Health Economy

Consider the following 4 examples of health stock over the life cycle.

From birth on, pairwise compare the lives by who gets greater utility from health (hint: use health (H) instead of age). Or, suppose that utility only depends on health. Fill in your answer in the 1^st column of the table by indicating who gets greater utility. If utility is equal, mark an “=” sign; if it’s ambiguous, write “?”
From age = T on, pairwise compare the lives by who gets greater utility from health (hint: use health (H) instead of age). Or, suppose that utility only depends on health. Fill in your answer in the 2^nd
Repeat the exercise in part a) (from birth on) if the utility function only depends on remaining years of life (hint: use age instead of health (H)). Use the 3^rd
Repeat the exercise in part c) (from age = T) if the utility function only depends on remaining years of life (hint: use age instead of health (H)). Use the 4^th column

	From birth	From age=T	From birth (care about remaining years only)	From age=T (care about remaining years only)
A vs. B
A vs. C
A vs. D
B vs. C
B vs. D
C vs. D

Consider two 30 year old males. Richard has a family history of prostate cancer and started getting annual screenings at the age of 30. He and his family have decided that they will “fight” until the end should anything happen to Richard. Larry also has a similar family history of prostate cancer, refuses to go the doctor, has been smoking 2 packs of cigarettes a day since he was 16, and will not “fight” until the end.

Sketch out a projected life cycle profile of each person’s health stock in a manner similar to question 2 (i.e., how does a person’s health change as he ages). Be sure to label events that are likely to happen, as well as treatments.
Accompanying your sketches, discuss each person’s health: who has higher health at each point in time? Who will live longer? Compare outcomes when a terminal disease first onsets (i.e., how does health change, as well as life expectancy, if both get prostate cancer at the same age?).
Compare spending on healthcare over their lifetimes. Who spends more, who spends less? Is it obvious?
How would your sketches change if Richard stopped getting screening, or if Larry quit smoking right away?

Suppose that our utility function, which depends ONLY on health (H) is given by the following function: . This means that the marginal utility of health function is given by . Answer the following questions:

Fill in the following table:

Quantity of Health (H)	Total Utility	Marginal Utility
1
2
3
4
5
6
7
8
9
10

After what unit of health (if any) does diminishing marginal utility kick in?

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