Useful Public Spending, Taylor Principle, and Macroeconomic Instability

This paper analyzes the stationary welfare and local stability implication of useful public spending in a discrete‐time one‐sector monetary economy with Taylor rule. Public spending, financed through a flat income tax, is useful and exerts externalities on production. In our economy, money is needed for transaction purposes. We show that the introduction of a public spending exerting externality in the production may lead to multiplicity and indeterminacy. When the externality in production is low enough, under a passive interest rate feedback rule, two steady states emerge and could be either locally determinate or indeterminate, depending on the interplay between the intertemporal elasticity of substitution of consumption and the elasticity of the interest rate, while under an active interest rate feedback rule, two interior locally determinate steady states and two liquidity trap locally determinate steady states exist. When externality in production is high enough, a unique local determinate interior steady state occurs, while under an active interest feedback rule, a unique liquidity trap steady state and a unique interior steady state occur, and both are locally determinate. When both two interior steady states and two liquidity trap steady states exist, when the capital stock is low, the interior steady state has a higher level of capital than the one of the liquidity trap, while, when the capital stock is high, it is the liquidity trap steady having a higher level of capital. Finally, liquidity trap equilbria Pareto‐dominate the interior equilibria in view of the zero cost of money.