Variables: e = Education h = health s = school inputs (things like good teaching

Question

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?  

Explanation / Answer

a.

b. a two-factor production function with CRS, satisfying FK > 0, FL > 0, and FKK < 0, FLL < 0, has always FKL > 0, i.e., there is gross complementarity between K and L. This assertion is implied by the following observations on homogeneous functions. Let Y = F(K, L) be a twice continuously differentiable production function with FK > 0 and FL > 0 everywhere. Assume F is homogeneous of degree h > 0, that is, for all possible (K, L) and all > 0, F(K, L) = hF(K, L).

c. If the School increase the input by 1 unit the education equilibrium also increae.

d. Small changes in school input also changes in health and a small changes in medical input also changes education.

Related Questions

Navigate

• Browse (All)
• Browse V
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.