Variables:

e = Education

h = health

s = school inputs (things like good teaching and school supplies)

m = medical inputs (treatment you receive)

Given the production functions:

e = min[s, 1.05h]

h= min[m, 2e].

s=m=10

a. Graph these functions and find the non-zero equilibrium.

b. Prove that the equilibrium at (0,0) is not stable.

c. Suppose that school inputs improve by one unit, from 10 to 11. What is the immediate impact on education (before health can adjust)? What is the equilibrium impact on education?

d. Starting at this equilibrium, do small changes in school inputs change health? Do small changes in medical inputs change education?