# The Demand for health and healthcare - Grossman Model

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The Demand for health and healthcare - Grossman Model
Dr Emma Frew Health Economics Unit Medical School

Learning objectives How individuals allocate their resources to produce Health – role of age, wage and education Cost of Capital and Marginal Efficiency of Investment (MEI) Understand how the four-quadrant Grossman model works

Outline MEI Changes in equilibrium due to age, wage and education
Depiction of integrated Grossman model

Demand for Health Capital (1)
Individuals invest in themselves through education, training and health. The goal is to increase earnings Two important concepts: Cost of Capital and MEI Cost of Capital (C) C = Opportunity cost (cost of foregone alternatives i.e. interest rate) + rate at which capital good depreciates C = r + δ

Demand for Health Capital (2)
MEI – Rate of return vs amount of resources invested If rate of return on capital good is greater (less) than cost of capital, then the good will (not) be purchased. Capital good will be purchased only up to point where: Rate of return = Cost of Capital

Relationship of healthy days to Health stock
Hmin Health Stock See Murray et al (2003) p9

Production of Healthy Days
Health is a productive good which produces healthy days Greater health stock leads to more healthy days – however with diminishing returns Hmin is health stock minimum – production of healthy days at this point is zero i.e. death Natural Maximum of 365 days See Murray et al (2003) p9

Optimal Health Stock Cost of MEI Capital r + δ0 A Health H0 Stock
See Murray et al (2003) p9

MEI If cost of capital is r + δ0 , then the optimal quantity of capital is H0, A represents the point of equilibrium An x-ray machine that costs £50,000 and has 20 % rate of return (£10,000) will only be purchased if (r + δD) ≤ £10,000 A 2nd machine will only be purchased if its rate of return ≥ (r + δD) Diminishing Marginal Returns to investment - The rate of return of a 2nd machine would probably be less than the first, therefore MEI is downward sloping See Murray et al (2003) p9

Practical questions What effect on optimal health stock or demand for health inputs do the following have: Increases in life expectancy? Getting a higher salary? Going to college? See Murray et al (2003) p9

Changes in Equilibrium - Age
The rate at which health stock may depreciate may increase during some periods of life and decline during others. As an individual ages the δ rate of health stock is likely to increase (from δ0 to δ1 and finally to δD) i.e. the health of older individuals is likely to deteriorate faster than the health of younger individuals. Assume that wage and other factors determining MEI are not substantially altered by aging Optimal health stock decreases with age (i.e. HO > H1)

Changes in Equilibrium - Age
Cost of MEI Capital B r + δD r + δ1 r + δ0 A Health Hmin H H Stock See Murray et al (2003) p9

Changes in Equilibrium - Wage
Wage change will not affect cost of capital (r + δD is constant) Increased wage rate will increase returns obtained from health days, hence a higher MEI curve i.e. 8 £4/hr = £36 8 £5/hr = £40 If original MEI curve represents lower-wage case, then optimal health stock is HO . MEI2 shows MEI for someone with higher wages, with higher optimal health stock (H2) Optimal health stock increases with level of wages (i.e. H2 > H0). Benefits of being healthy are greater for higher-wage workers

Changes in Equilibrium - Wage
Cost of MEI Capital MEI2 C r + δ0 A Health H H2 Stock See Murray et al (2003) p9

Changes in Equilibrium – Education
Education improves efficiency in production Higher education level raises marginal product of direct inputs i.e. less inputs are needed to produce a given amount of investment. A given investment can be generated at less cost for an educated person , hence higher rate of return to a given stock of health Higher education level means a higher MEI curve (similar to effect of increased wage rate). Optimal health stock increases with level of education (i.e. H2 > H0). A more educated person will choose a higher optimal stock of health than the less educated person.

