Consider the continuous-time Solow growth model as discussed in the lecture. The economy is on its balanced growth path with labor augmenting technological progress at rate g and population growth at rate n. The depreciation rate is 8. (a) Derive the dynamic equation of aggregate capital K. (b) Normalize the aggregate capital K by technology A and population L and denote the capital per unit of effective labor as k = K/(AL). Derive the dynamic equation of k . (c) Use the phase diagram to illustrate the steady state level of k and the dynamics of k if k starts from a level lower than the steady state level.
Consider the continuous-time Solow growth model as discussed in the lecture. The economy is on its balanced growth path with labor augmenting technological progress at rate g and population growth at rate n. The
(a) Derive the dynamic equation of aggregate capital K.
(b) Normalize the aggregate capital K by technology A and population L and denote the capital per unit of effective labor as k = K/(AL). Derive the dynamic equation of k .
(c) Use the phase diagram to illustrate the steady state level of k and the dynamics of k if k starts from a level lower than the steady state level.
(d) Suppose that the economy is on its balanced growth path at time to. Unex- pectedly, the population growth rate drops down to n' <n at to, stays at n' until t1, and resumes to n after t1. How does k respond, between to and t1, and afterwards?
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