317_L5_Jan 16, 2008 J. Schaafsma 1 Review of the Last Lecture Are discussing the production function for health (section III of the course outline): HS=HS(HC) discussed the concept of an output elasticity for health and why one might want to estimate it discussed two problems that must be resolved if one is to estimate an output elasticity for health: - a proxy is needed for health status - must use regression analysis to isolate the impact of real healthcare spending on health status from all other effects Today begin by looking at empirical estimates of the output elasticity for health

317_L5_Jan 16, 2008 J. Schaafsma 2 Empirical Estimates of Output Elasticities Output elasticity estimates based on different proxies for HS (Text 3 rd ed., p See overhead transparency, Table 5.2): Proxy for HS: mortality rates (inverse measure of HS): Auster et. al (1969) U.S. statewide data Hadley (1982 and 1988) U.S. county data Proxy for HS: activity/mobility index Sickles and Yazbeck (1998) US data for individuals followed over time Note: 1.HC matters but we are nearly on the “flat of the curve”. 2.The production function shift variables are also important and their effect depends on gender and race (overhead transparency of Table 5.3, Text, 3 rd ed., p. 109 from Hadley (1982). ///

317_L5_Jan 16, 2008 J. Schaafsma 3 Substitution in the Production of Health As we have discussed, health can be produced in a variety of ways. This raises the possibility of substitution in production Two types of substitution: 1. Substitution in the production of health between spending on HC vs. spending on non-healthcare programs that improve health: examples: highway safety improvements, lifestyle modification, 2. Substitution among HC factor inputs e.g., substituting equipment for labour, substituting one type of labour for another (nurses for doctors) We’ll briefly look at both types of substitutions and the efficiency implications

317_L5_Jan 16, 2008 J. Schaafsma 4 Substitution across determinants of health status HC isn’t the only input into generating health. environment, socioeconomic characteristics, human biology etc also matter (production function shift variables) this raises the policy question of whether a given health status is best pursued with an expansion in HC or whether changes should be effected in one or more of the other influences on HS We will look briefly at highway safety and Lifestyle vs HC in achieving HS

317_L5_Jan 16, 2008 J. Schaafsma 5 Substitution between Healthcare Expenditures and Highway Safety goods: the Isoquant Map public health can be improved with more HC goods or with more highway safety goods let Q HCG be the quantity of HC goods, let Q HSG be the quantity of the highway safety goods assume that public health is proxied with the variable: life expectancy at birth Can draw an isoquant map (DIAGRAM)

317_L5_Jan 16, 2008 J. Schaafsma 6 The slope of the Isoquant The isoquants are convex (to the origin) due to the concept of diminishing MPP of both HC goods and highway safety goods the slope of an isoquant is ΔQ HCG / ΔQ HSG (Diagram) along an isoquant there is no change in output (same life expectancy) Thus: (ΔQ HCG ).MPP HCG + (ΔQ HSG ).MPP HSG = 0 (1) can solve equation (1) for the slope this yields slope = ΔQ HCG / ΔQ HSG = - MPP HSG / MPP HCG

317_L5_Jan 16, 2008 J. Schaafsma 7 The Budget Constraint let P HCG be the price of the healthcare good let P HSG be the price of the highway safety good Let the available funds be exp can draw the budget constraint cuts the vertical axis if all the funds spent on healthcare goods: exp/P HCG cuts the horizontal axis if all the funds spent on highway safety goods: exp/P HSG slope of the budget constraint is: rise/run = - (exp/P HCG )/(exp/P HSG ) = - P HSG / P HCG

317_L5_Jan 16, 2008 J. Schaafsma 8 Policy Options when Highway Safety and HC affect HS can draw the budget constraint on the isoquant map (diagram) allocating all the available funds to HC is inefficient! with the same expenditure can reach a higher life expectancy by shifting some funds to highway safety goods Alternatively, could opt for the same life expectancy but lower the cost of achieving it, spend the savings somewhere else efficiency in production occurs where the budget constraint is tangent to an isoquant

317_L5_Jan 16, 2008 J. Schaafsma 9 The Efficiency Conditions in Production recall that the slope of the isoquant is: - MPP HSG / MPP HCG Recall that the slope of the budget constraint is: - P HSG / P HCG since efficiency requires that the budget constraint be tangent to the isoquant the efficiency condition is: MPP HSG / MPP HCG = P HSG / P HCG (2) equation (2) can be rewritten as: MPP HSG / P HSG = MPP HCG / P HCG (3) equation (3) states that efficiency requires that the last dollar spent on each input creates the same addition to total output

317_L5_Jan 16, 2008 J. Schaafsma 10 Shifts in the Budget Constraint an increase in funding will: (i) result in increased spending on both healthcare and highway safety (ii) more output (longer life expectancy) So what should the funding level for HC and highway safety be????? => Depends on how we value life expectancy at the margin a change in relative input prices will change the factor input combination (as the price of healthcare goods rises relative to the price of highway safety goods => shift out of HCG into HSG (DIAGRAM) two reasons: 1. relative price effect 2. wealth effect

317_L5_Jan 16, 2008 J. Schaafsma 11 The Objective of Public Policy: Social Welfare Maximization have shown that a combination HCG and HSG can achieve a given HS at a lower cost than using all the funds for HC only => strong argument for finding the optimal allocation of the funds between HCG and HSG However, efficiency is not the ultimate objective of public policy social welfare maximization is the ultimate objective of public policy Social welfare depends on the utility (level of satisfaction or enjoyment in life) experienced by individual members of society and on the distribution of utility across the members. Individual utility depends on personal tastes and preferences, and on income

317_L5_Jan 16, 2008 J. Schaafsma 12 Does an Efficiency Gain Necessarily Result in a Social Welfare Gain? Might Argue (incorrectly): Shifting resources from HC to highway safety to lower the cost of achieving the current aggregate life expectancy must increase social welfare => HC and highway safety goods do not appear in an individual’s consumption bundle, and aggregate life expectancy which does, is unchanged Furthermore, the cost of achieving current aggregate life expectancy has decreased => taxes can be cut, or more public goods supplied => at least some people better off, no one worse off => Social Welfare increases THERE IS A PROBLEM WITH THIS ARGUMENT!!!

317_L5_Jan 16, 2008 J. Schaafsma 13 Efficiency Gains May Have distributional Effects The problem with the highway safety vs healthcare spending example in the preceding slide is that while aggregate life expectancy is not changed by the substitution of highway safety goods for HCG, the life expectancy of groups within society likely changes safer highways mean a lower death rate for reckless drivers, but this comes at the expense of less healthcare, and thus a higher death rate, for those struck by illness/disease. There is a redistribution of life expectancy across these two groups, while the average remains the same (same isoquant) Is this redistribution Social welfare enhancing or reducing?

317_L5_Jan 16, 2008 J. Schaafsma 14 Redistribution and Social Welfare A move to greater efficiency in the combination of HCG and HSG has a positive effect on social welfare from lower cost production and thus lower taxes and/or more public goods the move to more efficiency may also redistribute personal utility across society This redistribution may increase or reduce social welfare It increases social welfare if the redistribution is consistent with social preferences, it reduces social welfare if it goes against social preferences The positive social welfare gain from greater efficiency could thus be offset by an adverse redistributional effect => Social Welfare could decline despite the efficiency gain!