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Suppose that the economy's production function is: Y= ?K?N The saving rate is equal to s, the capital depreciates at rate ?, population grows at rate n.
1. Find the dynamics of capital per worker (Write Kt+1 - Kt as a function of output per worker yt).
2. What is the steady state capital per worker k*? Output per worker y*? Illustrate your answer graphically.
3. What is the growth rate of aggregate capital in the long run in this economy? Of aggregate output?
4. The golden rule capital per worker k^GR is the level of capital per worker that maximizes consumption per worker at the steady state. Write the expression of the steady state consumption per worker c* as a function of k and derive the golden rule capital per worker. Suppose that the economy's production function is now given by: Y= ?K?(AN) with productivity A growing at rate ?
5. What it the growth rate of aggregate output in this economy? Of output per worker?
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