Published by De Gruyter October 25, 2016

# Consumers’ Misevaluation and Public Promotion

• Atsushi Yamagishi

## Abstract:

I analyze markets in which consumers may misestimate the true value of goods and the government can affect the valuation through public promotion. When entry of firms is not allowed, the government makes consumers overvalue the goods to mitigate welfare loss from underproduction in an oligopolistic market, provided that the promotion cost is sufficiently low. On the contrary, in a free-entry market, no matter how low the promotion cost is, the government may make consumers undervalue them in order not to induce wasteful entries despite the remaining underproduction problem. In addition, my result in a free-entry market suggests that the main finding of Glaeser and Ujhelyi (J Public Econ 94: 247-257, 2010)crucially depends on the barriers to entry and the opposite result may be obtained under free entry.

JEL Classification: L13; L38; M37

## Acknowledgements

I would like to thank Toshihiro Matsumura and all seminar participants at The University of Tokyo. I am also indebted to an anonymous referee and the editor-in-chief, Sandra Ludwig, for their helpful comments and suggestions. Needless to say, I am responsible for any remaining errors.

## Appendix

### Proof of Proposition 1

By applying the implicit function theorem to eq. [3], I have

za=n(n+1)2bC′′(z)+n2(n+1)2>0,
zb=C(z)bC′′(z)+n2(n+1)2<x=x>0,
zg=nn+1bC′′(z)+n2(n+1)2>0.

where

z/b<(>,=)0

if

z>(<.=)0

.

Now I prove Proposition 1(ii). When C(g)<(>,=)(a+g)nb(n+1)2, LHS <(>,=) RHS in eq. [3] at z=g. Remember that z always exists and is unique. z>(<,0)g follows because, in eq. [3], LHS <(>,=) RHS at z=g, the LHS is strictly increasing in z, and the RHS is independent of z. Q.E.D.

### Proof of Proposition 2

Note that z is always well defined and determined uniquely. When g>(<,=)0, C(g)>(<,=)0. Since LHS >(<,=) RHS at z=g in eq. [6], the LHS of eq. [6] is strictly increasing, and the RHS of eq. [6] does not depend on z, z<(>,=)g holds. Q.E.D.

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Published Online: 2016-10-25
Published in Print: 2016-10-1

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