# The production function is Cobb-Douglas – Get an Orginal Paper (homeworkcorp.com/order)

Homework 3

E317

Due by 9/17, 4:30 pm

1. Show mathematically that the Cobb-Douglas production function exhibits constant returns to

scale.

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 =

1/2

. Suppose

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 =

1/2

. The depreciation rate is 1%. The investment rate ( ) is determined as

follows:

= 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

steady state(s).

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