The purpose of this question is to study the predictions of the Solow model for capital flows between rich and poor countries. In the Solow model, firms hire capital and pay a rental rate r for the services of k. Production is given by y = Akº and r is determined as the rate that maximizes profits or that solves: Akark To maximize the previous expression capital must be rented until the marginal product of capital, MPK equals the return: [You don't need to maximize profits but just assume that returns are equal to MPK] r = a Aka-1
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- (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…Solow-Swan Model Assume an economy with a production function that exhibits constant returns to capital.1 Ineach of the following cases, draw a Solow-Swan diagram and use is to explain whether andhow the economy converges to a steady state. Clearly identify any steady state(s) or otherwiseexplain why there is no steady state. (i) Assume the sum of population growth and the depreciation rate is greater than the savingrate.(ii) Instead assume the sum of population growth and the depreciation rate is less than thesaving rate.(iii) Instead assume that the sum of population growth and the depreciation rate is equal tothe saving rate. What is the importance of diminishing returns to capital in the Solow-Swan model?2. Solow-Swan Model (a) You will demonstrate the importance of diminishing returns to capital in the Solow-Swanmodel. Draw a Solow-Swan diagram in which there are constant returns to capital. Thiswould happen if the production function were Yt= AKt, where A = 1. Furthermore,assume that the sum of population growth and the depreciation rate is greater than thesaving rate. Does the economy converge to a steady state in this case? To answer thisquestion, you should draw a Solow-Swan diagram in terms of output per person, as we didin class. Use this diagram to explain why the economy converges to a steady state or doesnot. (b) Assume, instead, that the sum of population growth and the depreciation rate is equal tothe saving rate. In this case, are there any steady states? If yes, describe the steady-statelevels of capital per person. If no, explain why not. (Note: Diagram is not needed for thispart.)
- Using the one factor Ricardian model concept and the unit labor requirements information in the table below, determine d) In what commodity production, foreign has a comparative advantage.Explain.e) Which country has an absolute advantage. Explainf) If PC is the price of Cheese and PW is the price of Wine, and PC = PW, thenWhat commodities will domestic specialize in?g) If PC is the price of Cheese and PW is the price of Wine, and PC = PW, thenwhat commodities will foreign specialize in?h) Using the comparative advantage information above, determine the commodity thatexported and imported by domestic and foreign respectively?i) If PC = PW or PC/PW = 1, what is the gain from trade obtaineddomestic and foreign if each country specializes inwhich production has a comparative advantage? Explain.j) If if PC = PW = $9, what is the wage relative to trade.Which country's workforce benefits from the trade?Consider Romer Model 2. Suppose there are two countries, rich and poorone. Both countries have the same population size, L and the same knowledgegeneration productivity parameter, z. At the beginning, time 0, the rich countryhas more knowledge stock than the poor one, Ar0 > Ap0, where subscript labelstime and superscript labels country being rich or poor. However, the fractionof researchers in poor country is larger than the one in rich country, ̄lp > ̄lr .Question 4 Part aIn which country, would you prefer to live in the short-run? How about in thelong-run?How long would it take for the poor country to reach rich one’s per capitaoutput level? Show your results analytically and graphically as well. (If you pre-fer solving this question numerically by assigning values to the above parametersand variables, feel free to do soThis model states that output depends on the economy’s initial endowment of capital and labor. Y = f (K,L)a. Harrod-Domar Modelb. Rostow’s Stages of Growth Modelc. Solow Modeld. Power-Balance Model
- Consider the basic Solow model with no population growth and no technological progress and a production function of the form F (K, H ), where H denotes the efficiency units of labor (human capital) given by where N is the set of all individuals in the population, and hi is the human capital of individual i. Assume that H is fixed. Suppose there are no human capital externalities and factor markets are competitive. (a) Calculate the steady-state equilibrium of this economy. (b) Prove that if 10% higher h at the individual level is associated with a% higher earnings, then a 10% increase in the country’s stock of human capital H will lead to a% increase in steadystate output. Compare this result to the immediate impact of an unanticipated 10% increase in H (i.e., consider the impact of a 10% increase in H with the stock of capital unchanged).Exercise 4: Growth and capital over-accumulationSuppose two countries, A and B, with the same production function Y = KαL1−α. Thevalue of α is 0.30, the growth rate of population is 2% and the depreciation rate is 5%.a) Show that with price-taking firms the share of labor must be 1 − α.b) Compute the stock of capital, output and consumption per unit of labor in the steadystate if the savings rates were 25% for country A and 35% for country B.c) Compare both economies to the Golden Rule.d) Explain what would happen to both countries if suddenly their savings rate becamethe Golden Rule savings rate.answer all! Consider the Endogenous Growth Model with the representative consumer. The efficiency parameter of human capital accumulation technology is b = 5. The total productivity factor is given by z = 60. Denote by Ht the human capital accumulated in period t, and by ut the time spent working in period t. Assume u0 = 0.85 and H0 = 1. 1. Compute the consumer consumption Ct for periods 0 and 1. 2. Starting from year 2, the government applies a policy that raises b to 9. Now assume that in face of this increased value of human capital in the economy, the consumer responds optimally by decreasing ut to 0.75. Calculate the consumption Ct for periods 2 and 3.
- Question 2 If a natural disaster destroys a large portion of a country's capital stock but the saving and depreciation rates are unchanged, the Solow model predicts that the economy will grow and eventually reach:a. A lower steady-state level of output than it would have before the disasterb. None of these answers is correctC. The same steady-state level of output as it would have before the disasterd. A higher steady-state level of output than it would have before the disaster e. Not enough information is given now suppose you are given the data for Brazil and Portugal. In Brazil, the saving rate is 0.1 and the depreciation rate is 0.1, while in Portugal saving rate is 0.2 and the depreciation rate is 0.1. Using the Solow model, you conclude that in the steady-state: a. Brazil has a higher capital-output ratio than Portugal b. Portugal has a higher capital-output ratio than Brazil c. Brazil has a higher level of output than Portugal d. Portugal has a higher level of output than…Consider an H-O economy in which there are two countries (US and France), two goods (wine and cheese) and two factors (capital and labor). In each question below you are given partial information about the model and asked to infer some other part. Treat each question separately and independently. 1. Suppose a decrease in the price of cheese causes a decrease in the wage rate in the US economy. Which factor is used intensively in cheese production in France? Which H-O theorem is used to get this answer? Explain. 2. Suppose France exports wine, the capital-intensive good. Which factor benefits from free trade in the US? Explain. 3. Suppose workers in France benefit when tariffs are increased on cheese imports. Which factor is used intensively in cheese production? What is France's abundant factor? Explain.One view of the consumption function is that workers have high propensities to consume and capitalists have low propensities to consume. To explore the implications of this view, suppose an economy consumes all wage income and saves all capital income. Show that if factors of production earn their marginal product, this economy reaches the Golden rule level of capital. Using Solow growth model, explain. please explain it without plagiarism