1. 317_L7_Jan 22, 2008 J. Schaafsma 1 Review of the Last Lecture Are discussing the production of health: section III of the course outline have discussed the aggregate production function HS=HS(HC) and some of its properties have discussed substitution in production between HC and Non-HC goods (looked at highway safety and lifestyle) began our discussion of substitution in production between different healthcare goods doctors and nurses => finish this today then begin our discussion of the demand for healthcare

2. 317_L7_Jan 22, 2008 J. Schaafsma 2 Substitution between Healthcare Goods Now consider that HC is not a homogeneous good => consists of many components: doctors, nurses, hospital beds etc. Question is: is there substitutability in production across these HC inputs? e.g., can nurses substitute for doctors, or can equipment substitute for labour input, etc.? Can draw the isoquant diagram using doctors and nurses time as inputs: fixed factor proportions or substitutability at the margin? Expect some substitutability => US studies suggest that properly trained nurses could substitute for 25 – 50 % of doctor’s services without loss of quality.

3. 317_L7_Jan 22, 2008 J. Schaafsma 3 Can we be Confident that the Combination of HC goods is Efficient? can we be confident that the combination of nurses and doctors time is efficient, i.e., that at the current combination the budget constraint is tangent to the isoquant (diagram) if yes => we are getting the maximum HS for our expenditure on doctors and nurses if no => we can in principle reallocate the funds to achieve the same HS at a lower cost

4. 317_L7_Jan 22, 2008 J. Schaafsma 4 Empirical Evidence: the ratio of Doctors to Nurses is too High empirical evidence suggests that the current combination of doctor/nurses inputs is inefficient could substitute lower cost nurses’ time for some doctors’ time without lowering HS outcomes (DIAGRAM) why does this inefficiency exist? likely reason => tradition and physician preferences, not relative factor prices, determine factor input combinations (we’ll return to this later in the context of modeling the practitioner firm)

5. 317_L7_Jan 22, 2008 J. Schaafsma 5 The Demand for Health and Health Care NEW TOPIC Section IV of the course outline Subsection 1. The Demand for health main focus of subsection 1 : the Grossman model of the demand for health capital.///

6. 317_L7_Jan 22, 2008 J. Schaafsma 6 Health Capital and Health Status The demand for HC is a derived demand, i.e., derived from the demand for health. (HC only yields to the extent health status improves) Two aspects to the concept of health: health capital (HK) and health status HS refers to how your health is at a point in time (flow). HK refers to your ability to fight off disease and to function physically at a high level (stock). can think of HS as a function of HK, i.e., HS = HS(HK,  ), where  (epsilon) is a random error term capturing the effect of illness. In the absence of illness HS is at its highest for any given HK. To understand the demand for HC, first consider the demand for HK.///

7. 317_L7_Jan 22, 2008 J. Schaafsma 7 The Grossman Model The Michael Grossman model of the demand for health capital (1970) is a constrained utility maximization model In this model utility is a function of three variables: HK, consumption of non-HC goods (NHC), and leisure time. L., i.e., U = U(HK, NHC, L) We will simplify the model by assuming that that there is a standard work week, i.e., L is fixed (not a choice variable) and therefore drops out of the analysis. The simplified utility function is thus U = U(HK, NHC) Utility is maximized subject to a consumption-possibilities boundary, CPB.///

8. 317_L7_Jan 22, 2008 J. Schaafsma 8 The Consumption-Possibilities Boundary in the Simplified Grossman Model The consumption-possibilities boundary (CPB) in the simplified Grossman model shows a person’s maximum possible consumption of NHC goods for each value for HK. (Diagram) ( It is a boundary on a set of choices, not a causal relationship!!) This boundary starts at some minimum positive values for both HK and non-HC goods, rises, reaches a maximum and then declines. The CPB shows that there is an initial range where the person can have more of both goods, NHC and HK! This is unusual! Normally a person can only get more of one good by giving up units of another good.

