Suppose that the per-worker production (labour productivity) function in South Korea is Y over L equals A open parentheses K over L close parentheses to the power of 0.4 end exponent open parentheses H over L close parentheses to the power of 0.6 end exponent. South Korea's labor productivity rises 6% per year, capital-labour ratio rises 5% per year, and human capital per worker rises 2% per year. This information suggests that total factor productivity grows at _________ per year.

Assume that a country's production function is Y = K/2*L/2 and there is no population growth or technological change. a. What is the per-worker production function y = f (k)? b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What is Y? What is labor productivity computed from the per-worker production function? Is this value the same as labor productivity computed from the original production function? c. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital- labor ratio.)

The production function used by the Australian Bureau of Statistics is written Y = AK L rY where Y is aggregate output, A is total-factor productivity, K is aggregate capital, L is the size of the labor force, I is aggregate intermediate input (e.g., energy, material), and the exponents are constants. Given this production function, which of the following expressions correctly represents the growth rate of per-capita income, 9Y? = gA + agK + BgL + Y9I = gA + agk + (1 – B) gL +ygı = 9A + agk + (B– 1) gL +Yg1 O None of the choices given is correct.

The aggregate production function is Y = 5KL. If there are 18 units of capital and 50 units of labor, the capital productivity is ___________.

Country A and country B both have the production function Y = F(K, L) = K^0,5L^0,5 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 or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent 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. Theen 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 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator or a computer spreadsheet…

Countries X and Z produce a composite output Y by employing two factors labor (N) and capital (K), when the given state of technology is A. The production function of Y is Y = √(K)(AN) In a particular year, Country X's growth rate of output per worker is 4.2%, growth rate of employment is 3.1%, and growth rate of capital is 3.9%. In the same year, Country Z's growth rate of output per worker is 7%, growth rate of employment is 1%, and growth rate of capital is 8%. What is the growth rate of technological progress for the two countries? (Round your responses to two decimal places.) Country X: gax= Country Z: 9AZ = % Given the above information, which combinations of the following statements are true? a) Country X and Country Z are investing heavily in innovation and R&D. b) Country X has achieved its balanced growth path. c) Country Z could be using a combination of heavy capital formation and import of technology. d) Country Z has a higher standard of living than Country X. O A. a, b…

Assume the production function takes the general form: Y=Z*F (K,L,A)where all marginal products are positive.Which 3 of the following statements are correct?a. If A is fixed, then population growth acts as a drag on growth of output per person.b. If A is fixed, then population growth acts as a drag on growth, and so Malthus was correct that populationgrowth will always reverse the impact of technological improvements.c. Both rises in z and rises in K/L (capital intensity) will boost output per worker.d. Growth in output per worker can occur due to rises in z (technology) or rises in K/L (capital intensity), orboth.

Problem 3: Write each production function given below in terms of output per person y = Y/L and capital per person k = K/L. Plot these per person versions in a graph with y on the vertical axis and k on the horizontal axis. (You can assume à is a constant positive number). (a) Y=AK 1/3 L2/3 and Y = AK3/4L1/4 (plot them on the same graph). (b) Y = K. (c) Y = KL (d) YK-AL

Assume an aggregate production function with a constant marginal product of capital and with capital as the only factor of production, such that Y = aK. If there is neither population growth nor depreciation of capital, the growth rate of output is

Country A and country B both have the production function   Y = F(K, L) = K1/3L2/3   Does this production function have constant returns to scale? Explain.   Find Solow’s production function, y = f (k)?   Assume that neither country experiences population growth or technological progress and that 20 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 30 percent of output each year. 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.   Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker?   Remembering that the change in the capital stock is investment less depreciation, use a calculator (or, better yet, a computer spreadsheet) to show how the capital stock per worker will evolve over time in both countries. For…