a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?
A CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H:
where 0
a. Set up the Hamiltonian and find the first-order conditions.
b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like?
c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗?
d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)?
e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?
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