Indifference curves and budget constraints

Use consumer theory (i.e. indifference curves and budget constraints), where the usual assumptions apply, to illustrate the following:

Assume the individualâ??s utility is an increasing function of medical goods (m) and all other goods (X). That is,

Utility =U (m,x) where delta u/delta m >0, delta u/delta x >0 , and H = f(m) where delta H/deltam > 0.

That is, health or health status increases utility and health is an increasing function of medical goods.

a. Illustrate the individualâ??s utility-maximizing choice of .
b. Next, on the same graph, show the effects of the individual â??getting sick.â? When doing this, assume that the illness harms the individualâ??s ability to earn as much income as before the illness. Label the new optimum .
c. Next, suppose instead, that the individual has sick-loss insurance or sick leave from work and this would replace any income lost from missing work (do I hear a duck? Aflac!). Label this outcome .
d. This exercise is an illustration that illness has caused three potentially observable things to happen. What are they?