Hi, I've been given a tricky question and need help solving. Thanks in advance!
This is a simplified variant of the neoclassical growth model. Here we assume(contrary to the Solow growth model) that labor L does not change over time and that L = 1. We assume Y = 5/2 * K(1/5), where Y is output and K is capital. We assume for the change in capital stock dK/dt = 1/2 * Y. Consider the resulting differential equation for capital:
dK/dt =5/4 * K(1/5).
We are interested in the time path of K from time t = 0 onwards. Assume that K(0) = 0. Then there is an obvious solution, namely K(t) = 0 for all t ≥ 0. Hence, for this solution, K = 0 is a steady state! But there is also another solution such that K(0) = 0, but K(t) > 0, for all t > 0. For this alternative solution K = 0 is not a steady state!
a) Please find this alternative solution!
This is a simplified variant of the neoclassical growth model. Here we assume(contrary to the Solow growth model) that labor L does not change over time and that L = 1. We assume Y = 5/2 * K(1/5), where Y is output and K is capital. We assume for the change in capital stock dK/dt = 1/2 * Y. Consider the resulting differential equation for capital:
dK/dt =5/4 * K(1/5).
We are interested in the time path of K from time t = 0 onwards. Assume that K(0) = 0. Then there is an obvious solution, namely K(t) = 0 for all t ≥ 0. Hence, for this solution, K = 0 is a steady state! But there is also another solution such that K(0) = 0, but K(t) > 0, for all t > 0. For this alternative solution K = 0 is not a steady state!
a) Please find this alternative solution!