Abstract
This paper develops a novel approach to modeling preferences in monopolistic competition models with a continuum of goods. In contrast to the commonly used constant elasticity of substitution preferences, which do not capture the effects of consumer income and the intensity of competition on equilibrium prices, the present preferences can capture both effects. The relationship between consumers’ incomes and product prices is then analyzed for two cases: with and without income heterogeneity.
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Notes
To simplify the analysis, I assume that there are no fixed costs of production. However, the model can be easily extended to the case when firms incur fixed costs as well.
The IPFR property was first established in Singh and Maddala (1976), who describe the size distribution of incomes. The property means that the hazard rate of the distribution does not decrease too fast.
This effect is similar to that described in Melitz and Ottaviano (2008).
The framework can be easily extended to the case of a continuos distribution of income.
It is sufficient to introduce some quality index in the utility function.
References
Anderson S, de Palma A, Thisse J-F (1992) Discrete choice theory of product differentiation. MIT Press, Cambridge
Behrens K, Murata Y (2007) General equilibrium models of monopolistic competition: a new approach. J Econ Theory 136:776–787
Behrens K, Murata Y (2012) Globalization and individual gains from trade. J Monet Econ 59:703–720
Deaton A, Muellbauer J (1980) Economics and consumer behavior. Cambridge University Press, Cambridge
Dixit A, Stiglitz J (1977) Monopolistic competition and optimum product diversity. Am Econ Rev 67(3):297–308
Flach L (2013) Quality upgrading and price heterogeneity: evidence from Brazilian exporters (mimeo)
Foellmi R, Zweimueller J (2006) Income distribution and demand-induced innovations. Rev Econ Stud 73(4):941–960
Hummels D, Lugovskyy V (2009) International pricing in a generalized model of ideal variety. J Money Credit Bank 41(1):3–33
Hunter L, Markusen J (1988) Per-capita income as a determinant of trade. In: Feenstra R (ed) Empirical methods for international trade. MIT Press, Cambridge
Melitz M (2003) The impact of trade on intraindustry reallocations and aggregate industry productivity. Econometrica 71(6):1695–1725
Melitz M, Ottaviano G (2008) Market size, trade, and productivity. Rev Econ Stud 75(1):295–316
Murata Y (2009) On the number and the composition of varieties. Econ J 119:1065–1087
Perloff J, Salop S (1985) Equilibrium with product differentiation. Rev Econ Stud 52(1):107–120
Saure P (2012) Bounded love of variety and patterns of trade. Open Econ Rev 23:645–674
Simonovska I (2013) Income differences and prices of tradables (mimeo)
Singh S, Maddala G (1976) A function for size distributions of incomes. Econometrica 44:963–970
Tarasov A (2009) Income distribution, market structure, and individual welfare. BE J Theor Econ (Contrib) 9, Article 39
Van den Berg J (2007) On the uniqueness of optimal prices set by monopolistic sellers. J Econom 141: 482–491
Verhoogen E (2008) Trade, quality upgrading, and wage inequality in the Mexican manufacturing sector. Q J Econ 123(2):489–530
Acknowledgments
An earlier version of the paper was circulated under the title “Consumer Preferences in Monopolistic Competition Models”. I would like to thank Maxim Ivanov, Kala Krishna, Sergey Lychagin, Andrés Rodríguez-Clare, and Michael Seitz for helpful comments and discussion. This paper has also benefited from comments by the editor and an anonymous referee. All remaining errors are mine.
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Appendices
Appendix A
In this part of Appendix, I analyze the properties of the price function \( p(\varphi ,\,Q)\) determined by the profit maximization problem. Recall that if the solution of the maximization problem in (8) is interior, then the optimal price solves
If \(F(\varepsilon )\) satisfies the IPFR property, then \(\frac{\varepsilon f(\varepsilon )}{1-F(\varepsilon )}\) is strictly increasing on \(\left[ \varepsilon _{L},\,\varepsilon _{H}\right] .\) This implies that the right-hand side of the above equation is strictly increasing as a function of \(p.\) Remember that for the interior solution, \(p\) must belong to \(\left[ \frac{\varepsilon _{L}}{Q},\,\frac{ \varepsilon _{H}}{Q}\right] .\) Hence, taking into account that the left-hand side is strictly decreasing in \(p,\) Eq. (22) has a unique solution on \(\left[ \frac{\varepsilon _{L}}{Q},\,\frac{\varepsilon _{H}}{Q}\right] \) if and only if
The latter is equivalent to
Next, I provide the proofs of Lemmas 2 and 3.
1.1 The Proof of Lemma 2
From Lemma 1, if \(\varphi >\frac{f(\varepsilon _{L})Q}{ f(\varepsilon _{L})\varepsilon _{L}-1},\) then \(p(\varphi ,\,Q)\) is equal to \( {\varepsilon _{L}}/{Q}\) and, therefore, is decreasing in \(Q.\) If \(\varphi \in \left[ \frac{Q}{\varepsilon _{H}},\,\frac{f(\varepsilon _{L})Q}{ f(\varepsilon _{L})\varepsilon _{L}-1}\right] ,\) then \(p(\varphi ,\,Q)\) is the solution of
As \(F(\varepsilon )\) satisfies the IPFR property, \(\frac{1-F(pQ)}{pQf(pQ)}\) is decreasing in \(Q\) for any \(p.\) This implies that for any \(p,\) the right-hand side of the above equation is increasing in \(Q\!:\) higher \(Q\) shifts the function \(1-\frac{1-F(pQ)}{pQf(pQ)}\) upward. As a result, the value of \(p(\varphi ,\,Q)\) decreases.
1.2 The Proof of Lemma 3
Consider \(\varphi \in \left[ \frac{Q}{\varepsilon _{H}},\,\frac{f(\varepsilon _{L})Q}{f(\varepsilon _{L})\varepsilon _{L}-1}\right] .\) It is straightforward to see that in this case, \(p(\varphi ,\,Q)Q\) solves
with respect to \(x.\) Higher \(Q\) shifts the left-hand side of the equation upward. This means that the value of \(p(\varphi ,\,Q)Q\) increases, as the right-hand side is increasing in \(x.\)
Appendix B
In this Appendix, I explore the effects of a rise in population size \(L\) on the equilibrium outcomes in the long run. In the long run, the equilibrium is determined by
where \(\pi (\varphi ,\,Q)\) is given by (11). As can be seen from the equations, population size affects the equilibrium only through \(\pi (\varphi ,\,Q).\) Specifically, a rise in \(L\) increases \(\pi (\varphi ,\,Q)\) for any \(\varphi ,\,Q.\) In other words, higher \(L\) increases the firm’s expected profits, implying that the left-hand side of the free entry equation rises. From Lemmas 2 and 3, it is straightforward to show that \(\pi (\varphi ,\,Q)\) is a decreasing function of \(Q\) (for any \(\varphi \)). Thus, in order the free entry condition is satisfied, a rise in \(L\) has to be compensated by a rise in \(Q.\) A rise in \(Q\) in turn results in lower prices charged by firms (as it is shown in Lemma 2).
Finally, the mass of entrants can be found from
As the denominator is decreasing in \(Q\) and consumer income \(y\) is fixed, a rise in \(L\) results in more entry into the market (higher \(M_{e}\)).
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Tarasov, A. Preferences and income effects in monopolistic competition models. Soc Choice Welf 42, 647–669 (2014). https://doi.org/10.1007/s00355-013-0748-9
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DOI: https://doi.org/10.1007/s00355-013-0748-9