Suppose that the country of Westonia saves 12.5% of its income and has a capital-output ratio of 2.5. Using the Harrod-Domar model, calculate the growth rate of total output in Westonia, if the depreciation rate is 4 percent.
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- Consider a country with production function unction ? = 5? 1/2, where y is the output per worker and kis capital per worker. Suppose the investment in capital occurs at a rate of 35% of income perworker every period, the depreciation rate is 1.5% and the population growth rate is 2%. Use excel toplot the production function, investment line and capital depletion line with k on the x-axis (usethe attached spreadsheet to draw your graphs).a. What is the steady state level of y and k.b. Suppose TFP increases by 20%. What happens to the steady state y and k?c. Suppose the investment rate increases to 40%. What happens to the steady state y and k?1 1 1. Assume that a country's production function is Y = K2L2. Assume there is no population growth or technological change = f(k)? b. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to What is the per-worker production function y а. make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital-labor ratio.) (Ctrl) -Given a saving rate of 4%, a depreciation rate of 1%, and a production function inwhich y = k0.5 where y is output per worker and k is capital per worker, calculate thesteady state values fori. capital, ii. output, iii. consumption, and calculate the golden rule steady state level of capital
- Calculate the steady state level of investment in an economy with a savings rate of 15%, population growth of -1%, depreciation of 10%, and a= 2/35. The US has pledged to give $1 billion to Haiti for the next 12 months. The per capita income of Haiti is about $1000 and its population is 10 million and growing by 2% per year. Haiti has a capital-output ratio of 5, a savings rate of 10%, and a depreciation rate of 1%. Using the Harrod-Domar model, calculate the following: [a.] how will this infusion of cash change the rate of growth of its GDP and GDP per capita? [b.] how much will it add to per capita income next year? [c.] If this aid were in the form of free food, how would its impact be different?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.
- Population Growth and Technological Progress – Work It Out In the nation of Winknam, the capital share of GDP is 35 percent, the average growth in output is 3.0 percent per year, the depreciation rate is 5.5 percent per year, and the capital-output ratio is 3.0. Suppose that the production function is Cobb- Douglas and that Winknam has been in a steady state. Round answers to two places after the decimal when necessary. b. In the initial steady state, what is the marginal product of capital (MPK)? MPK =Use the following table to find the steady-state values of the capital-labor ratio and output if the per-worker production 03 function is y=2k S Saving rate 8 Depreciation rate n Population growth rate A Technology 0.35 0.02 0.06 2 k* = Steady-state capital-labor ratio = y*= Steady-state output = (Round your responses to two decimal places.) CHILD Output, Investment, and Depreciation Capital-Labor Ratio Output Depreciation Investment After plotting the final point of your multipoint curve, press the Esc key on your keyboard to end the line QSuppose 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 the 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 level of output than Brazil c. Portugal has a higher capital-output ratio than Brazil d. Portugal and Brazil have the same capital-output ratio e. Brazil has a higher level of output than Portugal
- 4. Assume an endogenous growth model with a production function that in per capita terms can be written as y = 0.8k. If the savings rate is s = 0.3, the rate of growth of population is n = 0.03, and the rate of depreciation is d = 0.1, how high is the rate of growth of output per capita? A. 14% B. 17% C. 13% D. 11% E. There is not enough information to calculate it.4. Assume an endogenous growth model with a production function that in per capita terms can be written as y = 0.8k. If the savings rate is s = 0.3, the rate of growth of population is n = 0.03, and the rate of depreciation is d = 0.1, how high is the rate of growth of output per capita? А. 14% В. 17% C. 13% D. 11% E. There is not enough information to calculate it.1 1 1. Assume that a country's production function is Y = K2L2. Assume there is no population growth or technological change What is labor productivity computed from the per-worker production function? Is this value the same as labor productivity computed from the original production function а. b. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital-labor ratio.)