Question

2. Using Grossman’s pure investment model of the demand for health, consider the impact of the following on the marginal efficiency of investment (MEI) and related optimal health stock (include a graph in your explanation):

a. Rather than having stopped school with a high school diploma, by age 22 Poppy obtained an undergraduate degree in public health. How would this education decision impact her optimal level of health?

b. Suppose that after age 22 her wage rate stayed the same, what happens to her optimal stock of health capital by age 30?

Answer 1

2.a)

In the model developed by Grossman, the demand for health care is determined by marginal efficiency to invest (MEI). The MEI is the negative relationship between cost of capital (which is rate of return plus depreciation) and stock of capital. The curve depicts that as cost of capital increases the stock of health falls. The equilibrium occurs where cost of capital intersects the MEI curve.

The MEI curve for the consumer is given in the figure below by MEI. The cost of capital curve is given by the straight line parallel to the x-axis given by . Given this John’s optimal health stock H₀ determined by the intersection between cost of capital and MEI curve at point A.

In the study of demand for health, higher education is most often related to better health. The education may improve the efficiency with which one can produce investment to health and home goods. The education increases wage and shifts MEI curve upward.

Suppose the consumer earns a higher wage, it will instantly increase his return from given investment and MEI curve will shift upward to MEI’. Given the cost of capital the equilibrium occurs at B, her optimal health stock increases to H₁.

Now as her age increases to 22, consumer's health depreciates with age; then the cost of capital increases to . The cost of capital line shifts up to. This causes her equilibrium to move up along the MEI’ curve to C and Sara’s optimal health stock decreases to H₂. Now if this decrease outweighs the increase in health stock due to increased wage; her optimal health stock falls than before. In both cases the increase in health stock due to increased wage is dampened by the cost of depreciation.

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b)

Capital slowly loses its value and productive capacity, wears out, and becomes obsolete as the time progresses. This deterioration of value is called the depreciation of capital. Like all other capital health also depreciates by the time. The health stock of a consumer can fall overtime. The decrease in health stock overtime is called the depreciation of health capital. It can happen slowly with growing age as older people are prone to various diseases and tend to lose strength. If we consider human body as a machine, it loses its working ability with age just like a machine. So, with age the health capital decreases. The health can depreciates rapidly with illness or injury just like a machine with broken or damaged parts.

Now as her age increases to 22, consumer's health depreciates with age; then the cost of capital increases to. The cost of capital line shifts up to. This causes Sara’s equilibrium to move up along the MEI curve to B and Sara’s optimal health stock decreases to H₁.