Assume an endogenous growth model with a production function that in per capita terms can be written as y = 0.8k. If the savings rate is s 0.3, the rate of growth of population is n = 0.03, and the rate of depreciation is d = 0.1, how high is the rate of growth of output per capita? A. 14% B. 17% C. 13% D. 11% E. There is not enough information to calculate it.
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- (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…2. Solow-Swan Model (a) You will demonstrate the importance of diminishing returns to capital in the Solow-Swanmodel. Draw a Solow-Swan diagram in which there are constant returns to capital. Thiswould happen if the production function were Yt= AKt, where A = 1. Furthermore,assume that the sum of population growth and the depreciation rate is greater than thesaving rate. Does the economy converge to a steady state in this case? To answer thisquestion, you should draw a Solow-Swan diagram in terms of output per person, as we didin class. Use this diagram to explain why the economy converges to a steady state or doesnot. (b) Assume, instead, that the sum of population growth and the depreciation rate is equal tothe saving rate. In this case, are there any steady states? If yes, describe the steady-statelevels of capital per person. If no, explain why not. (Note: Diagram is not needed for thispart.)Suppose a Solow economy is initially at its steady state k∗, and suddenly is hit by a decrease in the depreciation rate δ, from δ to δ1. This change does not alter any of the other exogenous parameters in the model Depict this situation in a graph What happens to steady state level of capital per capita in this situation? What happens to the level of capital per capita over time? Depict this in a graph and explain intuitively.
- Suppose that the production function is Y= 10(K)1/4 (L)3/4 and capital lasts for an average of 50 years so that 2% of capital wears out every year. Assume that the rate of growth of population equals 0. If the saving rate, s =0.128, calculate the steady-state level of capital per worker, output per worker, consumption per worker, saving and investment per worker and depreciation per worker.3 Assume a closed economy, perfectly elastic labor supply, and linear technology. Suppose the incremental capital-output ratio (ICOR) is 3, the depreciation rate is 3%, and the gross savings rate is 10%. Use the Harrod-Domar growth equation to determine the rate of growth. What would the gross savings rate have to be to achieve 5% growth? Assuming a perfectly elastic labour supply, state one criticism of this model from an exogenous growth theory viewpoint and another criticism of this model from an endogenous growth theory viewpoint.4.The Solow growth model differs from the Harrod-Domar because: a.Assumes that depreciation rate and population growth are exogenous b.Assumes that the rate of technological progress varies from country to country. c.Predicts that permanent growth is achievable only through technological progress d.Predicts that poorer countries will grow faster than richer countries.
- In 1998, Brazil had a per capita GDP of about $4,500, compared to per capita GDP of about $28,000 in the US. (A) If per capita growth were to average 2% per year indefinitely in the US and 5% per year in Brazil, how many years would it take Brazil to catch up with the US? (B) Using the assumptions of the Cobb-Douglas production function, how fast would capital stock have to grow for per capita GDP to rise 5% per year? How does that compare with capital stock growth of 3% per year in the US (assume technology advances 1% per year in both countries)? (C) In mature industrialized societies, the capital/output ratio is approximately 3.0. If the average depreciation rate is 0.04, what would be the current saving and investment ratio in the US? What would it be in Brazil if per capita GDP rose 5% per year?Sweden and Norway are two neighboring countries in Northern Europe with similar savings rates, population growth rates, technology growth rates, and depreciation rates. However, Norway differs from Sweden in that Norway has large deposits of oil all along its coast, which makes it very easy for Norway to produce large quantities of crude oil every year with relatively little capital and labor. a) Draw a Solow Growth diagram that compares Sweden and Norway. What is the main difference between the two countries in the diagram? b) According to the Solow Growth Model, which country would have a higher standard of living in the long run? Which country would have a higher growth rate of its standard of living in the long run? c) Suppose now that, in the long run, oil becomes obsolete and has no value because it is uneconomical relative to renewable energy sources like solar and wind power. What would this do to your Solow Growth diagram in part a? How would the standard of living in Norway…Consider a Solow–Swan model with saving rate s = 0.4, labour force growth gL = 0.05, constant productivity A = 1, and depreciation ?δ = 0.05. If output per worker is y = Y/L = 200 and capital per worker is k = K/L = 1000, which of the following is true? Group of answer choices - Effective depreciation per worker is 80, saving per worker is 100 and k will increase towards the steady state - Effective depreciation per worker is 100, saving per worker is 80 and k will decrease towards the steady state - Effective depreciation per worker is 100, saving per worker is 80 and k is at the steady state - Effective depreciation per worker is 80, saving per worker is 100 and k will decrease towards the steady state
- Consider a steady-state equilibrium in the model of Section 14.4. Suppose that κ = 0 and G’ (0) ∗ ≡ G’−1 ((1− λ)/ρ), and suppose also that (a) Show that in this case the steady-state equilibrium has zero growth. (b) Show that κ > 0 leads to a positive growth rate. Interpret this result, and contrast it to the negative effects of relaxing the protection of IPR in the baseline model of Schumpeterian growth.An economy has the per-worker production function yt=f(kt)=4kt)0.4, where yt is the output per worker and kt is the capital-labor ratio. The depreciation rate is 0.15, and the population growth rate is 0.04. Saving is St=0.5Yt, where St is total national saving and Yt is total output. The slope of the per worker production function is given by f' (kt)=1.6kt-0.6 . What is the steady state value of capital-labor ratio, k*? Round your answer to at least 2 decimal places.Population Growth Population growth in the US has, for a very long time been about 1% per year.Take the production function to be y = k0.5, where y and k are output andcapital per capita. The depreciation rate is about 10% per year and the savingsrate is about 20%. 1. What is the steady state capital per capita rate?2. From one period to the next, at what rate does total capital (not percapita) grow.3. If the population growth rate grew to 1.5%, how much would steady statecapital per capita change? Then how much is total capital changing atthis steady state?