# A One-Period Model

We may explain this theorem in a one-period model intuitively. In the one-period model, the before-tax budget constraint is given as

Consumption c is equal to labor income, wL. Thus, the tax bases of consumption tax and labor income tax are the same. The after-tax budget constraint is

As long as Eq. (9.27) holds, both constraints, Eqs. (9.29) and (9.30), are the same. Hence, the economic effect of taxation is the same between t_{c} and t_{w}.

From Eqs. (9.29) and (9.30), it is easy to derive

The government collects the same tax revenue as long as condition (9.27) is satisfied.

Note that this equivalence result holds even if labor supply is endogenously determined. The disincentive effect of labor income tax on labor supply is the same as the disincentive effect of consumption on labor supply since the budget constraint is affected in the same way. Similarly, the disincentive effect of consumption tax on consumption is the same as the disincentive effect of labor income tax on consumption. Labor income tax does not have a stronger disincentive effect on labor than consumption tax. Similarly, consumption tax does not have a stronger effect on consumption than labor income tax. Both taxes are the same from the viewpoint of efficiency costs.