Suppose that the population growth rate of a developing economy drops. Using carefully labeled diagrams explain what the effect is, in the neoclassical (Solow) growth model in both, (i) the short run, and (ii) the long run. What is the growth rate of aggregate capital in the original and new steady states as well as in the transition from one steady state to the other?
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- In a neoclassical (Solow) growth model, does a decrease in the savings rate permanently affectsthe growth rate of real output? Why or why not? Explain and show graphically.2. Recall that general form of fundamental equation of growth in Solow model is described as follows: k: = s f(k) – (gs + 5)ka %3D Noting that at steady-state ks = 0 and hence a Using the fact kss= 0, show the steady-state graphically and provide economic interpretation of the steady-state condition s- f(k ss) = (gs + 8)k s- b. Using the same graph you draw in part (a) explaim the transitional dynamics of the Solow. Hint: Define what happens if k. ks-4. Assume our endogenous growth model with 0<1. Now assume that a more open immigration policy suddenly boosts the US population growth rate to a higher constant rate: n'. Graph the short and long-run effects of this in a graph of the growth rate in ideas over time.
- 5. Use the Solow Model. Suppose an economy begins in steady state. By what proportion does per capita GDP change in the long run in response to each of the following changes? (a) The investment rate falls by 35% (b) the depreciation rate rises by 20% (c) The productivity level falls by 15%5. Consider the Solow growth model. The production function is: Y = Kª(AN)!-«, the is the capital depreciation rate is & per year, the population and technology savıng rate grow at annual rates of n and g respectively. Calculate K/N, K/(AN), Y /N and Y/(AN) in the steady state. Does the change in s affect the growth rate? Explain. S, 6. Suppose that the model of the economy is given by Y = C +I+G + X 99 sunny hp 10 f8 144 14 is & 6. 7. 8. 24n the endogenous growth model, suppose that there are three possible uses of time. Let u = the fraction of time spent working s = fraction of time spent neither working nor accumulating human capital (unemployment) 1 – u – s = fraction of time spent accumulating human capital If z = 1, b = 5, and the economy begins in period 1 with 100 units of human capital, find the values of Y, H, and Y’ for each of the scenarios below. In this model, does the scenario with the greater human capital accumulation lead to the highest per capita income (Yes/No)? u s H Y H' Y' .7 .05 100 .6 .15 100 .6 .05 100 .5 .10 100 Does the scenario with the greater human capital accumulation lead to the highest per capita income (Yes/No)?
- Assume that a E (0, 1). Draw a diagram that describes the evolution of kt, and show that there exists a unique steady state, k* > 0. Label properly. Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. , Now, assume that α = 1. Draw a diagram that describes the evolution of kt, and show that income per worker can grow indefinitely in this case. Label properly.How can we measure growth over the very long run? Te poorest countries in the world have a per capita income of about $600 today. We can reason-ably assume that it is nearly impossible to live on an income below half this level (below $300). Per capita income in the United States in 2015 was about$51,000. With this information in mind, consider the following questions.(a) For how long is it possible that per capita income in the United Stateshas been growing at an average annual rate of 2% per year?(b) Some economists have argued that growth rates are mismeasured. Forexample, it may be difcult to compare per capita income today with percapita income a century ago when so many of the goods we can buy todaywere not available at any price then. Suppose the true growth rate in thepast century was 3% per year rather than 2%. What would the level of percapita income in 1800 have been in this case? Is this answer plausible?According to Solow growth model, which are the main factors leading to expect convergence across regions. In addition, discuss which factors, if any, may lead to expect no convergence. b) In 2010, GDP per capita of the region of Brussels (Belgium) was €55000, while that of Severozapaden (Bulgaria) was €6.500. Assume that, from 2010 onwards Brussels maintains a constant anual growth of 2% during 50 years. • Obtain the (constant) annual growth rate at which the region of Severozapaden should grow in order to attain the same GDP per capita of Brussels after this period (50 years). Hint: use instantaneous annual growth rates. c) Discuss the implications of your answers in sections a) and b) for EU's regional policy.
- Consider a two-sector model of growth, with two kinds of investment opportunities—one with a diminishing marginal product and one with a constant marginal product. a. What does the production function for this problem look like? b. Characterize the set of equilibria for this model. Does output in any of the equilibria have nonzero per capita growth? c. What can this model help us explain that strict endogenous and neoclassical growth models cannot?What is the mechanism in the Solow model that generates growth? Why isthis an appealing mechanism? Why does it fail to deliver economic growth inthe long run?2.Define the steady-state growth rate in the Solow model either graphically or mathematically. Using that tool, show how faster population growth affects the steady state? Explain why the answer you got makes sense.