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Below are data on the levels of aggregate output (Y ), capital (K), the amount of labor working in production (LY ), and the population (L) for 2005 and 2011. Complete the following table. Then, solve for the average annual growth rate of total factor productivity (A) using the production function. To do so, you should derive a growth accounting formula for y = Y/L and use the values you have entered in the table.

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Related questions

Country A and country B both have the production function:

Y = F(K,L) = K^(1/3)L^(2/3).

a) Does this production function have constant returns to scale? Explain.

b) What is the per-worker production function, y = f(k)

c) Assume that neither country experiences population growth nor technological progress and that 20-percent of capital depreciates each year. Assume further that country A saves 10% of output each year and country B saves 30% of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the steady-state levels of income per worker and consumption per worker.

d) Suppose that both countries start off with a capital stock per worker of 1. What are the levels of income per worker and consumption per worker?

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?

Suppose the output per effective worker is production function is y=10k1/2, 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?

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