1 Jan 19, 2005, lecture 6, J. Schaafsma 1 Review of the Last Lecture * began our discussion of the demand for HC * the demand for HC is a derived demand (from demand for HK) * discussed the difference between HK (a stock) and HS (a flow) * began our discussion of the Grossman model of the demand for HK * today consider a simplified version of the Grossman model Grossman model Jan 19, 2005, lecture 6, J. Schaafsma 2 The Grossman Model * The Michael Grossman model (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./// Jan 19, 2005, lecture 6, J. Schaafsma 3 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. (see blackboard) * This boundary starts at some minimum positive values for 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./// Jan 19, 2005, lecture 6, J. Schaafsma 4 Understanding the Shape of the CPB * The positive slope of the CPB occurs because in the Grossman model HK is an investment, 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. /// 2 Jan 19, 2005, lecture 6, J. Schaafsma 5 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 is off work only 5 days per year due to illness. * 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)./// Jan 19, 2005, lecture 6, J. Schaafsma 6 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./// Jan 19, 2005, lecture 6, J. Schaafsma 7 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. * If HK is produced efficiently (i.e., with the lowest cost combination of HC goods and own time) the person will be on the CPB. * If HK is produced inefficiently the consumption bundle of HK and NHC goods will lie below the CPB. Explain. /// Jan 19, 2005, lecture 6, J. Schaafsma 8 Optimal HK If There Is Only an Investment Demand for HK. * If there is no consumption demand for HK, only an investment demand, the consumer will choose HK where the consumption of NHC goods is at a maximum. * This occurs where the CPB reaches its peak., i.e., where the improvement in HK as a result of 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 than one gets back in additional income and thus would result in a decline in the consumption of NHC. * It is unlikely that the consumer will choose the HK that maximizes the consumption of NHC goods! WHY? /// 3 Jan 19, 2005, lecture 6, J. Schaafsma 9 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./// Jan 19, 2005, lecture 6, J. Schaafsma 10 Shifts in the CPB and the Demand for HK: Education * Suppose the consumer acquires more education but everything else, including the wage rate, stays constant. How will this affect the demand for HK? * KEY POINT: better educated consumer => more efficient producer of HK (healthier lifestyle, more efficient HC choices) => spend less on HC to achieve a given HK => spend less on HC to achieve the next unit of HK * Thus the CPB will: shift up, be steeper, reach a peak at a larger HK, and have a flatter downward sloping arm ( see diagram). /// Jan 19, 2005, lecture 6, J. Schaafsma 11 The Income and Price Effects: Education * Education ~> CPB shifts ~> income and price effects on the demand for HK * The income effect: better educated => more efficient producer => higher cons'n of NHC goods at any level of HK larger budget to allocate than before => consume more of all goods => HK is a good => more HK consumed. * The Price Effect: opportunity cost of HK (amount of NHC goods that needs to be given up for one more unit of HK) , i.e., the price of HK in terms of NHC goods ~> consumer selects more HK * Note: income and price effects work in the same direction.///