Population Growth and Technological Progress-Work It Out An economy has a Cobb-Douglas production function: Y = K"(LE)¹- The economy has a capital share of 0.20, a saving rate of 49 percent, a depreciation rate of 4.00 percent, a rate of population growth of 1.50 percent, and a rate of labor-augmenting technological change of 4.0 percent. It is in steady state. a. At what rates do total output and output per worker grow? Total output growth rate: % Output per worker growth rate: %
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- Population Growth and Technological Progress – Work It Out PLEASE WRITE ANSWERS CLEARLY An economy has a Cobb-Douglas production function: Y = K“(LE)'-a The economy has a capital share of 0.30, a saving rate of 42 percent, a depreciation rate of 4.00 percent, a rate of population growth of 5.25 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital. k* = y* = marginal product of capital =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.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.
- Production function is given by Y= (1/2)K^a(AN)^(1-a), where a=2/3. The rate of depreciation of capital is equal to 15 percent, the rate of technological progress is equal to 3 percent, and the rate of population growth is equal to 2 percent. The economy was in the steady state at time tand the level of technology was equal to A=80. Use the Solow growth model to answer the following questions. 1. If the saving rate s=80 percent, the steady state level of output per unit of effective labor at time tis equal to ... 2. If the saving rate s=80 percent, the steady state level of consumption per unit of effective labor at time tis equal to ... 3. If the saving rate s=80 percent, the steady state level of consumption per worker at time tis equal to ..QUESTION 22 whereas in the Solow model In the Romer model, the balanced growth path is equal to OAG-A; the steady-state level of capital is zero OB.0; infinity ; the growth rate declines as economy approaches the steady state O D. the level of the number researchers in an economy; capital is scarce OE. g=lL: there is a steady state G H. K. V. M Control Alt 無要換 AltConsider an economy as per solow model, with a Cobb-Douglas production function with constant returns to scale with respect to K and L. Moreover, you know that the economy is producing 80 units of total output and the productivity parameter is equal to 1. If the depreciation rate is 10%, the investment rate is 10%, and there are 75 workers, the growth rate of GDP per person ____________. a) is equal to zero because the economy is at its steady state b) is negative because the economy is above its steady state c) is positive because the economy is below its steady state d)cannot be determined
- please answer the following, I have attached an image of the question for better format. Thanks! 3. Suppose that the production function of a country is given by Y=KaL1-a, where 0<a<1, Y is output, L is labour, and K is capital, Derive the equation for steady state capital per worker, output per worker, and consumption per worker in terms of the saving rate (s) and depreciation rate (d).= 2. Consider a Solow growth model in which the production function is Yt AK²N₁¹/2, where A = 1. Moreover, assume that the depreciation rate is d = 0.02, the rate of population growth is n = 0.02, and the saving rate is s = = 0.2. a. Compute the value of the capital stock per worker in steady state. b. Draw a graph that represents the steady-state equilibrium of the model. c. Suppose that the capital-labor ration in year t is 90. What will the level of the capital- labor ratio be in year t+1? Will it increase or decrease in future periods? Explain. d. Compute the rate of change of the capital labor ratio between time t and t + 1. How does it compare to the rate of growth of the capital-labor ratio in steady state?Economic Growth II- Work It Out Question 1 An economy has a Cobb-Douglas production function: Y = K (LE)¹- The economy has a capital share of 0.35, a saving rate of 45 percent, a depreciation rate of 5.00 percent, a rate of population growth of 5.50 percent, and a rate of labor- augmenting technological change of 4.0 percent. It is in steady state. c. The economy has capital than at the Golden Rule steady state. To achieve the Golden Rule steady state, the saving rate needs to d. Suppose the change in the saving rate you described in part c occurs. During the transition to the Golden Rule steady state, the growth rate of output per worker will be the rate you derived in part a. After the economy reaches its new steady state, the growth rate of output per worker will be
- 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. 241 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) -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.