# Laffer Curve

### United Kingdom (2013)

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.