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Intermediate Macroeconomics problem set. Does anyone know how to solve these problem sets or can help? I am

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ECON-UA 12 — Intermediate Macroeconomics Professor: Jaroslav Boroviˇ cka TA: Jonathan Payne Fall 2016 Problem Set 1 Due on September 23, in your recitation Please read the instructions on problem sets in the syllabus carefully. 1 True or false? For each of the following statements, decide whether it is true or false, and explain your answer in at most two sentences using the material you learned in the course . No points will be given without an appropriate explanation! Question 1.1 Countries across the world have been growing persistently since at least year 1200. Question 1.2 We use the logarithmic scale to plot the graph of a variable so that the same growth rates at di±erent levels of that variable appear as the same slopes of the graph. Question 1.3 China and India are important for global economic growth because their slow growth rates in the last decade slowed down the world economy signi²cantly. Question 1.4 The model of production we used to explain cross-country di±erences in GDP per capita is a success because we were able to explain a large share of those di±erences using cross-country di±erences in total factor productivity. Question 1.5 The Cobb-Douglas production function is a plausible model of aggregate production technology because as the country grows richer, a larger and larger share of income goes to the hands of capital owners. Question 1.6 When a production function exhibits constant returns to scale, it must also exhibit a constant marginal product of capital. 1
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Question 1.7 Firms in our model earn zero economic proft because they are using easily replicable technology which anybody can use ±or ±ree. Question 1.8 There is a strong empirical relationship between the amount o± capital per capita and GDP per capita across countries. Di²erences in capital per capita there±ore explain the di²erences in output per capita. 2 Quantitative exercises 2.1 Growth rates Question 2.1 Sketch the graph o± the ±unction f ( t ) = e 0 . 02 t on the interval x [0 , 100]. Sketch the graph o± the ±unction g ( t ) = ln ( f ( t )). Now sketch the graph o± the ±unction f ( t ) using a logarithmic (ratio) vertical scale. Explain the relationship between the latter two graphs. Do the same three exercises ±or the ±unction f ( t ) = e - 0 . 01 t . Interpret these graphs ±rom the perspective o± the GDP per capita ±or a country that grows 2% per year, or, on the other hand, declines at 1% per year. Use whatever method you fnd suitable. You can do it by hand, evaluating the ±unction at a couple o± points and connecting the dots. Or ask your graphical calculator. You can also go to the brilliant Wol±ram Alpha ( http://www.wol± ) and type in plot exp ( 0 . 02t ) ( t from 0 to 100 ) In any case, you must properly label the graphs so that it is clear what they show. Note : I± you decide to use Wol±ram Alpha, I recommend you consult the additional handout ( logplot.pdf ) prepared by Jonathan Payne. Question 2.2 Consider the Cobb-Douglas production ±unction with equal capital and labor shares: Y t = F ( K t ,L t ) = A t K 1 / 2 t L 1 / 2 t . I± GDP grows at 3%, total ±actor productivity at 1%, and capital at 3%, what is the pop- ulation growth rate? What is the growth rate o± GDP per capita? Provide a mathematical derivation with your answer. Question 2.3 Consider the Cobb-Douglas production ±unction with capital share α : Y t = F ( K t ,L t ) = A t K α t L 1 - α t . I± GDP grows at 3.25%, total ±actor productivity at 2%, capital at 2%, and population at 1%, what must the capital share be? 2
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