(1+\alpha -c\left( \alpha \right) -c\left( 1\right) )}{14t}\).

Note that \(c\left( \alpha \right) <\alpha \) is necessary for the condition in footnote 4 to hold. Thus, since \(\alpha =1\) for the stronger firm, its marginal cost is bound in the range \(\left( 0,1\right) \).

As an alternative to cross-price elasticity, the literature has also used the diversion ratio: the share of the sales lost by one product that is captured by another when the price of the former increases (Werden 1996). In our model, we did not find a situation where bringing products closer in characteristics space would decrease diversion ratios.

As earlier, at \(y>y_{\max },\) the demand function changes discontinuously to a local monopoly situation. As expected, Fig. 2 shows that if disutility t from buying away from ideal point is large, then firms become local monopolies at smaller y.

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Titel: Product Similarity and Cross-Price Elasticity
verfasst von: Sreya Kolay
Rajeev K. Tyagi
Publikationsdatum: 08.06.2017
Verlag: Springer US
Erschienen in: Review of Industrial Organization / Ausgabe 1/2018
Print ISSN: 0889-938X
Elektronische ISSN: 1573-7160
DOI: https://doi.org/10.1007/s11151-017-9578-8

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