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Production Function

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1) If a country's labor is paid a total of $6 billion, its capital is paid a total of $2 billion, and profits are zero, what is the level of output?

2) Consider a production function that omits the stock of natural resources. When, if ever, will this omission have serious consequences?

3) Consider a production function: Y = AF (K,N,Z), where Z is a measure of natural resources used in production. Assume this production function has constant returns to scale and diminishing returns in each factor.

a) What will happen to output per head if capital and labor both grow but Z is fixed?
b) Reconsider (a), but add technical progress (growth in A).
c) In the 1970's there were fears that we were running out of natural resources and that this would limit growth. Discuss this view using your answers to (a) and (b).

4) Consider the following production function: Y = K.5 (AN).5 , where both the population and the pool of labor are growing at a rate n = .07, the capital stock is depreciating at a rate d = .03, and A is normalized to 1.

a) What are capital's and labor's shares of income?
b) What is the form of this production function?
c) Find the steady-state values of k and y when s = .20.
d) At what rate is per capita output growing at the steady state? At what rate is total out-put growing? What if total factor productivity is increasing at a rate of 2 percent per year (g = .02)?

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Solution Summary

The growth rates in output per person are found.

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