Show your work economics 110a spring 2015 dr maria

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Economics 110A Spring 2015 Dr. Maria Cândido 9 7. (12 points) Consider the following Romer model of economic growth: Y t = A t L yt Δ A t + 1 = z A t L at L at + L yt = L L at = l L a. Derive the growth rate of knowledge (ideas) using the model above. b. Derive the expression for output per capita in this economy, using the model above. c. If A 0 = 10, l = 0.02, z = 1/1,000 and L = 2,000, what is the growth rate of knowledge in this economy? Show your work.
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Economics 110A Spring 2015 Dr. Maria Cândido 10 d. If A 0 = 10, l = 0.02, z = 1/1,000 and L = 2,000, what is the level of per capita output in year 10? Show your work. 8. (5 points) Consider the following figure: Romer Model: Per Capita Output (Ratio Scale) What do you think is an appropriate explanation for what happened at t 0 ? In particular, which one coefficient might have changed to justify a graph such as the one above? Explain in words what happens in the short run and in the long run as a result of that parameter shift.
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Economics 110A Spring 2015 Dr. Maria Cândido 11 9. (6 points) A case study in your textbook compares Luxembourg with the US. The U.S. population is about 600 times larger than Luxembourg. Suppose that the countries are similar in all other aspects. a. What would the Romer model predict the U.S. growth rate of output per capita to be relative to the one of Luxembourg? Explain. b. In the last 50 years, the growth rate of per capita GDP in the U.S. averaged 2.3 percent per year while growth in Luxembourg has been about 3.2 percent per year in the same period. Does this prove that the Romer model is wrong? Explain carefully. 10. (8 points) Consider the Solow model we presented in this course. a. “ A reduction in the saving rate will cause a permanent reduction in the rate of growth of output.” Is this sentence true or false? Explain. In your answer, focus on the long-term effect of a reduction in the saving rate.
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Economics 110A Spring 2015 Dr. Maria Cândido 12 b. Will a reduction in the saving rate have an impact on the growth rate of output in the short-term? Explain carefully. Use two graphs to illustrate your answer. In the first one, put stock of capital (K) in the horizontal axis and output (Y) in the vertical axis. In the other, put time in the horizontal axis and output (Y) in the vertical axis. c. Suppose the production function is Y t = A K t α L t 1- α . If the economy is characterized by the following parameters: A = 1, L = 100; α = ¼ ; and d = 0.1. What is the level of capital that maximizes steady-state consumption (the golden-rule level of capital)? Explain. Show your computations.
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Economics 110A Spring 2015 Dr. Maria Cândido 13 SCRATCH PAPER:
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