Health-Wealth Tradeoffs

a	b
0.5	0.5
utilityfunction	0.5 h 0.5 w

utility functionparameter controls

cost of health care parameters

c

1

f

1

cost to improve health by δ: -1+

δ



An individual's happiness (or "utility") often depends on their wealth and their health. Spending on medical services, however, can often improve one's health. This Demonstration explores tradeoffs between wealth and health permitted by medical technology. You use a two-dimensional slider to select the parameters of a utility function from a family of transcendental logarithmic functions that depends on health and wealth. A sketch of the resulting utility surface appears to the left of the control. The cost of medical services to improve health from some baseline by an amount

δ

is modeled by the solution to the differential equation

m'(δ)=f

cδ

e

, subject to the constraint that

m(0)=0

. You choose the parameters

c

and

f

. You select baseline wealth and health using a locator. The Demonstration responds with a graphic showing the different utility contours and with a black locus showing the possible wealth-health states permitted by medical technology. A red point shows the optimal level of wealth and health given a baseline position and the cost of medical services.