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Assume that a country's production is Y = L^0.5K0.5. Capital lasts 20 years. Savings rate is 20%. How much is capital per worker in steady state?

a) How much is output per worker in steady state?

b)How much is consumption per worker in steady state?

c) How much is the golden rule capital stock?

d) What is the savings rate consistent with the golden rule capital stock?

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Samantha Balando
Samantha BalandoLv7
28 Sep 2019

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Related questions

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?

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?

3 . Country A and country B both have the same production function Y = F(K; L) = K^.47L^.53

a) Capital depreciates at the rate of 5 percent each year in both countries. Country A saves 15 percent of output while country B saves 22 percent of output each year. Find the steady-state level of capital per worker for each country. Then Önd the steady state levels of output and consumption per worker.

b) Suppose that both countries start off with a capital stock per worker of 1.5. What are the levels of output per worker and consumption per worker? Remembering that the change in the capital stock is investment minus depreciation, use a calculator to show how the capital stock per worker will evolve over time in both countries (see also p.213 in the book for what such a table would look like). How many years will it be before the consumption in country B is higher than the consumption in country A?

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