## Division Rules, Network Formation, and the Evolution of Wealth

### by Nejat Anbarci and John H. Boyd III

Working Paper, Florida International University, August 2005.

In our model, each of *n > 2* agents is endowed with an exogenous
amount of initial wealth. Each individual may establish at most one link
with any agent he prefers each period. A surplus will be generated from
each link and the agents involved in that link will bargain over its
division. The payoffs obtained by an agent at each period will be added to
the existing wealth (ideal payoff) level of the agent. Suppose in a society
(or in a group of individuals), all agents adhere to a particular division
rule.

A variety of long-run wealth distributions can arise, depending on the division rule and initial wealth distribution. These can range from situations where the richest agent remains richest to cases where the poor are continually becoming rich. We examine several division rules in detail: egalitarian, equal sacrifice, proportional, dictatorship of the rich, dictatorship of the poor.

From the analysis of these cases, we find that two factors determine the long-run wealth distribution: the size of the gain from a link, and the incentive to link to rich or poor. Acrobat PDF

## Sustained Growth with Heterogeneous Households

### by John H. Boyd III

Working Paper, Florida International University, June 2000.

I examine a model where agents differ in their discount factors. It has long been known that in the long-run, the most patient household or individual ends up owning all the capital, provided there is a maximum sustainable stock. I show that this is no longer true when there is sustained growth. I examine a model where there is endogenous growth due to learning-by-doing, the “Arrow-Romer” model. It is still the case that one household ends up with all the capital, but that household is no longer necessarily the one who has the lowest discount rate. The appropriate measure of impatience depends not just on the discount rate, but also on the form of the felicity function, and the technology. Different technologies can lead to a re-ranking of the households. In some cases, different technologies can even completely reverse the patience ordering, and alter the long-run distribution of capital. There is even the possibility that the most patient household may change depending on the state of development of the economy, causing capital to shift from one household to another as the economy develops. Acrobat PDF

## 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