The Low‐Quality Advantage in Vertical Product Differentiation

Schubert, Stefanie

doi:10.1002/mde.2825

Cited by 8 publications

(42 citation statements)

References 8 publications

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“…Following Schubert (), we consider a market with two firms producing two goods that differ in quality and are sold to a population of consumers. Firm i produces a good with a quality level of s i , which is sold at a price p i ( i = 1, 2.).…”

Section: The Modelmentioning

confidence: 99%

“…Firm 2 is called the high‐quality firm and Firm 1 is called the low‐quality firm because s 2 > s 1 . As in Schubert (), consumers are distributed with different density along the interval

([],, 0, \overset{true¯}{θ})

, with more consumers having a low WTP that follows a triangular distribution. Without and loss of generalization, we let

\overset{θ}{true} = 1

in order to be able to derive explicit solutions of the model.…”

Section: The Modelmentioning

confidence: 99%

“…Without and loss of generalization, we let

\overset{θ}{true} = 1

in order to be able to derive explicit solutions of the model. On the basis of the model of Schubert () and replacing

\overset{θ}{true} = 1

, we arrive at the density distribution function of consumers as follows:

f ((), θ) = 2 ((), 1 - θ) .

Each consumer may purchase at most one good from the market. A consumer's utility is described as follows:

U = ({, \begin{array}{c} italicθs {}_{i}- p_{i} \\ 0 \end{array}) \begin{matrix} centertrue \\ if buying the good \\ if not buying \end{matrix},

where s i is quality units of the good and p i is the price paid by the consumer.…”

Section: The Modelmentioning

confidence: 99%

“…A consumer's utility is described as follows:

U = ({, \begin{array}{c} italicθs {}_{i}- p_{i} \\ 0 \end{array}) \begin{matrix} centertrue \\ if buying the good \\ if not buying \end{matrix},

where s i is quality units of the good and p i is the price paid by the consumer. Basically, this function can be obtained from the utility function in Schubert () with R = 0. This utility function has been widely used in many papers such as Sutton (), Wauthy (), and Nguyen ().…”

Section: The Modelmentioning

confidence: 99%

“…Following Wauthy (), Motta (), and Schubert (), we derive profit functions of the two firms as follows:

({, \begin{array}{l} Π_{2} = {(1 - \frac{p_{2} - p_{1}}{s_{2} - s_{1}})}^{2} p_{2} - \frac{s_{2}^{2}}{2} \\ Π_{1} = ((), 2 - \frac{p {}_{1}}{s_{1}} - \frac{p_{2} - p_{1}}{s_{2} - s_{1}}) ((), \frac{p_{2} - p_{1}}{s_{2} - s_{1}} - \frac{p_{1}}{s_{1}}) p_{1} - \frac{s_{1}^{2}}{2} \end{array})

…”

Section: The Modelmentioning

confidence: 99%

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A note on the low‐quality advantage in vertical product differentiation

Niem

2019

Manage Decis Econ

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In this paper, we modify the analysis of Schubert (2017), who found low‐quality advantage arising from vertical differentiation. Here, we relax the assumption of a sufficiently high reservation utility (so that consumers will always buy the good) to include the case in which they can refrain from buying the good. We find an explicit solution to profit functions, with the result that low‐quality advantage disappears.

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Section: The Modelmentioning

confidence: 99%

“…Firm 2 is called the high‐quality firm and Firm 1 is called the low‐quality firm because s 2 > s 1 . As in Schubert (), consumers are distributed with different density along the interval

([],, 0, \overset{true¯}{θ})

, with more consumers having a low WTP that follows a triangular distribution. Without and loss of generalization, we let

\overset{θ}{true} = 1

in order to be able to derive explicit solutions of the model.…”

Section: The Modelmentioning

confidence: 99%

“…Without and loss of generalization, we let

\overset{θ}{true} = 1

in order to be able to derive explicit solutions of the model. On the basis of the model of Schubert () and replacing

\overset{θ}{true} = 1

, we arrive at the density distribution function of consumers as follows:

f ((), θ) = 2 ((), 1 - θ) .

Each consumer may purchase at most one good from the market. A consumer's utility is described as follows:

U = ({, \begin{array}{c} italicθs {}_{i}- p_{i} \\ 0 \end{array}) \begin{matrix} centertrue \\ if buying the good \\ if not buying \end{matrix},

where s i is quality units of the good and p i is the price paid by the consumer.…”

Section: The Modelmentioning

confidence: 99%

“…A consumer's utility is described as follows:

U = ({, \begin{array}{c} italicθs {}_{i}- p_{i} \\ 0 \end{array}) \begin{matrix} centertrue \\ if buying the good \\ if not buying \end{matrix},

Section: The Modelmentioning

confidence: 99%

“…Following Wauthy (), Motta (), and Schubert (), we derive profit functions of the two firms as follows:

({, \begin{array}{l} Π_{2} = {(1 - \frac{p_{2} - p_{1}}{s_{2} - s_{1}})}^{2} p_{2} - \frac{s_{2}^{2}}{2} \\ Π_{1} = ((), 2 - \frac{p {}_{1}}{s_{1}} - \frac{p_{2} - p_{1}}{s_{2} - s_{1}}) ((), \frac{p_{2} - p_{1}}{s_{2} - s_{1}} - \frac{p_{1}}{s_{1}}) p_{1} - \frac{s_{1}^{2}}{2} \end{array})

…”

Section: The Modelmentioning

confidence: 99%

See 3 more Smart Citations

A note on the low‐quality advantage in vertical product differentiation

Niem

2019

Manage Decis Econ

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show abstract

Quality investment timing by the startup and the established firm

2017

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This study investigates quality investment timing decisions of the established firm and the startup by a duopoly model, where firms can position quality early (demand uncertainty is high) or late (uncertainty has been resolved), possibly at different costs. The startup positions quality to maximize its survival probability, whereas the established firm maximizes profits. Results indicate that the startup positions quality earlier than the established firm when the demand uncertainty is high and costs do not decline sharply over time. Additionally, policy analysis shows that subsidies work better than direct funds in encouraging quality innovation of the startup.

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Market configurations when marginal costs are quality‐dependent

Pires,

Jorge,

Catalão‐Lopes

et al. 2024

Manage Decis Econ

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Most quality‐then‐price decision models under vertical product differentiation consider a predetermined market configuration. We endogenize market configuration considering quality‐dependent marginal costs and conclude that a strictly interior full coverage duopoly holds for some parameter values, unveiling the relevance of this commonly assumed market structure. Moreover, we show that a monopoly never arises in equilibrium, and (i) there are multiple equilibria at the frontier between interior and corner full coverage duopoly, (ii) the market is fully (partially) covered when relative tastes' heterogeneity is low (high), and (iii) there is a discontinuity in the transition from partial coverage to full coverage duopoly.

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The Low‐Quality Advantage in Vertical Product Differentiation

Cited by 8 publications

References 8 publications

A note on the low‐quality advantage in vertical product differentiation

A note on the low‐quality advantage in vertical product differentiation

Quality investment timing by the startup and the established firm

Market configurations when marginal costs are quality‐dependent

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