ECO 7550 - Lecture 4

1. ECO 7550 - Lecture 4 Grossman Model Chapter 7

2. Grossman Model Labor-Leisure Choice Labor Leisure Trade-off Optimization in a Single Time Period What is Impact of Health? (A> Shifts out Budget Constraint) Investment Decision Book example Cost of Capital Optimal Investment Rule Grossman's Model How do we allocate resources to health and non-health activities in a given period? How do we allocate resources to health and non-health activities over time?

4. Demand for Health Care as Derived from Demand for Health Early work found that some of the things that we might have expected, did not necessarily occur. If we look at the demand for medical care inputs, we might expect that some fairly normal types of things would occur. If we do: QD = QD (p, y, Educ, Age, ...)

5. Labor-Leisure Tradeoff Let's start first with some review of the labor-leisure trade-off. In the simplest case, we can speak of an individual with 365 days/year. However, the individual is typically sick 10 days per year, so there is only 355 days available.

6. Comparative Statics Increase in dividend income.

7. Comparative Statics Increase in wage rate

8. How health comes in Even within this simple diagram, we might consider the impacts of improved health. What are they? A.1> More healthy time (shifts out LL curve) A.2> Increased productivity (increases wage) This kind of analysis suggests that we want to consider a whole set of individual decisions about allocating resources. Within a given period, we want to ask: amount of labor, leisure, income division of leisure into health and non-health activities division of income into medical and non-medical goods combination of time and goods into health and �bread� how these vary over time

9. Discounting and the Evaluation of Health Care Investments Since the investment aspect to health expenditure is critical to the model of demand for health capital, it is appropriate to discuss the evaluation of investments. Economists are often asked to compare investments that provide different streams of income over a number of periods. Why, for example, should George pay for a physical check-up (Investment H), when instead he can have his car serviced (Investment S) for the same cost.

10. Evaluating Investments Compare Investment H, which provides $20 at the end of Year 1, and $20 at the end of Year 2, with Investment S, which provides $28 at the end of Year 1, and $11 at the end of Year 2.

11. Evaluating Investments Compare Investment H, which provides $20 at the end of Year 1, and $20 at the end of Year 2, with Investment S, which provides $28 at the end of Year 1, and $11 at the end of Year 2.

12. Investment Over Time - (Cost of Capital) Since health is a capital good, it is necessary to understand the cost of capital as well as the capital good demand process. A health clinic, for example, purchases hundreds of thousands of dollars of X-ray equipment. The return to the X-ray equipment is in the future earnings that ownership of the equipment can provide. Suppose that an X-ray machine costs $50,000, and that its price does not change over time. Suppose that the annual income attributable to the use of the X-ray machine is $10,000. Is this a good investment? What did the capital cost (e.g. what did we GIVE UP because we purchased the capital?) How to consider: Suppose that instead of purchasing the X-ray machine the clinic could have put the $50,000 in a savings account, at 5 percent interest, yielding:

13. Cost of Capital 50,000 * 1.05 = 52,500, at the end of Year 1. 52,500 * 1.05 = 55,125, at the end of Year 2. 55,125 * 1.05 = 57,881, at the end of Year 3. 57,881 * 1.05 = 60,775, at the end of Year 4. 60,775 * 1.05 = 63,814, at the end of Year 5. For the investment in an X-ray machine to be desirable by these criteria, it should provide at least $13,810 in incremental revenue over the five years.

14. Cost of Capital The problem is more complicated, however, because most capital goods depreciate over time. Suppose that the clinic knows that the X-ray machine will wear out (or depreciate), so that after five years, it will be worth only half its original value. The clinic must earn enough not only to cover the opportunity cost from the bank, but also to maintain the value of the machine. For the investment to be worthwhile, then, it must not only earn the competitive 5 percent return each year, but it must also provide enough return to cover depreciation of the machine.

15. Depreciation Applies of course to other goods, and the depreciation may be economic. Consider desktop computers or printers. What is a 5 year old computer worth? Why? If we do not put aside funds to replace it, it will be economically useless after 5 years. Why?

16. Cost of capital This suggests that the cost of holding this capital good for any one year, as well as over time, will equal the opportunity cost of the capital (interest foregone) plus the depreciation (deterioration of value). Had the price of the asset changed, leading to capital losses or gains, this feature too would have to be considered. How do we consider this? <A> If there is an expected capital gain, we expect a lower cost of holding the capital.