Suppose there is an increase in the saving rate. Explain what effect this will have on output,
output per worker, the rate of growth of output, and the rate of growth of output per worker.

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2 Jun 2021

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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 described by the production function F(K, L) = K± (EL) 1± . Originally, the economy was at the steady state. There was a one-time outbreak of disease that killed 5 percent of the population. Population growth then returns to normal after that. Assume there is no technology growth in this economy.

A. What is the immediate effect of the disease outbreak on total output? What is the immediate effect on output per worker? [It is sufficient to give qualitative description.]

B. How does the disease outbreak affect the steady-state level of capital per worker?

C. What is the growth rate of output per worker immediately after the disease outbreak compared to that before the outbreak? [It is sufficient to give qualitative description.]

D. Suppose that when the disease outbreak occurred, the economy was also hit by a natural disaster that destroyed capital stock by 5 percent as well. What is the growth rate of output per worker after the incidents?