Progressive income taxation regimes can be modelled as a weighted portfolio of European Call options over an individual's gross taxable income. These options are struck at the tax bracket lower bound and weighted by the increment in the marginal tax rate. The government holds a long position in...

To compare the systems of child benefits and of family tax deductions, we create a model with endogenous fertility and a basic income, also financed from proportional wage taxes. The deduction's efficiency is presumably lower than the benefit's and may even be lower than that of pure basic income.