The Size Distribution of Firms, Cournot, and Optimal Taxation

IMF Working Papers, December 1, 2006

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Tax laws and administrations often treat different size firms differently; the paper models consequences of such differentiation.
Oligopolists with different efficiencies determine the size distribution of firms.
A government that maximizes a weighted sum of consumer surplus, profits, and tax receipts can tax firms with different efficiencies differently and provides a reference point for other, more restricted differential tax systems.
Analytic and simulation results are provided.

Taxes modeled include:
- a specific sales tax,
- an ad valorem sales tax,
- a profits tax with imperfect deductibility of capital cost,
- and a combination of the last two (ad valorem + imperfect profits tax).
The pattern of optimal tax rates varies by firm efficiency and is heavily dependent on the social valuation of tax receipts.

There is, in general, a pattern of tax rates by efficiency of firm.
The optimal pattern of tax rates is heavily dependent on the social valuation of tax receipts.
When both ad valorem taxes and the imperfect profits tax are combined, simulations suggest:
- the ad valorem rate is higher for relatively inefficient firms, and
- the imperfect profits tax rate is lower for relatively inefficient firms.

Differential taxation by firm efficiency can be justified when a government maximizes a weighted sum of consumer surplus, profits, and tax receipts.
The results provide a reference point for designing differential tax systems that are more restricted in practice.
Understanding the dependence of optimal tax patterns on the social valuation of tax receipts is crucial for tax policy design.