9. 317_L7_Jan 22, 2008 J. Schaafsma 9 The Reason for the Initial Positive Slope of the CPB The slope of the CPB is initially positive because HK is an investment good, as well as a consumption good. It is a consumption good because it yields satisfaction directly through HS It is an investment good because it yields satisfaction indirectly. Healthier people are more productive (less time off sick and higher wage rate) and earn more and can thus consume more. The +ve slope of the CPB occurs because initially spending some non-leisure time and money on healthcare increases productivity by so much that both the stock of HK and the consumption of NHC rise. ///

10. 317_L7_Jan 22, 2008 J. Schaafsma 10 Example of Why the CPB May Rise Initially Suppose that without any time or money spent on HC a person is off work 20 days a year due to ill health and is docked pay for those days. Now suppose that over the course of the year this person spends the equivalent of one day’s pay on HC and as a result reduces time off work due to illness by 3 days => net gain of two days pay. by allocating a day’s pay to the consumption of HC the person will have both a higher HK (or HS) and a higher consumption of NHC (since earnings are higher).///

11. 317_L7_Jan 22, 2008 J. Schaafsma 11 The CPB Peaks at Some Point As the amount of HC consumed increases the CPB will continue to rise but at a decreasing rate until it peaks. Reason: Due to the diminishing MPP of HC an outlay in time and money on HC yields ever smaller gains in HK and therefore exerts an ever smaller +ve effect on income and thus on NHC. Eventually the CPB reaches a maximum, i.e., the additional income attributable to the improved HK is exactly offset by the cost of the additional HC to achieve the higher HK. Higher levels of HK can be achieved, but only by foregoing NHC goods and services.///

12. 317_L7_Jan 22, 2008 J. Schaafsma 12 Why Is It a Consumption Possibilities BOUNDARY? The CPB locus is a boundary to the set of NHC and HK combinations that are available for consumption. Any combination below the boundary is available for consumption Any combination on the CPB is also also available for consumption Combinations above the CPB are not available for consumption, i.e., they are not consumption possibilities. Each person has his/her CPB that reflects his/her ability to produce HK, this productivity depends on the person’s characteristics, which determine the choices they make Given the person’s characteristics, HK is produced efficiently if the consumption bundle of HK and NHC goods lies on the CPB. Explain.

13. 317_L7_Jan 22, 2008 J. Schaafsma 13 Choosing the Optimal Point on the CPB In order to choose the optimal point on the CPB an indifference curve map is needed Each curve in the map shows the combinations of HK and NHC goods that yield the same level of satisfaction. Can draw two types of indifference curves to solve the Grossman model In one type, HK is only demanded for its investment good aspect (for its impact on productivity) In the other type, HK is not only an investment good but also yields consumption benefits directly

14. 317_L7_Jan 22, 2008 J. Schaafsma 14 Optimal HK If There Is Only an Investment Demand for HK. If there is no consumption demand for HK, only an investment demand (for HK’s effect on income) the indifference curves are horizontal (if NHC is measured along the vertical axis) (DIAGRAM) Utility maximization occurs where the CPB is is tangent to the highest flat indifference curve, i.e., where it reaches a peak At this HK the last dollar spent on HC causes income to rise by one dollar, and there is thus no change in the ability to purchase NHC goods. pursuing HK beyond this point would require spending more on HC (investment in HK) than one gets back in additional income and thus would result in a decline in the consumption of NHC.

15. 317_L7_Jan 22, 2008 J. Schaafsma 15 The indifference curves when HK is both and investment and consumption good It is unlikely that the consumer will choose the HK that maximizes the consumption of NHC goods! WHY? Health capital also has yields benefits directly in consumption When this happens the indifference curves have the normal convex to the origin shape. (DIAGRAM)

16. 317_L7_Jan 22, 2008 J. Schaafsma 16 Optimal HK When HK Is Both an Investment and a Cons’n Good. When there is also a consumption demand for HK the consumer chooses the combination of HK and NHC that maximizes utility. This is not the (HK, NHC) combination where NHC is a maximum (see diagram) Rather a higher level of utility can be achieved by trading off some NHC goods for more HK. (see diagram of indifference curves superimposed on the CPB). Once the utility maximization problem has been solved, the utility maximizing HK is determined. Associated with it is an efficient consumption of HC to sustain it.///