Consider education (e) and health (h). Education depends on school inputs (like good teaching and school supplies), denoted s, and on health. School inputs and health are perfect substitutes in the production of education:
e = s +0.4 h.
Health depends on medical inputs (m) and education. If you are more educated, you will know more about taking care of yourself and will be able to deal with doctors and insurance companies better. Again, medical inputs and education are perfect substitutes in the production of health:
h = m+ 0.4 e.
a. Find the equilibrium levels of health and education as functions of school inputs (s) and medical inputs (m).
b. Suppose school inputs improve by one unit. What is the immediate impact on education (before health can adjust)? What is the equilibrium impact on education (allowing for adjustment of health)? What is the equilibrium impact on health?
c. Both school inputs and medical inputs are subject to independent shocks that are also independent over time. In any period, medical inputs equal 2 with probability ½ and 0 with probability ½. The same is true for school inputs. Periods are long enough that within each period equilibrium is attained. For each of the four (equally probable) combinations of school and medical inputs ((2,2), (2,0), (0,2), and (0,0)) find and graph the equilibrium levels of health and education (the axes should be health and education).
d. On your graph, think about what the regression line would look like if you were to regress health on education (I’m not asking you to run a regression). If you want to draw it by eyeball, do so. Does it slope up or down or is it flat?
e. Over time, is education positively correlated with health? Why or why not?