Larry E. Jones

A Convex Model of Equilibrium Growth: Theory and Policy Implications

Our aim in this paper is to exposit a convex model of equilibrium growth. The model has two features that distinguish it from most other work on the subject: first, that the model is convex on the technological side, and second, that fixed factors are explicitly included. Existence and characterization results are provided along with some preliminary analyses of taxation and international trade policies. It is shown that the long-run growth rate in per capita consumption depends, in the natural way, on the parameters describing tastes, technology, and policies. It is demonstrated that in a free-trade equilibrium with taxation, national growth rates of consumption and output need not converge.

Optimal Taxation in Models of Endogenous Growth

We study the problem of optimal taxation in three infinite-horizon, representative-agent endogenous growth models. The first model is a convex model in which physical and human capital are perfectly symmetric. Our second model incorporates elastic labor supply through a Lucas-style technology. Analysis of these two models points out the danger of assuming that government expenditures are exogenous. In our third model, we include government expenditures as a productive input in capital formation, showing that the limiting tax rate on capital is no longer zero. In numerical simulations, we find similar effects on growth and welfare in all three models.

The sources of growth

In this paper, we survey the principal theoretical models of endogenous growth and explore their common components through analyzing a series of planning problems. Our aim is to provide the reader with a consistent approach to the emerging literature on growth as an introduction to the field.

COMPLEMENTS VERSUS SUBSTITUTES AND TRENDS IN FERTILITY CHOICE IN DYNASTIC MODELS

The Barro-Becker model is a simple intuitive model of fertility choice. In its original formulation, however, it has not been very successful at reproducing the changes in fertility choice in response to decreased mortality and increased income growth that demographers have emphasized in explaining the demographic transition. In this paper we show that this is due to an implicit assumption that number and utility of children are complements, which is a byproduct of the high intertemporal elasticity of substitution (IES) typically assumed in the fertility literature. We show that, not only is this assumption not necessary, but both the qualitative and quantitative properties of the model in terms of fertility choice change dramatically when substitutability and high curvature are assumed. To do so, we first derive analytical comparative statics and perform quantitative experiments. We find that if IES is less than one, model predictions of changes in fertility amount to about two-thirds of those observed in U.S. data since 1800. There are two major sources to these predicted changes, the increase in the growth rate of productivity which accounts for about 90 percent of the predicted fall in fertility before 1880, and changes in mortality which account for 90 percent of the predicted change from 1880 to 1950.

Chapter 5 An Economic History of Fertility in the United States: 1826–1960

In this paper, we use data from the US census to document the history of the relationship between fertility choice and key economic indicators at the individual level for women born between 1826 and 1960. We find that this data suggests several new facts that should be useful for researchers trying to model fertility. (1) The reduction in fertility known as the Demographic Transition (or the Fertility Transition) seems to be much sharper based on cohort fertility measures compared to usual measures like Total Fertility Rate; (2) The baby boom was not quite as large as is suggested by some previous work; (3) We find a strong negative relationship between income and fertility for all cohorts and estimate an overall income elasticity of about −0.38 for the period; (4) We also find systematic deviations from a time invariant, iso-elastic, relationship between income and fertility. The most interesting of these is an increase in the income elasticity of demand for children for the 1876–1880 to 1906–1910 birth cohorts. This implies an increased spread in fertility by income which was followed by a dramatic compression.

Chapter 1 Neoclassical Models of Endogenous Growth: The Effects of Fiscal Policy, Innovation and Fluctuations

Despite its role as the centerpiece of modern growth theory, the Solow model is decidedly silent on some of its basic questions: Why is average growth in per capita income so much higher now than it was 200 years ago? Why is per capita income so much higher in the member countries of the OECD than in the less developed countries (LDC) of the world? In this chapter we review the recent literature on endogenous growth. We concentrate on convex models and we restrict attention to the case in which markets are competitive.After a brief review of the basic mechanisms that produces growth, we concentrate on three topics: the impact of fiscal policies on growth, the role of innovation and the relationship between uncertainty and growth.

Existence of equilibria with infinitely many consumers and infinitely many commodities: A theorem based on models of commodity differentiation

Abstract This paper presents a general result on the existence of competitive equilibria in exchange economies in which consumers and commodities are both infinite in number. The result shows that — in this framework at least — the added assumptions necessary to handle models with infinitely many agents are remarkably similar to the additional restrictions needed when only finitely many commodities are available for trade. It is shown that the results apply, in a straightforward manner, to two of the common models of consumer choice when commodity differentiation is an important consideration.

Complements Versus Substitutes and Trends in Fertility Choice in Dynastic Models

The Barro-Becker model is a simple intuitive model of fertility choice. In its original formulation, however, it has not been very successful at reproducing the changes in fertility choice in response to decreased mortality and increased income growth that demographers have emphasized in explaining the demographic transition. In this paper we show that this is due to an implicit assumption that number and utility of children are complements, which is a byproduct of the high intertemporal elasticity of substitution (IES) typically assumed in the fertility literature. We show that, not only is this assumption not necessary, but both the qualitative and quantitative properties of the model in terms of fertility choice change dramatically when substitutability and high curvature are assumed. To do so, we first derive analytical comparative statics and perform quantitative experiments. We find that if IES is less than one, model predictions of changes in fertility amount to about two-thirds of those observed in U.S. data since 1800. There are two major sources to these predicted changes, the increase in the growth rate of productivity which accounts for about 90 percent of the predicted fall in fertility before 1880, and changes in mortality which account for 90 percent of the predicted change from 1880 to 1950.

Existence of equilibria with infinitely many commodities: Banach lattices reconsidered

Abstract The purpose of this paper is twofold. The first aim is to present an extension of the results on the existence of Walrasian equilibrium to the infinite dimensional setting. The result depends on two crucial assumptions. These are the compactness of the collection of feasible allocations and the non-emptiness of the interior of the production set. The proof is a direct generalization of Bewleys (1972) proof for the L∞ case. The second purpose of this paper is to show that the recent result of Mas-Colell (1986) on the existence of equilibrium for exchange economies on Banach lattices can be obtained through an argument based on the result outlined above. That is, exchange economies on Banach lattices with ‘uniformly proper’ preferences behave as though they were production economies in which the production sets have non-empty interior.

The Characteristics Model, Hedonic Prices, and the Clientele Effect

In this paper, the characteristics model of Lancaster is reconsidered. It is shown by example that equilibrium prices need not be linearly decomposable. It does follow that equilibrium prices must be a convex function of characteristics, however. Further, it is shown that this fact holds independent of the form of firm competition (e.g., perfect or monopolistic). Finally, the predictions of the theory are discussed in the context of two empirical examples.