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Steady-state capital per worker

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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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PRODUCTION FUNCTION

Assume an economy has the following production function: Y=F(K,L)=K0.4L0.6

a. State the per-worker production function.

b. If the savings rate is 0.2 and the depreciation rate is 0.05, calculate the steady-state capital stock per worker, output per worker, and consumption per worker.

c. Now suppose the government increases spending, reducing the country's savings rate to 0.1. Redo the calculations in (b) based upon this change. What is the effect on the government spending on the economy.

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