Consider the Solow model with population growth. The Cobb-Douglas production function is Y = KL, where...
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Consider the Solow model with population growth. The Cobb-Douglas production function is Y = √KL, where K is the capital stock, L is the labor force, the saving rate s, physical depreciation rate 8, and the population growth rate n. Define the steady states properly and answer the following questions. (1) (5 points) What does the Golden Rule intend to maximize? Write down the optimization problem and derive the first order condition. (2) (2 points) Derive the optimal saving rate associated with the Golden Rule. (3) (8 points) Suppose that the saving rate has been set to the Golden Rule level, and the economy is already in its Golden Rule steady state. Now if the deprecation rate is higher, do we need to adjust the saving rate to lead the economy to the new Golden Rule steady state? Draw well-labeled separate graphs to show the dynamics of capital per worker, consumption per worker and the growth rate of output per worker during the transition to the new Golden Rule steady state. Consider the Solow model with population growth. The Cobb-Douglas production function is Y = √KL, where K is the capital stock, L is the labor force, the saving rate s, physical depreciation rate 8, and the population growth rate n. Define the steady states properly and answer the following questions. (1) (5 points) What does the Golden Rule intend to maximize? Write down the optimization problem and derive the first order condition. (2) (2 points) Derive the optimal saving rate associated with the Golden Rule. (3) (8 points) Suppose that the saving rate has been set to the Golden Rule level, and the economy is already in its Golden Rule steady state. Now if the deprecation rate is higher, do we need to adjust the saving rate to lead the economy to the new Golden Rule steady state? Draw well-labeled separate graphs to show the dynamics of capital per worker, consumption per worker and the growth rate of output per worker during the transition to the new Golden Rule steady state.
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1 What does the Golden Rule intend to maximize Write down the optimization problem and derive the first order condition The Golden Rule is an economic ... View the full answer
Related Book For
Macroeconomics
ISBN: 978-1464168505
5th Canadian Edition
Authors: N. Gregory Mankiw, William M. Scarth
Posted Date:
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