5. Suppose that the economy's production function is Y = √K√LA where K is capital, L is labor, and A is the state of technology. Suppose that the saving rate (s) is equal to 2.4%, the rate of depreciation of capital (8) is equal to 3%, the number of workers grow at 0.7% per year and the rate of technological progress is 3%. (a) Find the steady state values of: i. 11. 111. capital stock per effective worker output per effective worker growth rate of output per effective worker
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- Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Suppose that now there is labor augmenting technology, the rate of labor-augmenting technological is 2 percent. At what rate does total output, output per worker, and output per effective worker grow?c. You are given the following information about an economy. Y = C + I Y = F(K, L) The aggregate production function for this economy exhibits constant returns to scale and the marginal products of labor and capital are both subject to diminishing returns. s = saving rate (assume this is constant) per year δ= depreciation rate (assume this is a constant) per year y = Y/L k = K/L k* = steady state of capital per worker (K/L) and sf(k) < δk. i. What is sf(k) ii. What is δk? iii. Interpret the meaning of sf(k) < δk?In class we argued that if people could accumulate human as well as physical capital, the production function would look like the “AK” production function. • (a) If the production function is AK and the savings rate is constant at rate “s”, and the rates of depreciation and populati on growth are δ and n respectively, what would the growth rate of the economy be? • (b) What would be the macroeconomic consequences of decreasing the savings rate in this economy? • (c) What would be the consequences of an increase in fertility in this economy? • (d) Would the consequences of decreasing fertility be UNAMBIGUOUSLY GOOD? • (e) Can human capital grow without bounds? Explain why or why not (make sure you discuss the physical nature of human capital). • (f) What is the growth rate of the economy (in the absence of technological progress) if human capital cannot grow without bounds?
- 1.Many countries, including Pakistan, import substantial amounts of goods and services from other countries. However, economists claim that a country can enjoy a high standard of living only if it can produce a large quantity of goods and services itself. Can you reconcile these two facts? (Maximum 100 words). 2.Given the production function Y= AF (L, K, H, N), explain the determinants of productivity. ( Maximum100 words). 3.Population growth has a variety of effects on productivity. Explain this statement and justify your answer. (Maximum 200 words).Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].Consider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.
- Computing growth rates (II): Suppose k, l, and m grow at constant rates givenby g k, gl , and gm. What is the growth rate of y in each of the following cases?(a) y = k 1/3(b) y = k 1/3l 2/3(c) y = mk 1/3l 2/3(d) y = mk 1/4l 3/4(e) y = mk 3/4l 1/4(f ) y = 1klm2 1/2(g) y = 1kl2 1/4 11/m2 3/4Give typing answer with explanation and conclusion The production function is given by Y=AK, where K is the capital stock and A denotes the level of technology and equals 1.2 (the rate of technological progress equals 0). The rate of population growth is 2% and people save 15% of their incomes. The capital stock is 12000 and consumption of fixed capital is equal to 120 (and it always represents this percentage of the capital stock). Calculate the rate of growth of output per worker.The COVID-19 pandemic has caused an unprecedented increase in savings in many countries around the world. In the EU, the savings rate of households has jumped from 12.5% to 17%. In 2008-2009, it had moved from 12.5% to 14% (Dossche and Zlatanos 2020). Even if the source of 2020 surge in savings is different from the one of 2008, it is obvious that this increase does not result in more investment and growth. QUESTION: 1. With reference to the paradox of thrift discuss the appropriate approach by the government to get the economy out of economic downturn swiftly
- Assume that total output is determined by this formula: number of workers × productivity = total output Hint: Assume there are 100 workers and each worker produces $100 of output. If productivity increases by 3 percent and the number of workers increases by 2 percent a year, how fast will output grow?31) Given the narrow interpretation of technology, technology will include which of the following? A) how well firms are run B) the organization and sophistication of markets C) the political environment D) none of the above 32) Suppose there are two countries that are identical with the following exception. The saving rate in country A is greater than the saving rate in country B. Given this information, we know that in the long run A) the growth rate of output per capita will be greater in B than in A. B) the growth rate of output per capita will be greater in A than in B. C) the capital-labor ratios (K/N) will be the same in both countries. D) the growth rate of output per capita will be the same in both countries. 33) Suppose there are two countries that are identical with the following exception. The saving rate in country A is greater than the saving rate in country B. Given this information, we know that in the long run A) the capital-labor ratio…Give only typing answer with explanation and conclusion The production function in an economy is given by Y = K0.4L0.6, where Y is output level, K is capital input, and L is labour input. The saving rate is 24%, the annual population growth rate is 4%, and annual depreciation rate is 2%.