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Explain the absolute convergence and conditional convergence hypotheses in the Solow-Swan model (provide country examples as well).
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- Which of the graphs (if any) show a surprising or seemingly incorrect relationship based on what you know about conditional convergence and the Solow model?Assume the following scenario for a society: A terrible disease increases the mortality rate of women of childbearing age. Using (i) the Malthusian and (ii) Solow models (initially at steady- state), determine what the income per capita would be for each model in the short-run and in the long-run. Use graphical analyses as an aid in your explanation. Make sure to conclude your explanations with the differences in income per capita, if any, that are predicted by the two models for this scenario.Convergence Refer to the version of the Solow model with TP and H accummulation examined in class. a-) Define absolute convergence. How would the per capita income differntials across countries be explained if the absolute convergence prediction of the model were accepted to be true? b -) Define conditional convergence. How would the per capita income differentials across countries be explained if the conditional convergence prediction of the model were accepted to be true? (Please work on a diagram correctly labeled while answering.)
- Derive the expression for the speed of convergence for k in the Solow model. Show this is also the speed of convergence for output y. Interpret.Consider two countries (A and B) identical in everything except that country A has higher capital. According to the Solow model, which of these statements is true? A Country A will grow as fast as country B and will end up with a higher equilibrium capitalK* B. Country A will grow faster than country B and will end up with the same equilibrium capital K C. Country A will grow as fast as country B and will end up with a lower equilibrium capital K* D. Country A will grow slower than country B and will end up with the same equilibrium capital K* cheik pieConsider the Solow-Swan growth model, with a savings rate, s, a depreciation rate,8, and a population growth rate, n. The production function is given by: Y = AK + BK¹/2 H¹/4L¹/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb-Douglas production function. (a) Express output per person, y =Y/L, as a function of capital per person, k =K/L.
- In the Schumpeterian model, a higher level of technology A) Makes new discoveries less probable in any given period of time B)Makes new discoveries more probable in any given period of time C) Increases the growth rate of income, but not capital per worker D)Does not affect the probability of new discoveries in any given period of timeConsider the Solow model. Using suitable diagrams, compare the different dynamics for the levels and growth rates of capital per capita and output per capita following: (a) a new wave of immigration, (b) an increase in the saving rate, (c) a one-shot foreign investment which increase the size of the available stock of capital, (d) an important technological advance.In the early 1980s, Brazil and South Korea had similar saving rates (around 17% of GDP) and similar levels of income per capita (around $6,000 in 1996 dollars). In the 1980-2010 period, the saving rate stayed around 17% in Brazil, whereas it increased to more than 30 % in Korea. (a) Use the Solow model to predict the effects on the steady-state income per capita for both countries (assuming their multifactor productivity gains were exactly the same) and compare. (b) In 2010, income per capita was $9,000 in Brazil, and $28,000 in Korea. Is this consistent with your predictions?
- (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…Suppose the economy of an island behaves as the Solow model (Y=AK1/2L1/2), version 1.0 (constant population). Suppose that the productivity parameter is A=90, the depreciation rate is d=1/10, the savings (investment) rate is s=0.10, and the labor force is equal to 2 million (and constant over time). 1-Due to climate change, from 2011 onward, every year the island is hit by hurricanes of increasing force that destroy capital. As a result, the depreciation rate doubles. What will be the new long-run (steady state) value for income per worker (Y/L)? Pick the closest value. Also label the new steady-state GDP as point C in the diagram. Between 75 and 85 None of the other options Between 4,500 and 5,200 Between 8,000 and 8,500 Between 44 and 49 2-In year 2021 investors recognize that the depreciation rate is higher than a decade earlier. They also recognize that the actual returns to their investments in physical capital over the previous decade have consistently fallen below their…The economic growth model(s) of ( ) below can be recognized as an endogenous model. A Slow-Swan model; B Ricardo’s model; C Romer-Lucas model; D Harrod-Domar model; E Aghiot-Howitt model.