Abstract
We revisit the wholesale model and the agency model in differentiated markets of Lu (Review of Industrial Organization, 51, 151–172, 2017) and show the changes of the equilibrium outcomes of consumer surplus and social welfare. Unlike Lu (Review of Industrial Organization, 51, 151–172, 2017), we find that: (i) social welfare is always greater in agency model than in wholesale model; and (ii) different rankings of equilibrium aggregate profits and social welfare are obtained under the two models.
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Notes
However, Lu (2017) computed consumer surplus, CS as with U in Eq. (1) ignoring the budget constraint and the three part s of \(- \left( {\frac{{(q_{{ - i}}^{j} )^{2} }}{2} + \frac{{(q_{i}^{{ - j}} )^{2} }}{2} + \frac{{(q_{{ - i}}^{{ - j}} )^{2} }}{2}} \right)\). Following this setting, we find Lu's (2017) incorrect computations in terms of consumer surplus and social welfare between the wholesale and agency models. See our Appendix for Lu's (2017) computations.
Note that \(q^{*} = \frac{1}{{\left( {2 - \beta } \right)\left( {1 + \beta } \right)\left( {2 - \gamma } \right)\left( {1 + \gamma } \right)}},~p^{*} = \frac{{\left( {1 - \beta } \right)\left( {2 - \gamma } \right) + 1 - \gamma }}{{\left( {2 - \beta } \right)\left( {2 - \gamma } \right)}}\) under wholesale model and \(q_{A}^{*} = \frac{1}{{\left( {1 + \beta } \right)\left( {2 - \gamma } \right)\left( {1 + \gamma } \right)}},~p_{A}^{*} = \frac{{1 - \gamma }}{{2 - \gamma }}\) under agency model.
References
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Acknowledgements
We greatly appreciate the General Editor, Prof. Lawrence J. White. Thanks to his thoughtful comments and suggestions on our paper, we definitely believe the paper has been greatly improved.
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Appendix: Lu's (2017) Calculations
Appendix: Lu's (2017) Calculations
Based on the Lu's (2017, pp. 169–170) calculations of consumer surplus (\(CS\) and \(CS_{A}\)) and ignoring the budget constraint, we have the exactly same results as in Lu (2017):
In each second term of the RHS of consumer surplus, there exists an incorrect calculation with \(\frac{1}{2}(q_{i}^{j} )^{2}\), which leads to an incorrect comparison of social welfare. It should be \(CS = \frac{2}{{\left( {1 + \beta } \right)\left( {1 + \gamma } \right)(2 - \beta )^{2} (2 - \gamma )^{2} }}\) and \(CS_{A} = \frac{2}{{\left( {1 + \beta } \right)\left( {1 + \gamma } \right)(2 - \gamma )^{2} }}\) in each second term of the RHS of consumer surplus.
Following Lu's (2017) computation from her definition of CS, we are able to reach the same results.
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Choi, K., Lim, S. Comment on “A Comparison of the Wholesale Model and the Agency Model in Differentiated Markets”. Rev Ind Organ 61, 373–377 (2022). https://doi.org/10.1007/s11151-022-09871-0
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DOI: https://doi.org/10.1007/s11151-022-09871-0