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Unformatted text preview: HOMEWORK ASSIGNMENT 3
Due: Tue 10/25/2010
1. Country A and B both have the same production function Y=F(K,L)=K1/3L2/3 . Assume
that population grows at 3% per year, capital depreciates at 7% per year, and there is no
technological progress in both countries. Country A saves 20% of its output each year
while country B saves 30%.
a. Derive the production function per worker for these economies.
b. Compute capital per worker, income per worker, consumption per worker for
each country in steady state.
c. Compute capital per worker in Golden Rule steady state and the saving rate
necessary to achieve this Golden Rule state.
2. Prove each of the following statements about the steady state with population growth and
a. The capital–output ratio is constant.
b. MPK is constant in steady state
c. Capital and labor each earn a constant share of an economy’s income.
d. Total capital income and total labor income both grow at the rate of population
growth plus the rate of technological progress, n + g.
e. The real rental price of capital is constant, and the real wage grows at the rate
of technological progress g. (Hint: The real rental price of capital equals total
capital income divided by the capital stock, and the real wage equals total
labor income divided by the labor force.)
3. This question asks you to analyze in more detail the two-sector endogenous growth model
presented in the text.
a. Rewrite the production function for manufactured goods in terms of output per
effective worker and capital per effective worker.
b. In this economy, what is break-even investment (the amount of investment
needed to keep capital per effective worker constant)?
c. Write down the equation of motion for k, which shows Δk as saving minus
break-even investment. Use this equation to draw a graph showing the
determination of steady-state k. (Hint: This graph will look much like those
we used to analyze the Solow model.)
d. In this economy, what is the steady-state growth rate of output per worker
Y/L? How do the saving rate s and the fraction of the labor force in universities
u affect this steady state growth rate?
e. Using your graph, show the impact of an increase in u. (Hint: This change
affects both curves.) Describe both the immediate and the steady-state effects. ...
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- Spring '10