ECON 202 Lecture 1: Chapter+6-answers.pdf

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16 Apr 2015

School

University of Waterloo

Department

Economics

Course

ECON 202

Professor

Anis Rahman

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Document Summary

Chapter 6 - answers: output per worker yt = 4kt1/3, the saving rate is 30 percent, and the depreciation rate is 0. 133. Calculate the steady-state values of capital per worker and consumption per worker. Calculate the growth rates of output per worker and capital per worker. Answer: the solow residual ga = 0. 05 - 0. 3 0. 05 - 0. 7 0. 02 = 0. 021. Given the values of s, , k* solve for y* y*= 38: in a steady-state economy with no population growth, consumption per worker is 45, the saving rate is 25 percent, and the depreciation rate is 15 percent. C =(1 s)y ,so given c and s first find y. Then use the steady state condition, syt = kt to find k* The level of capital per worker is 100: consumption per worker is 72, depreciation is 12. 5%, and capital per worker is 64. Given the production function y = 20k1/3, show that this economy is in a steady state.

Related Questions

Suppose the output per effective worker is production function is y=10k^1/2, where k equals the amount of capital per effective worker and the capital lasts an average of 10 years. Assume that the saving rate is 32 percent, the rate of growth of population is 4 percent and the rate of technological growth is 2 percent.

a) Solve for the steady state levels of capital per effective worker, output per effective worker, investment per effective worker and consumption per effective worker.

b) Calculate the growth rate of total capital income and the growth rate of total labor income at the steady state.(Hint: Capital and labor each earn a constant share of the economy's income ).

c) Prove, at the steady state, (i) the capital-output ratio is constant;(ii) the real wage grows at the rate of 2 percent.

d) Calculate all of the following at their Golden Rule levels: Capital per effective worker, output per effective worker, saving and investment per effective worker, and the consumption per effective worker.

e) Whether the saving rate is too high or too low?

crimsonhound401

Consider an economy described by the production function: Y = F(K,L) = K^0.4 L^0.6

a. What is the per-worker production function?

b. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.

c. Assuming that the depreciation rate is 15% per year, make a table showing steady state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, 30 percent, and so on. What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?

d. Use information from Chapter 3 to find the marginal product of capital. Add to your table, from part (c) the marginal product of capital net of depreciation for each of the saving rates. What does your table show about the relationship between the net marginal product of capita and steady-state consumption?

cyanbee395

Consider an economy with the following production function:

Y = AK.5L.5
The labor force is constant. The rate of depreciation is Î´ = .1, the savings rate is s = .3.

a. Has this production function constant returns to scale? Why?

b. Write the production function in per worker variables.

c. Does the per worker production function have diminishing marginal returns to capital? Why?

d. Write the fundamental Solow equation in per worker variables.

e. Depict the steady state of this economy.

f. What are the growth rates of per worker output and capital in steady state?

g. Calculate the steady state level of capital, output, consumption and savings.

h. Redraw the initial equilibrium and show what happens when the savings rate increases. Do the growth

rates change?

i. Redraw the initial equilibrium and show what happens when there is a one time increase in population.

. Do the growth rates change?

j. Redraw the initial equilibrium and show what happens when there is a one time innovation that increases

productivity. Do the growth rates change?

k. Redraw the initial equilibrium and show what happens when there is constant productivity growth. Do

the growth rates change?

ECON 202 Lecture 1: Chapter+6-answers.pdf

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