Fake Spare Parts When No Domestic Brand Names Can Be Trusted

Abstract

This chapter considers fake motorcycle spare parts whose value is determined by duration and quality. A bad image about domestic products, which is often present in developing countries, causes consumers to distrust domestic brand names. That is a major reason why fake packaging was pervasive in Vietnam. I first explain the fact, obtained by field research, that repairpersons have incentives not only to use fake spare parts but also to mitigate incomplete consumer information about quality. I then analyse this phenomenon in a theoretical model, indicating inconsistent incentives concerning social welfare and consumers’ surpluses. I also consider a counterfeiting game between counterfeiters producing products of differing quality and show that a counterfeiter producing second-tier products does not always prefer no enforcement, while a counterfeiter producing lowest quality products always prefers it.

Appendix

Appendix 3.1. Proof of ${{{{d}}\pi^{F*} } \mathord{\left/ {\vphantom {{d\pi^{F*} } {d\lambda }}} \right. \kern-0pt} {{{d}}\lambda }} < 0$.

$$ \pi^{F*} = \left( {p^{F*} - t^{F} } \right)q^{F*} = \left( {\frac{{\overline{v} - 1}}{2}t^{F} - \frac{{\lambda \overline{v} - 1}}{2}t^{D} } \right)\left( {\frac{{\overline{v} }}{2} - \frac{{t^{F} - t^{D} }}{2\Delta t}} \right), $$

and we define

$$ f(\lambda ) \equiv \left( {\frac{{\overline{v} - 1}}{2}t^{F} - \frac{{\lambda \overline{v} - 1}}{2}t^{D} } \right)\quad {\text{and}}\quad g(\lambda ) \equiv \left( {\frac{{\overline{v} }}{2} - \frac{{t^{F} - t^{D} }}{2\Delta t}} \right). $$

For a meaningful model, $f(\lambda ) > 0$ and $g(\lambda ) > 0$, and

$$ \frac{{{d}}f}{{{d}}\lambda } = - \frac{{\bar{v}t^{D} }}{2} < 0,\,\frac{{{d}}g}{{{d}}\lambda } = - \frac{{\lambda \left( {t^{F} - t^{D} } \right)}}{{2\Delta t^{2} }} < 0. $$

By using these results, we obtain

$$ \frac{{{{d}}\pi^{F * } }}{{{d}}\lambda } = \frac{{{d}}f}{{{d}}\lambda }g + f\frac{{{d}}g}{{{d}}\lambda } < 0. $$

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Appendix 3.2. Calculations of profits in Proposition 3.2.

The following conditions are satisfied by assumptions underlying the parameters:

$$ \begin{gathered} \pi _{{{{OO}}}}^{M} < \pi _{{{{FO}}}}^{M} \; \Leftrightarrow \;3c^{M} < a^{H} + 2c^{H} , \hfill \\ \pi _{{{{OF}}}}^{M} < \pi _{{{{FF}}}}^{M} \; \Leftrightarrow \;4c^{M} < a^{H} + 3c^{H} ,\;{\kern 1pt} \hfill \\ \pi _{{{{OO}}}}^{L} < \pi _{{{{OF}}}}^{L} \; \Leftrightarrow \;2c^{L} < a^{M} + c^{M} . \hfill \\ \end{gathered} $$

Regarding $\pi_{{FO}}^{L} < \pi_{{FF}}^{L}$, we must consider two markets, M and H markets, separately. If $2c^{L} < a^{M} + c^{M}$ for M market and $5c^{L} < a^{H} + 4c^{H}$ for H market, then $\pi_{{FO}}^{L} < \pi_{{FF}}^{L}$. From the parameters’ assumptions, two inequalities in both markets are satisfied. □