Changes in Equilibrium – Education
Cost of MEI Capital MEI2 C r + δ0 A Health H H2 Stock See Murray et al (2003) p9

The Integrated Grossman Model (1)
In maximising utility subject both to time and money in a given period, a consumer must: Allocate time between work and leisure Spend remaining leisure time on health and nonhealth activities Spend income earned on health (medical) and nonhealth (e.g. baking) resources Produce health capital that may help in future years See Murray et al (2003) p9

The Integrated Grossman Model (2)
Quadrant 1 labour-leisure trade-off with respect to allocation of time to wage-earning activities Budget constraint (BC-BC) indicates trade-off between labour and leisure (steeper line indicates higher wages) Slope of indifference curve (U1) shows consumer’s subjective trade-off between leisure and earnings Consumer’s optimal division between market work (TW) and leisure is equilibrium point A – Assuming no days are lost to illness (TL), he will work for (365-OT*) days and earn income G* [to be spent on medical inputs (for health production) and home good inputs]

The Integrated Grossman Model (3)
Quadrant 2 Trade-off between health investment (I) and home good (B) given consumer’s income and time Consumer divides his time and money in producing I and B based on his preferences & his productivity The Production Possibility Curve (PPC) shows all efficient combinations of I and B that can be produced when all of consumer’s income (G*) and time (OT*) are used to their full potential

The Integrated Grossman Model (4)
Quadrant 4 Shows production of either I or B based on his preferences Width of ‘Edgeworth box’ is amount of time remaining after allocation of time between work and leisure and height is income that was earned Contract curve – shows only combinations that are efficient for consumer to produce I or B If he spends no time or money on health, he spends all of both on B and is at O; if he spends all his money (G*) and time (TH=nonwork time) on health, he is spending none on B and is at southeast corner of box

The Integrated Grossman Model (5)
Quadrant 3 Relates medical expenditure (M) to level of health investment (I) If he spends TH time and M* amount of money on producing health, then I* level of health investment will be made Note that he will spend (OT*- TH) on, and invest B* in, the home good The higher M is, the higher I will be

Optimal levels of Labour - Leisure Health Investment PPC G* Trade-off
Income (£) II I BC Optimal levels of Labour - Leisure Health Investment PPC G* Trade-off and the Home Good A B* U1 Imax O TH T* BC Health Leisure Investment I* contract curve Medical M* Expenditure Production of Health and Health and the Home Good Investment III IV Medical expenditures (£)

Equilibrium in the Integrated Grossman Model
Consumer picks point A in QI, generating income of G* and has OT* leisure time. From QII, consumer’s equilibrium is at A1, giving optimal investment in health of I* and in home good of B* In QIV, TH and M* are spent on health care. M* is translated through QIII to determine level of health in investment I*

II I Health Leisure Investment I* BC Four-Quadrant
Income (£) II I BC Four-Quadrant PPC G* representation of A the Grossman model A1 B* U1 Imax O TH T* BC Health Leisure Investment I* contract curve M* III IV Medical expenditures (£)

Key messages from Grossman Model
To maximise utility, a consumer must: Allocate time between work and leisure Spend remaining leisure time on health and nonhealth activities Spend income earned on health and nonhealth resources Produce or invest in health capital for future use See Murray et al (2003) p9

Summary Optimal health stock will decline as the person ages if the depreciation rate of health increases as a person ages Benefits of good health are greater for high wage workers so they demand higher optimal health stock The more educated people are, the less costly it is to generate health resulting in a higher optimal health stock for this group Individuals will allocate resources in order to produce health capital. Performance indicator should include 1) Inputs and/or resources 2) the functions 3) results or intermediate objectives 4) final objectives of the system Assessment of methodology of HS performance must be done in close collaboration with countries & their own experts in regions

Conclusions Grossman model has been influential in health economics.
Demand for health care inputs is demand derived from demand for health itself Performance indicator should include 1) Inputs and/or resources 2) the functions 3) results or intermediate objectives 4) final objectives of the system Assessment of methodology of HS performance must be done in close collaboration with countries & their own experts in regions

References Grossman, M. (1972) On the concept of health capital and the demand for health, Journal of Political Economy 80: Wagstaff, A. (1993), The demand for health: an empirical reformulation of the Grossman model, Health Economics 2: McGuire, A., Henderson, J. & Mooney, G. (1988). The Economics of Health Care. London: Routledge and Kegan Paul Morris, S., Devlin, N. & Parkin, D. (2007) Economic analysis in health care. Chichester: John Wiley & Sons Grossman, M. (1982) The demand for health after a decade, Journal of Health Economics 1: 1-13 Folland, S., Goodman, A. & Stano, M. (2004). Economics of Health and Health Care. London: Prentice Hall

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