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- Consider an economy that has access to a production technology Y = AKαL1−α where Y is output, A is the level of technology, K is capital and L is the amount of labor in the economy. Capital evolves according to K˙ = sY (thus, the depreciation rate δ = 0). The x˙ population growth rate is n. (Throughout, gx = x , where x can be any of the variables in the model.) (a) Assume that technology is determined by A = BKφ What sort of endogenous growth model is this? Find K/K in terms of the K, L, and other parameters of the model.Suppose the economy is on a balanced growth path in the Romer model, and then, in the year 2030, ̄l (lower case L bar) decreasesimmediately and permanently to the new level ̄l′ (lower case L bar one). (a) Solve for the new growth rate of knowledge and yt. (b) Make a graph of yt over time using a ratio scale.QESTION 6 for which of the following does the Solow model NOT provide adequate explanation? a. What causes long-term economic growth b. The case of productivity differences across countriesc. Why saving rates differ across countries d. All of these answers are correct e. Why population growth rates differ across countries Using the Solow model, if, in time, t=0, the initial capital stock is 100, investment is 25, the population is normalized to 1, and e 10 percent, then capital accumulation from period t=0 to period t=1 is: a. 15 b. 115 c. 35 d. D. 0 e. -15
- Assume that the growth rate of the capital stock in each period is determined by the level of output in the previous period. 1) An economy of 80 million people has ten percent of them engaged in research and development, where their productivity is 0.0035. The economy is on a balanced growth path, when suddenly 2.88 million people move from goods production into R&D, raising the fraction there to 13.6 percent. In the one period that begins with this labor reallocation, the growth rate of output is ________. [Refer to the instruction above.] A) 2.8% B) 0.0% C) 3.8% D) 2.2%Consider an economy with a Cobb-Douglas production function with α = 1/3 that begins in steady state with a growth rate of technological progress of g of 2 percent. Consider what happens when g increases to 3 percent. (a) What is the growth rate of output per worker before the change? What happens to this growth rate in the long run? (b) Perform a growth accounting exercise for the economy, decomposing the growth rate in output per capita into components contributed by capital per capita growth and technology growth. What is the contribution of the change in g to output per capita growth according to this formula? (c) In what sense is the growth accounting result in part b producing a misleading picture of this experiment? Explain why this is the case.Consider the simple innovation model studied in class. In this model, the society allocates a fraction "gamma" of workforce to innovation and the remaining fraction to production. Suppose that, for simplicity, total workforce is normalized to unity: L = 1. If the productivity growth rate is defined by d A t/dt = "theta"* "gamma" * A_t and real GDP per worker by yt = At* (1 - "gamma"), what is the long-run growth rate of y_t?
- As economic growth models become more and more inclusive of realistic conditions and incorporating complexities of the economy, disaggregation on inputs were introduced in capital (having physical and financial components). How does this labor disaggregation compare with that of capital, and its implications with less developed countries like the Philippines (aiming for a more robust economic growth)?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?Korea. Over the last 60 years or so, Korea has been one of the most successful economies in the world. What are the sources of this success? Consider the following data: GDP per capita is expressed in 2017 US dollars. Population and employment are in millions of heads. Capital is in thousands of dollars. Education is a human capital index based on the average years of schooling. (a) Compute the (average continuously compounded) growth rate of GDP per worker. (b) Use our growth accounting methodology to allocate growth in output per worker to TFP, capital per worker, and human capital. What factors are most important? (c) What is the growth rate of GDP per capita? How does it differ from growth in output per worker? Why?
- Consider the simple innovation model. In this model, the society allocates a fraction "gamma" of workforce to innovation and the remaining fraction to production. Suppose that, for simplicity, total workforce is normalized to unity: L = 1. If the productivity growth rate is defined by d A_t / d t = "theta" * "gamma" * A_t and real GDP per worker by y_t = A_t * ( 1 - "gamma" ), what is the long-run growth rate of y_t ?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.The Solow Growth Model is an exogenous model of economic growth that analyzes changes in the level of output in an economy over time as a result of changes in the population growth rate, the savings rate, and the rate of technological progress. Consider the Solow model. a) Explain using a graph why there is a poverty trap in this model b)Describe how an economy such as one characterized by this model may break out of a poverty trap.