## Interest Rate Rules and Nominal Determinacy

### by John H. Boyd III and Michael Dotsey

Working Paper, University of Rochester, Revised: June 1996.

In this paper we analyze issues concerning nominal determinacy when the monetary authority uses the interest rate as either an instrument or intermediate target. Analysis of this issue requires the development of a more general framework for investigating the properties of linear rational expectations models. With this framework we are able to show the viability of certain classes of interest rate pegs. Acrobat PDF

## Dynamic Tax Incidence with Heterogeneous Households

### by John H. Boyd III

Working Paper, University of Rochester,
current version: January 1997

This paper examines the utility gains and losses induced by changes in capital taxation in an economy with heterogeneous discount factors. A Ramsey equilibrium, where households earn wage income and accumulate capital, but may not borrow against future wage income, provides a natural setting for this analysis. In the short run, the agents with little or no capital gain from increased transfers following an increase in taxation. In the long run, everyone loses as the capital stock declines. The households with little or no capital are poor because they are relatively impatient. As a result, they prefer to get the short-run gains from taxation, in spite of the long-run (and thus heavily discounted) losses. Acrobat PDF

## The Existence of Equilibrium in Infinite-Dimensional Spaces: Some Examples

### by John H. Boyd III

Working Paper, University of Rochester, Revised June 1995.

This paper presents some examples that clarify certain topological and duality issues concerning the existence of equilibrium in infinite-dimensional spaces. One is a finite-dimensional version of an example due to Araujo (1985). It shows that equilibrium and Pareto optima can fail to exist even in finite-dimensional spaces if certain continuity conditions and compactness are not met. Araujo's example is not peculiar to infinite-dimensional economies. Re-examination of an example of Zame (1987) shows that economically reasonable equilibria may well exist even though prices fail to lie in the dual space specified by Zame. This suggests that the theorems of Zame and others be read as giving conditions for the existence of equilibrium prices in a particular dual, rather than for existence of equilibrium in general. Acrobat PDF

## Reciprocal Roots, Paired Roots and the Saddlepoint Property

### by John H. Boyd III

Working Paper, University of Rochester, January 1989.

The usual proof of the saddlepoint property in optimal growth models is based on the reciprocal root property. That proof is incomplete. It assumes there are no multiple roots. This paper repairs both the continuous and discrete time versions of the proof. Under a symmetry condition, the reciprocal root property is usually combined with results from the theory of pencils of quadratic forms to establish the saddlepoint property. I employ a simple spectral mapping argument to characterize the saddlepoint property. Acrobat PDF