Production function is given by Y = 3Kª(AN)-a, where a=2/3. The rate of depreciation of capital is equal to 12 percent, the rate of technological progress is equal to 5 percent, and the rate of population growth is equal to 3 percent. The economy was in the steady state at timet and the level of technology was equal to A=30. Use the Solow growth model to answer the following questions.
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- You were discussing the growth models with your friend Gaston during spring break. He summarized that the basic difference between the Solow model and the Romer model is that the Solow model suffers from diminishing returns-each additional unit of capital has less benefit than the previous unit. The Romer model doesn't have the same problem as labor used to generate new ideas doesn't have diminishing returns. He hypothesizes that if you changed the law of motion to At+1 = At + zol1/2A; that now the Romer model has diminishing returns to labor and will reach a steady state where growth is zero. Is he right?n the endogenous growth model, suppose that there are three possible uses of time. Let u = the fraction of time spent working s = fraction of time spent neither working nor accumulating human capital (unemployment) 1 – u – s = fraction of time spent accumulating human capital If z = 1, b = 5, and the economy begins in period 1 with 100 units of human capital, find the values of Y, H, and Y’ for each of the scenarios below. In this model, does the scenario with the greater human capital accumulation lead to the highest per capita income (Yes/No)? u s H Y H' Y' .7 .05 100 .6 .15 100 .6 .05 100 .5 .10 100 Does the scenario with the greater human capital accumulation lead to the highest per capita income (Yes/No)?Using logarithmic form of this GDP production function compute the TFP contribution to GDP growth rate assumingalpha=0.4, beta=0.50 while GDP growth rate is 4.0 percent, capital stock growth rate is 5percent, labor growth 3percent and human capital growth 2 percent.
- SOLOW’S MODEL Consider following information from China and New Zealand in table: China New Zealand Real per capita GDP growth, 2012-2019 (average %) 6.5% 1.6% Real GDP per capita, 2012 (in constant 2017 USD) 11,169 32,989 Real GDP per capita, 2019 (in constant 2017 USD) 16,655 45,555 Average savings rate, 2012-2019 (% of real GDP) 43.7% 21.4% Capital stock, 2019 (in millions of constant 2017 USD) 14,283,969 409,160 Population (in millions) 1,434 4.8 Population growth (in %) 0.5% 1% Capital depreciation rate (in %) 3% 3% Production function in both economies has following functional form: Yt = A* K1/3 * L2/3 Where Yt denotes aggregate GDP in period t, Kt is aggregate capital stock, Lt is employment (assumed equal for whole population) and A is total factor productivity. Using information provided in table, explain from SOLOW MODEL perspective what factors could explain differences in average GDP per capita…Suppose Westeros produces output according to the production function: Y = √K The fraction of output that is saved and invested in new capital is 20%. The depreciation rate is 5%. Use this information to answer the following questions. Macmillan Learning a. What is the steady-state amount of capital (K) in Westeros? b. What is the steady-state amount of output (Y*) in Westeros? c. If Westeros had started out with 25 units of capital, what would the Solow model predict would happen to its output in the long run? O It will decrease, since that is above its steady state level of output of 4 It will decrease, since that is above its steady state level of output of 16 It will increase, since that is below its steady state level of output of 16 It will increase, since that is above its steady state level of output of 41 It will remain at 25, since that is its steady state level of outputIn the Malthusian model, suppose that the quantity of land increases. A) using diagrams, determine what effects this has in the long-run steady state and explain your results. b)Plot what happens to the following variables over time as a result of the increase in the quantity of Land, population size and consumption per person
- (a) Consider an economy that is initially in a steady state equilibrium. Assume that in this equilibrium it has a saving rate of 50 per cent and a depreciation rate of 2 per cent. Further assume that the population growth rate is 3% and that the level of output produced can be represented by the following production function: = where A = 1 and = 0.5. Use the Solow-Swan model to determine the level of capital per worker and output per worker in this economy. (1 mark) (b) Now suppose the government introduces a set of policies to improve the institutional set up as well as better production technique which increases total factor productivity by double. What is the new steady state level of capital per worker and output per worker? (1 mark) (c) Use a Solow-Swan diagram to show the qualitative effects of this new government policy upon steady state output per worker and capital per worker. Briefly describe the intuition behind this result. (1 mark) (d) Now suppose, population growth rate…So what was the economic growth neoclassical growth model?1)Suppose that in the year 2015, the quantity of capital per worker in a certain country was equal to 60, the quantity of output per worker equaled 90, the fraction of output invested was 30%, and depreciation rate was 2%.The change in capital per worker equals to: 15 25.8 16.2 -15 2)Based on Malthusian model, predict what will happen to income-per-capita and population size if a famine destroyed the crops of the whole country. In short run income increases In the long run low income per capita generates a low pop growth rate, leading to move along the curve and back to steady state level of income per capita. In long run income decreases In the short run low income per capita generates a low pop growth rate, leading to move along the curve and back to steady state level of income per capita. 3)If two countries currently have the same output level and same factor accumulation, then which country will reach the steady state first? The one with higher investment level The one with lower…
- What is the effect of an increase in total factor productivity on steady state population and consumption per worker in the Malthusian model?Population Growth and Technological Progress – Work It Out PLEASE WRITE ANSWERS CLEARLY An economy has a Cobb-Douglas production function: Y = K“(LE)'-a The economy has a capital share of 0.30, a saving rate of 42 percent, a depreciation rate of 4.00 percent, a rate of population growth of 5.25 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 effective worker (y*), and the marginal product of capital. k* = y* = marginal product of capital =An increase in research productivity: Suppose the economy is on a balanced growth path in the Romer model, and then, in the year 2030, research productivity z̅ rises immediately and permanently to the new level z̅′. Solve for the new growth rate of knowledge and yt. Make a graph of yt over time using a ratio scale. Why might research productivity increase in an economy? I do not understand how to solve this, I'm confused. Am I supposed to make an equation or write out an answer?