y = A(1-ga) ere ga is the fraction of all workers that produce technologies. Further, suppose the growth of technology is given by the owing equation growth of A = (ga/m)(L) pose L = 1 and m = 7, and that initially g,A = 0.7. If g, fell to 0.8 the level of output per worker would: Impossible to say fall stay the same rise
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- Consider the economies of Hermes and Gobbledigook, both of which produce gobs of goo using only tools and workers. Suppose that, during the course of 20 years, the level of physical capital per worker rises by 4 tools per worker in each economy, but the size of each labour force remains the same. first dropdown question options are (larger or smaller), second dropdown question options are (the brain drain, inward orietned growth, diminishing returns, constant returns, increasing returns), the third dropdown question oprions are (more diffucult or easier)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.The “per person” versions of production functions: Write each productionfunction given below in terms of output per person y ; Y/L and capital perperson k ; K/L. Show what these “per person” versions look like in a graphwith k on the horizontal axis and y on the vertical axis. (Assume A is somefxed positive number.)(a) Y = K 1/3L2/3 and Y = K 3/4L1/4 (on the same graph) (b) Y = K(c) Y = K + AL(d) Y = K − AL
- Suppose that the production function of a company is given by q = qL^2 · qC and that the amount of labour qL and the amount of capital qC are functions of time t. At time t = 2, we know that qL = 9 andqC =8 and that the growth rateof qL is equal to 2 and the growth rate of qC is equal to 8. Find the growth rate of the production q at that moment.In 2000, the country of Cobra Island has an initial level of capital set at 10 units. The population of Cobra Island is unknown, but we do know that it grows each year at some constant rate. The level of total income is 500 cobra dollars. Finally, the total production function of Cobra Island can be described as Y=10*L1/2k1/2 a)What is the initial population of Cobra Island? b)Let the wage of labor is 0.4, and the rental rate of capital is 0.6. The capital to labor ratio after two years (in 2002) is 50 while the amount of workers is 1000. The growth rate of capital is 6,970%. The growth rate of labor is 100%. Find the GDP of Cobra Island. c)How much labor is there in Cobra Island one year after the initial year (or in 2001)? d)The growth rate of income is 1,089%. Find the Solow Residual. Do not give the answer as a percentageIn 2000, the country of Cobra Island has an initial level of capital set at 10 units. The population of Cobra Island is unknown, but we do know that it grows each year at some constant rate. The level of total income is 500 cobra dollars. Finally, the total production function of Cobra Island can be described as Y=10*L1/2k1/2 What is the initial population of Cobra Island? Let the wage of labor is 0.4, and the rental rate of capital is 0.6. The capital to labor ratio after two years (in 2002) is 50 while the amount of workers is 1000. The growth rate of capital is 6,970%. The growth rate of labor is 100%. Find the GDP of Cobra Island. How much labor is there in Cobra Island one year after the initial year (or in 2001)? The growth rate of income is 1,089%. Find the Solow Residual. Do not give the answer as a percentage. Zackland, a developing country, can be described using the Harrod-Domar Model. The ICOR of Zackland is 0.8. Assume that the economy is stable. In other…
- Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor 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 isY? What is labor productivity computed from the per-worker production function? Is thisvalue 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 isnecessary 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 ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker? Only D, other option answeredAssume that a country's production function is Y = K1/2L1/2 and there is no population growthor 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 isY? What is labor productivity computed from the per-worker production function? Is thisvalue 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 isnecessary 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 ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker?A CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H: where 0 a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?
- 1. Country A and B both have the production functionY = F (K, L) = K ½L ½or Y = K0.5 L0.5 a) What is the per-worker production function, y= f (k)? Please make sure to write specificfunctional form of the per-worker production function. b) Assume that neither country experiences population growth nor technological progressand that 4 percent of capital depreciates each year. Assume further that country A saves 24percent of output each year and country B saves 16 percent of output each year. Using youranswer from part a) and the steady-state condition, find the steady-state level of capital perworker for each country. Then find the steady-state levels of income per worker for eachcountry and steady-state level of consumption per worker for each country.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…Suppose the production function is Y = AK0.3N0.7. Suppose in 2010, K = 1000, N = 100, and Y = 199.5. In 2020, capital, labor, and output have doubled, so K = 2000, N = 200, and Y = 399. (a.) By what percentage did productivity grow from 2010 to 2020? (b.) If output had risen to 798 instead of 399, and capital and labor doubled, by what percentage would productivity have grown from 2010 to 2020?