. Consider a Solow growth model in which the production function is Yt = 1/2 t AK/2N ¹/², 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.
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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 =Production function is given by Y = 3K"(AN)!-a, where a=2/3. The rate of depreciation of capital is equal to 12 percent, the rate of technological progress is equal to 5 percent, and the rate of population growth is equal to 3 percent. The economy was in the steady state at time t and the level of technology was equal to A:=30. Use the Solow growth model to answer the following questions. (Please fill in numbers; use a comma as a decimal separator: 10,5) 1. If the saving rate s=40 percent, the steady state level of output per unit of effective labor at time t is equal to 2. If the saving rate s=40 percent, the steady state level of consumption per unit of effective labor at time t is equal to 3. If the saving rate s=40 percent, the steady state level of consumption per worker at time t is equal toConsider a Solow-Swan economy with a Cobb-Douglas production function with a constant savings rate. Imagine that the population growth rate "n" is a decreasing function of capital and it has the following functional form: for low values of k it's constant at some high level. For intermediate levels of k, it decreases rapidly. And for high values of k the population growth rate is constant again. In other words, the population growth rate looks like : a. Why may the population growth rate look like this? (make sure you discuss its three components and how each of them may be a function of k in the real world) b. Does a steady state necessarily exist? Will the steady state be necessarily unique? Will the steady state(s) be stable? Will there be a "poverty trap"? (define poverty trap) How can this model be used (and how has this model been used) to justify large increases in foreign development aid? Discuss THREE potential flaws of the "population poverty trap" model. C. d. е. f. g.
- 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 effective worker is constant in the steady state and does not change. increases in the steady state. declines in the steady state. % Output per worker growth rate: %Using the growth accounting equation, assume that the growth rate of output is 13%, the growth of labor is 8% and the growth of capital is 6%. If α=0.6 then growth from technology can be estimated to be: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).
- Production function is given by Y = Ka(AN)'¯ª, where a=2/3. Initially, the saving rate was equal to s and the economy was in the steady state. Use the Solow growth model to answer the following questions. (Please fill in numbers; use a yomma as a decimal separator: 10,5) 1. In order to increase capital per unit of effective labor in the steady state by a factor of 27 (i.e. to make it 27 times larger), the rate of saving needs to increase by a factor of 2. In order to increase output per unit of effective labor in the steady state by a factor of 4 (i.e. to make it 4 times larger), the rate of saving needs to increase by a factor of 3. Suppose that s=25 percent, the rate of depreciation of capital is equal to 5 percent, the rate of technological progress is equal to 1 percent, and the rate of population growth is equal to 0,25 percent, a=2/3. The steady state level of investment per unit of effective labor is equal toAssume that Country A has a production function as following. Y = AK Where A represents the technology available in the country and the aggregate capital. Let the national saving rate be equal to 30%, s=0.3. Also, assume that capital depreciates at a constant rate of 25, delta = 0.02 a) For this question, assume that A = 1 Say that we start at capital amount K=100. If we follow the Solow model, what will be the next period capital stock?Consider a Solow-Swan economy with a Cobb-Douglas production function with a constant savings rate. Imagine that the population growth rate "n" is a decreasing function of capital and it has the following functional form: for low values of k it's constant at some high level. For intermediate levels of k, it decreases rapidly. And for high values of k the population growth rate is constant again. In other words, the population growth rate looks like : Why may the population growth rate look like this? (make sure you discuss its three components and how each of them may be a function of k in the real world) Does a steady state necessarily exist? Will the steady state be necessarily unique? d. Will the steady state(s) be stable? Will there be a "poverty trap"? (define poverty trap) a. b. С. е. f. How can this model be used (and how has this model been used) to justify large increases in foreign development aid? g. Discuss THREE potential flaws of the "population poverty trap" model.
- 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.Consider the following numerical examples for the Solow Growth Model: Economy A z=1 s=0.5 F(K,N)=K0.3N0.7 n=0.01 d=0.1 Economy B z=1 s=0.2 F(K,N)=K0.3N0.7 n=0.01 d=0.1 In which economy is Consumption per capita higher in steady state? O Economy A O Economy B Not enough Information> Consider the data in the table below: Per capita GDP, 2017 Saving rate (%) TFP (Ā) United States 1.000 23.5 1.000 Switzerland 1.151 28.8 1.052 Answer the following questions using the Solow growth model. 9. Assuming no differences in TFP (ignore the last column) and no differences in the rate of depreciation between the U.S. and Switzerland, use the data in the table to predict the ratio of per capita GDP of Switzerland relative to that of the U.S. in the steady states. How much percent richer is Switzerland than the U.S. in steady state? 10. Now do the same exercise assuming TFP is given by the levels in the last column. Now how much percent richer is Switzerland than the U.S. in steady state? Consider the data in the table below: Per сapita GDP, 2017