In: Economics
Walras’ Law
In class, for the definition of tax distorted competitive equilibrium, I stated that the prices and allocations must satisfy the government budget constraint. Show that this requirement is redundant.
According to general equilibrium theory, Walras law implies that value of excess demand must add up to zero. Excess demand implies that aggregate demand is greater than aggregate supply at specific prices.
A government budget constraint consists of government purchases which are financed by lump-sum taxes and by issuing one period bond. Considering intertemporal government budget constraint, the present discount value of government purchases equals the present discount value of tax revenues. Now the tax distorted competitive equilibrium prices remain optimal given tax rates implies all that is relevant for determination of consumption, leisure and prices are the present value of government purchases. and the timing of taxes is irrelevant. This is stated in the Ricardian equivalence theorem.
Also note that when a representative firm receives a tax cut today, he or she knows that they will have to pay a higher tax in the future. Hence, the government creates debt today in order to finance an increase in government purchases.