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.