October 13 Handout Definition of a Competitive Equilibrium with Government Borrowing

A competitive equilibrium with government borrowing is a set of interest rates

{r(1), r(2), r(3). ... },
a consumption allocation
{ch1(1), ch2(2), ch3(3), ... }    "h
{ch0(1), ch1(2), ch2(3), ... }    "h,
and a government policy
{G(1), G(2), G(3), ... }
{B(1), B(2), B(3), ... }
{th1(1), th2(2), th3(3), ... }    "h
{th0(1), th1(2), th2(3), ... }    "h,
such that the goods market clears in every period, the market for private borrowing and lending clears in every period, the government bonds market clears in every period, consumers maximize their utility subject to their budget constraint and the government policy satisfies the goverment's budget constraint in every period.



Ricardian Equivalence, MW p.71

Given an initial equilibrium under some pattern of lump-sum taxation and government borrowing, alternative (intertemporal) patterns of lump-sum taxation that keep the present value (at the initial equilibrium's interest rates) of each individual's total tax liability equal to that in the initial equlibrium are equivalent in the following sense. Corresponding to each alternative taxation pattern is a pattern of government borrowing such that the initial equilibrium's consumption allocation, including consumption of the government, and the initial equilibrium's gross interest rates are an equilibrium under the alternative taxation pattern.


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