In a Cournot-oligopoly with free but costly entry and business stealing, output per firm is too low and the number of competitors excessive, assuming labor productivity to depend on the number of employees only or to be constant. However, a firm can raise the productivity of its workforce by paying higher wages. We show that such efficiency wages accentuate the distortions occurring in oligopoly. Specifically, excessive entry is aggravated and the welfare loss due to market power rises.
We are grateful for helpful comments by an anonymous referee, Florian Baumann, Michael Neugart, Alexander Rasch, Philipp Weinschenk and Ulrich Zierahn. We also thank participants of the European Society of Population Economics annual meeting 2018 (held in Antwerp) and seminar participants in Trier for inspiring discussions and Andreas Jung for his excellent research assistance.
Throughout the Appendix, we consider the case of a linear production function, i. e. . For simplicity, we suppress the respective underline notation (as employed in the main text).
A.2 Derivation of Proposition 2 Part (I)
Differentiating (10) with respect to γ yields:
The second derivative in square brackets can be expressed as:
Using the Solow-condition implies:
Differentiating (18) with respect to γ yields:
This shows that:
which proves the first part of Proposition 2.
A.3 Derivation of Proposition 2 Part (II)
A.4 Derivation of Proposition 2 Part (III)
This leads to:
Defining >0, we can calculate:
which proves the last part of Proposition 2.
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