Demand for Health: Grossman Health- I (Continued)

Summary:

Production of H and X

Market Budget Constraint

Second Role of Health in Grossman Model

Sick time and Productive time

Economic Definition of Death 

Production of H and X:

For both H and X, there are 2 distinct categories of inputs:

                             -Market goods

                             -Personal time

Market inputs:

-M: Market inputs for health (e.g.: healthcare or exercise equipment)

-J : Market inputs for the 'other goods X' (e.g.: jigsaw puzzle or video games)

Production function of Ht:

                               Ht = H( Ht-1, Tt, Mt )

Production function of Xt:

                                    Xt = X( Tt, Jt)

Market Budget Constraint:

Individual cannot spend more than earning. If,

W: Wage (rupee per unit of time)

Tt: Total time for working. 

Then, Total income (Yt) for period t is 

                      Yt = W. Tt

In any period, individual can spread her income on two items:

Market inputs into health (Mt) and other goods (Jt)

Note: Grossman model does not specify how wages W are determined, but presumably the individual's education and other factors determine the individual wages.

                                Pm. Mt + Pj. Jt = W. Tt = Yt.

Second role of health in Grossman Model:

Health is an input to the production of productive time. 

If a person is already healthy enough to have very little sick time, then additional improvements in health yield little additional productive time. 

If a person is very unhealthy, even small improvement in health can yield substantial decreases in sick time.

Sick time and productive time:

Healthier the individual is, the less time he spends sick in a given period and the more productive time Tp, he has available.

Productive time is simply the complement of Ts and is

                               Tp = Time- Ts = Tw + Tx + Th.

These are diminishing Marginal returns to productive time from health.

Economic Definition of Death:

The individual has no productive time left and cannot generate any more health. She remains at Hmin for all remaining periods and is effectively dead. Purpose of reducing sick time is to have more productive time for producing more H and X. 

Illness Avoidance Curve:

As health (H) increases, sick time (Ts) falls. At Hmin, there is no productive time for any other activities left since health is so low.