QUESTION 11 According to the Solow model, given the levels of total efficiency units of labor (H) and technology (A): O The ratio (I/Y) is constant. O Output grows faster when it is relatively closer to the steady-state level. O Efficiency units of labor do not play any role in the determination of the steady-state level of GDP. O The model is not able to explain catch-up growth.
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- For a high-income economy like the United States, what aggregate production function elements are most important in bringing about growth in GDP per capita? What about a middle-income country such as Brazil? A low-income country such as Niger?Suppose an economy begins in steady state. By what proportion does per capita GDP change in the long run in reponse to each of the following changes? Production function is Y=AK^1/3L^2/3 a. Investment rate doubles b. depreciation rate falls by 10% c. Productivity level rises by 10% d. Earthquake destrys 75% of the capital stock e. Generous immigration policy lead the population to doubleY - K"(LE) The economy has a capital share of 0.20, a saving rate of 45 percent, a depreciation rate of 3.75 percent, a rate of population growth of 5.00 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k"), output per elffective worker (y"), and the marginal product of capital. k' - y* = marginal product of capital =
- 5. Consider the Solow growth model. The production function is: Y = Kª(AN)!-«, the is the capital depreciation rate is & per year, the population and technology savıng rate grow at annual rates of n and g respectively. Calculate K/N, K/(AN), Y /N and Y/(AN) in the steady state. Does the change in s affect the growth rate? Explain. S, 6. Suppose that the model of the economy is given by Y = C +I+G + X 99 sunny hp 10 f8 144 14 is & 6. 7. 8. 24Figure 1 shows the China's Real GDP Growth Rate since 1981, the arrow indicator shows the trend of decreasing growth rate during the last 15 years. Explain the trend of growth rate using the concept of production function. Do you expect the trend the trend to have significant change in the near future? Figure 1: China's Real GDP Growth Rate 16 15 14 13 12 11 10 9. 7 4 3 Jan-81 Jan-85 Jan-89 Jan-93 Jan-97 Jan-01 Jan-05 Jan-09 Jan-13 Jan-17 Jan-21 00 LOConsider an economy in which the labour force grows by 2.7 percent per annum, physical capital grows by 4 percent per annum and human capital grows by 1.8 percent per annum. Suppose 45 percent of national income goes to labour and 40 percent to capital. Use a constant returns to scale production function to answer the following growth accounting questions: (a) If the Solow residual were zero what rate of growth would the economy achieve? (b) The country's actual rate of growth has been 4.5 percent per annum, which is faster than the growth rate generated by the accumulation of capital and labour stocks. Calculate the value of the residual.
- Let the production function be Q = K0.®L0.2 Solow's assumptions are K = sQ – 6K The symbols s represents a (constant) marginal propensity to save, n, a (constant) rate of growth of labor and 8 constant depreciation rate. (a) Derive the fundamental equation of Solow growth model for given production function. (b) Sketch graph of with k on the vertical axis and k on the horizontal take n = 0.01, s = 0.3, 8 = 0.1.1. 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.How can we measure growth over the very long run? Te poorest countries in the world have a per capita income of about $600 today. We can reason-ably assume that it is nearly impossible to live on an income below half this level (below $300). Per capita income in the United States in 2015 was about$51,000. With this information in mind, consider the following questions.(a) For how long is it possible that per capita income in the United Stateshas been growing at an average annual rate of 2% per year?(b) Some economists have argued that growth rates are mismeasured. Forexample, it may be difcult to compare per capita income today with percapita income a century ago when so many of the goods we can buy todaywere not available at any price then. Suppose the true growth rate in thepast century was 3% per year rather than 2%. What would the level of percapita income in 1800 have been in this case? Is this answer plausible?
- YIN CN Next question Suppose that the production function is given by Y- 05VR N 454 where Y is output, Kis capital, and N is the number of workers 4 Suppose that 60 05 With your favonte spreadsheet software, compute steady-state output per worker and steady-state consumption per worker for s 0, 801, a02, s1 Graph the steady-state level of output per worker and the steady-state level of consumption per worker as a function of the saving rate 25 1) Using the multipoint curve drawing tool, drawa curve showing the relationship between YIN and the saving rate. Properly label your curve 15 2) Using the multipoint curve drawing tool, draw a curve showing the relationship between CIN and the saving rate. Properly label your curve 0.5 Although the control ponts for your multpownt curves do not have to be exact try to plot them as accurately as possible 01 02 03 a'4 os o6 07 os 09 Saving rate, At what saving rates are YIN and CIN maximized? After plotting the final point of your multipoint curve…2. Recall that general form of fundamental equation of growth in Solow model is described as follows: k: = s f(k) – (gs + 5)ka %3D Noting that at steady-state ks = 0 and hence a Using the fact kss= 0, show the steady-state graphically and provide economic interpretation of the steady-state condition s- f(k ss) = (gs + 8)k s- b. Using the same graph you draw in part (a) explaim the transitional dynamics of the Solow. Hint: Define what happens if k. ks-Give 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.