Suppose we have a representation of the Ramsey-Cass-Koopmans model that allows for a
nonzero depreciation rate of capital. More specifically, the representative household problem is
characterized as follows: max0ept[1ct1]dts.t.kt=ktktct a) Briefly explain what the representative
household problem characterizes. b) Formulate and express the present value Hamiltonian. c)
Determine the first order conditions with respect to the present value Hamiltonian. d) Derive the
law of motion of consumption using the information from the first order conditions with respect to
the present value Hamiltonian. e) Linearize the law of motion of the capital stock and the law of
motion of consumption and express the system as a two-by-two differential equation system. f)
Compute the trace and determinant of the linearized differential equation system. Based on the
sign of the determinant, what type of dynamics and equilibrium does the two-bytwo linearized
differential equation system characterize?.
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Suppose we have a representation of the RamseyCassKoopmans.pdf
1. Suppose we have a representation of the Ramsey-Cass-Koopmans model that allows for a
nonzero depreciation rate of capital. More specifically, the representative household problem is
characterized as follows: max0ept[1ct1]dts.t.kt=ktktct a) Briefly explain what the representative
household problem characterizes. b) Formulate and express the present value Hamiltonian. c)
Determine the first order conditions with respect to the present value Hamiltonian. d) Derive the
law of motion of consumption using the information from the first order conditions with respect to
the present value Hamiltonian. e) Linearize the law of motion of the capital stock and the law of
motion of consumption and express the system as a two-by-two differential equation system. f)
Compute the trace and determinant of the linearized differential equation system. Based on the
sign of the determinant, what type of dynamics and equilibrium does the two-bytwo linearized
differential equation system characterize?
![Suppose we have a representation of the Ramsey-Cass-Koopmans model that allows for a
nonzero depreciation rate of capital. More specifically, the representative household problem is
characterized as follows: max0ept[1ct1]dts.t.kt=ktktct a) Briefly explain what the representative
household problem characterizes. b) Formulate and express the present value Hamiltonian. c)
Determine the first order conditions with respect to the present value Hamiltonian. d) Derive the
law of motion of consumption using the information from the first order conditions with respect to
the present value Hamiltonian. e) Linearize the law of motion of the capital stock and the law of
motion of consumption and express the system as a two-by-two differential equation system. f)
Compute the trace and determinant of the linearized differential equation system. Based on the
sign of the determinant, what type of dynamics and equilibrium does the two-bytwo linearized
differential equation system characterize?](https://image.slidesharecdn.com/supposewehavearepresentationoftheramseycasskoopmans-230321044055-a563f1fa/85/suppose-we-have-a-representation-of-the-ramseycasskoopmanspdf-1-320.jpg)
