Due by 9/17, 4:30 pm
1. Show mathematically that the Cobb-Douglas production function exhibits constant returns to
2. Show that when the production function is Cobb-Douglas, output per worker =
3. A country is described by the Solow model, with a production function of =
that is equal to 900. The fraction of output invested is 30%. The depreciation rate is 2%. Is the
country at its steady-state level of output per worker, above the steady state, or below the
steady state? Show how you reached your conclusion.
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4. In Country 1 the rate of investment is 6%, and in Country 2 it is 18%. The two countries have the
same levels of productivity, , and the same rate of depreciation, . Assuming that the value of
is 1/3, what is the ratio of steady-state output per worker in Country 1 to steady-state output
per worker in Country 2? What would the ratio be if the value of were 2/3?
5. In a country, output is produced with labor and physical capital. The production function in perworker terms is =
. The depreciation rate is 1%. The investment rate ( ) is determined as
= 0.10 ≤ 10
= 0.20 > 10
Draw a diagram showing the steady state(s) of this model. Calculate the values of any steady
state levels of and . Also, indicate on the diagram and describe briefly in words how the
levels of and behave outside of the steady state. Comment briefly on the stability of the
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