Lundberg uses the following expression to fit the Laffer Curve for the top rate of income tax:

\[
R = \tau (1 - \tau)^{\alpha \epsilon}
\]

Symbol

Description

\(R\)

Tax revenue.

\(\tau\)

Tax rate.

\(\alpha\)

The pareto parameter, a measure of the thinness of the right tail of the income distribution.

\(\epsilon\)

Elasticity of taxable income with respect to the net-of-tax rate.

For the UK in 2013, Lundberg estimated values of \(\alpha = 1.79\) and \(\epsilon = 0.2\). From this model, to maximise income, the tax rate would have to be increased by 18.6p/£, but of that only 4.4p would effectively be collected, i.e. taxpayers would only receive 23p in public services for each additional £1.00 spent on income tax.