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Steady-state interest rates

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Now we will solve for the steady state in a calibration of the US economy in 2000. In
this problem, you will assume that the rate of growth of the work force is n = 0.017 and
there is no exogenous technological progress. The aggregate production function for the
US economy in 2000 is Y = (11.5)K 1/3 L 2/3 . The units are billions of 1996 dollars. A
plausible value for the depreciation of the capital stock is δ= 0.036, and a good value for
the national savings rate is σ= 0.16.

6. Use the formula r =f'(k) to calculate the steady-state rentals rate. Explain why
the real interest rate is r-n-δ. (Hint: if you give up a unit of consumption,
you can buy a unit of capital. That capital will yield f'(k) units of output next
year, but a fraction δ is used up in production and another fraction n is needed
for new workers.)

7. Is the US economy saving at the golden rule? What is the golden rule savings rate
for our economy?

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Steady-state interest rates are assessed.

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Steady-state capital per worker

In this problem, assume that Mexico and the United States have the same aggregate production function, the same δ (value for depreciation of capital stock), and the same n . In Mexico, real GDP per worker in 2000 is about 40% what it is in the United States, but Mexico is not near its steady-state level of output.

1. If the capital-labor ratio is the same in both countries, how much capital per worker does Mexico have in 2000?

2. If the capital-labor ratio is the same in both countries, what does this model predict will be the real interest rate in Mexico?

3. Why it is not plausible to assume that Mexico and the United States have the same aggregate production function and that the capital labor ratio is the same both countries?

4. Actually, Mexico only has 40% as much capital per worker as the United States has. What does this fact imply about total factor productivity in Mexico? What about the real interest rate in Mexico?

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