Question 1: Neoclassical Growth with Endogenous Labor Supply Consider a neoclassical growth model augmented with labor supply decisions. In particular, total population is normalized to 1, and all households have utility U = "u(c(t), 1 – 1(t))dt, where I(t) € (0, 1) is labor supply. In a symmetric equilibrium, employment L(t) is equal to l(t). Assume that the production function is Y(t) = F(K(t), L(t)), which satisfies the standard properties. (i) Define a competitive equilibrium. (ii) Set up the current-value Hamiltonian that each household solves, taking wages and interest rates as given, and determine the necessary and sufficient conditions for the allocation of consumption over time and the leisure-labor trade-off.
Question 1: Neoclassical Growth with Endogenous Labor Supply Consider a neoclassical growth model augmented with labor supply decisions. In particular, total population is normalized to 1, and all households have utility U = "u(c(t), 1 – 1(t))dt, where I(t) € (0, 1) is labor supply. In a symmetric equilibrium, employment L(t) is equal to l(t). Assume that the production function is Y(t) = F(K(t), L(t)), which satisfies the standard properties. (i) Define a competitive equilibrium. (ii) Set up the current-value Hamiltonian that each household solves, taking wages and interest rates as given, and determine the necessary and sufficient conditions for the allocation of consumption over time and the leisure-labor trade-off.
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Transcribed Image Text:Question 1: Neoclassical Growth with Endogenous Labor Supply
Consider a neoclassical growth model augmented with labor supply decisions. In particular,
total population is normalized to 1, and all households have utility
U =
e u(c(t), 1 – 1(t))dt,
where 1(t) e (0, 1) is labor supply. In a symmetric equilibrium, employment L(t) is equal
to l(t). Assume that the production function is Y (t) = F(K(1), L(t)), which satisfies the
standard properties.
(i) Define a competitive equilibrium.
(ii) Set up the current-value Hamiltonian that each household solves, taking wages and
interest rates as given, and determine the necessary and sufficient conditions for the
allocation of consumption over time and the leisure-labor trade-off.
(iii) Set up the current-value Hamiltonian for a planner maximizing the utility of the repre-
sentative household, and derive the necessary and sufficient conditions for a solution.
(iv) Show that the two problems are equivalent given competitive markets.
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