Health, Lifestyle and Growth

Abstract

In this article, I attempt to explain why lifestyle may have a positive impact on economic growth. First, I consider the ways in which health affects a consumer’s utility, and I then define a Health Production Function for which health is the output and consumer good is the input. In this approach, the Lifestyle Return to Scale (LRS) parameter is defined. The first result is that an increase in a consumer’s personal income may have a positive or a negative effect on health. That is, health may be a normal or an inferior good, depending on the Lifestyle Return to Scale value. According to this result, I compute a health multiplier and then modify the Solow Growth Model in which health is labour-augmenting. The result is a model in which the Lifestyle Return to Scale positively affects per capita income and per capita income growth.

Appendix

1.1 A Generalization of Wagstaff’s Model

Starting with Michael Grossman’s Model (1972) and Wagstaff (1986) developed a one-period model of demand for health. The four hypotheses of the model include the following: (1) an individual’s health is determined by the consumption of health inputs $h\left( x \right) = x^{\rho } ;$ (2) preferences are non-lexicographic: individuals desire health but not above everything else; (3) individuals also consume other commodities that have a positive cost for consumers, so $U = u\left( {h,z} \right)$ with $\frac{dU}{dh},\frac{dU}{dz} > 0$ and $\frac{{d^{2} U\left( {h,z} \right)}}{dh},\frac{{d^{2} U\left( {h,z} \right)}}{dz} < 0;$ and (4) consumers have limited economic resources or budget constraints: $p_{x} x + p_{z} z = Y,$ where $p_{x}$ and $p_{z}$ are the prices of commodities x and z, respectively, and Y is the income.

Assuming a Cobb Douglas Utility function and a Health production function $h\left( x \right) = x^{\rho } ,$ the Wagstaff Model can be formulated with the following formulas:

$$ U\left( {h,z} \right) = h^{\alpha } z^{\delta } $$

(2.32)

$$ h\left( x \right) = x^{\rho } $$

(2.33)

$$ p_{x} x + p_{z} z = Y $$

(2.34)

where $0 < \alpha < 1$ and $0 < \delta < 1$ are the utility elasticities with respect to x and z, respectively, and $0 < \rho < 1$ is the elasticity of h with respect to x.

This is a special case of the Consumer’s model (Sect. 2) with $\beta = 0.$ The commodity x is not in the Consumer’s utility function with $\left( {\gamma = 0} \right);$ thus, z does not affect health.

The solutions can be obtained from two different methods. The first was proposed by Wagstaff:

$$ \mathop {\max }\limits_{h,z} U\left( {h,z} \right) = h^{\alpha } z^{\delta } \,{\text{s}} . {\text{t}} .\,p_{x} h^{ - \rho } + p_{z} z = Y $$

(2.35)

In this case the Budget Constraint is not linear. The consumer chooses between health and z. The second possible solution is

$$ \mathop {\max }\limits_{x,z} U\left( {x,z} \right) = x^{\rho \alpha } z^{\delta } \,{\text{s}} . {\text{t}} .\,p_{x} x + p_{z} z = Y $$

(2.36)

The consumer chooses the quantities of x and z that maximize utility.

Both methods yield the same solutions:

$$ x = \frac{\alpha \rho }{\delta + \alpha \rho }\frac{Y}{{p_{x} }} $$

(2.37)

$$ z = \frac{\delta }{\delta + \alpha \rho }\frac{Y}{{p_{z} }} $$

(2.38)

$$ h = \left( {\frac{\alpha \rho }{\delta + \alpha \rho }\frac{Y}{{p_{x} }}} \right)^{\rho } $$

(2.39)

The main differences include the following: (1) in the Wagstaff model, Health can only be a normal good because $\frac{dh}{dy} > 0$ (conversely, in the model proposed in this paper, Health may also be an inferior good), and (2) this result depends on the lifestyle of the consumer.