Use the Solow model to solve. Suppose, you are the chief economic advisor to a small African country with an aggregate per capita production function of y=2k1/2. Population grows at a rate of 1%. The savings rate is 12%, and the rate of depreciation is 5%.
(a) At the steady-state level of output, what is the numerical value of consumption? Identify the amount of consumption in your graph in part a. Show your work.
(b) Say that population growth decreases in this economy. What do you expect to happen to the growth rate of income per capita in the short run and long run?
(c) Say that this economy was in its steady state when a cyclone destroyed half of its capital stock. How does this change the steady state value of income per capita? Explain.
(d) On a graph show what happens to steady-state capital per worker and income per worker in response to a change in consumer preferences increases the savings rate.
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