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The purpose of this paper is to explore the manner in which the degree of substitutability between public and private health expenditures contributes towards the distribution of wealth and political economy outcomes in the long run.

An overlapping generations model with heterogeneous agents where a person’s probability of survival into old age is determined by a variable elasticity of substitution (VES) health production function with public and private expenditures as inputs is developed. Public expenditure on health is determined through a political economy process.

Analytical and numerical results reveal that higher substitutability between private and public expenditures at the aggregate level and a higher share of public spending in the production of health lead to higher long run wealth levels and lower inequality. In the political equilibrium, higher aggregate substitutability between public and private health expenditures is associated with more tax revenue allocated towards public health. For most parameter combinations, the political economy and welfare maximising proportions of tax revenue allocated towards public health care converge in the long run.

The paper is a theoretical investigation of how substitutability between public and private health expenditures affect transitional and long run macroeconomic outcomes. These results are amenable to further empirical investigation.

The findings indicate that policies to improve institutional aspects that yield higher substitutability between public and private health expenditures and returns to public health spending could lead to better long run economic outcomes.

The results provide a political economy explanation for the low investments in public health care in developing countries, where aggregate substitutability between public and private health expenditures is likely to be lower. Furthermore, comparing the political economy and welfare maximising paradigms broadens the scope of the framework developed herein to provide potential explanations for cross-country differences in health outcomes.

This paper adopts an innovative approach to exploring this issue of substitutability in health expenditures by introducing a VES health production function. In an environment where agents have heterogeneous wealth endowments, this specification enables a distinction to be made between substitutability of these expenditures at the aggregate and individual levels, which introduces a rich set of dynamics that feeds into long run outcomes and political economy results.

The purpose of this paper is to explore the properties of the variable elasticity of substitution (VES) production function, and examine the dynamics of growth associated with it.

The VES production function is incorporated into an otherwise standard Diamond overlapping generations model.

Depending on parameter combinations, the economy can achieve a unique and stable steady state akin to that observed in the Solow-Swan model, reach a poverty trap or transition towards an upper bound of per capita capital stock. A special case of the VES production function is also consistent with unbounded growth.

The paper is theoretical in nature. Further empirical analysis could shed deeper insights into the results presented in this study.

The VES production function, when applied to the context of the Diamond model, can capture a variety of growth experiences observed in the empirical literature.

In the context of the Diamond model, a higher value of a particular parameter in the production function leads to greater intergenerational income and consumption inequality. Hence, the study provides a potential explanation for intergenerational inequalities observed in practice.

The study demonstrates the empirical value of the VES production function in explaining observed differences in factor shares, rewards and elasticities within and between countries over time.