The aggregate change of consumption, (t) and the aggregate change of the capital stock, K(t), are...

 

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The aggregate change of consumption, (t) and the aggregate change of the capital stock, K(t), are given by the following system of differential equations: (t) = (0.25K(t)-0.7 -0.04)C(t) K(t) = 1.4K (t)0.2-0.06K (t) - C(t) (a) Find the steady-state of the capital stock and consumption (3 marks) (b) Write the above system of differential equations as a linear function of time around the steady-state (5 marks) (c) Find the time path of consumption and the capital stock for any level of initial conditions. What are the necessary mathematical conditions for the time paths for consumption and the capital stock to converge to the steady- state? (7 marks) (d) Following from your answers in (a), (b) and (c), is such as model of the capital stock and consumption plausible for a real world economy? (Answer must be typed). (5 marks) The aggregate change of consumption, (t) and the aggregate change of the capital stock, K(t), are given by the following system of differential equations: (t) = (0.25K(t)-0.7 -0.04)C(t) K(t) = 1.4K (t)0.2-0.06K (t) - C(t) (a) Find the steady-state of the capital stock and consumption (3 marks) (b) Write the above system of differential equations as a linear function of time around the steady-state (5 marks) (c) Find the time path of consumption and the capital stock for any level of initial conditions. What are the necessary mathematical conditions for the time paths for consumption and the capital stock to converge to the steady- state? (7 marks) (d) Following from your answers in (a), (b) and (c), is such as model of the capital stock and consumption plausible for a real world economy? (Answer must be typed). (5 marks)

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