Based on the notations used in class, suppose you are given the following information for the Solow growth model (with population growth and depreciation but without technological progress): y = k0.5,8 = 0.04, n = 0.01, and s = 0.25. What is the steady-state level of k? O a. 36 O b. 15 O c. 25 O d. 5
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- 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? %3D 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.In the Solow model with technological progress, suppose that the rate of depreciation is 10% per year, the population growth rate is 2% per year, and the growth rate of technology is 3% per year. Which of the following equals the annual growth rate of "effective labor" in the steady state in this economy? O 2% O 3% O 5% 10%
- 9. Consider a numerical example using the Solow growth model. Suppose that F(K, N) KO.5N0.5, with d = z = 1, and take a period to be a year. (a) Determine capital per worker, income per capita, and consumption per capita in the steady state. 0.1, s = 0.2, n = 0.01, and5. 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. 24Consider a basic Solow-Swan model. Suppose the aggregate production function is Y - AKL and that A=1, the depreciation rate is = 0.06 and the saving rate is s = 0.12. In steady state, d which of the following is TRUE? O Output per worker is 2.00 and consumption per worker is 0.24 O Output per worker is 2.00 and consumption per worker is 1.76 O Output per worker is 1.68 and consumption per worker is 1.48 O Qutput per worker is 1.68 and consumption per worker is 1.12
- Q5 Suppose in a Solow model, we have the following parameter values: n = 0, s = 0.5, a = 0.3. There is no growth in the total factor productivity so that A, = A = 1. Moreover, we know that at time 0, the economy is at a steady state so that k = k, =1. Now imagine that a foreign power invaded this %3D country. 1% of the population was killed and another 14% of the population fleeded the country to avoid violence. Moreover, 15% of capital stocks were destroyed. All of this happens in period t=1. After that, the war ended and there was no more destruction of capital or loss of population (but the refugee permanently settled outside of the country and will never return0. What is the growth rate of per-capita output in period t =4?= 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?1. Many endogenous growth models feature so called scale effects: per capita growth rises when population growth rises. Some economists have criticized these models for this reason, since countries with faster population growth do not in general appear to also experience faster per capita income growth. Consider an economy that has access to a production technology Y = AKª L¹-a where Y is output, A is the level of technology, K is capital and L is the amount of labor in the economy. Capital evolves according to K = SY (thus, the depreciation rate 6 = 0). The population growth rate is n. (Throughout, gx, where x can be any of the variables in the model). i. Assume that technology is determined by A =BK What sort of endogenous growth model is this? Find gk in terms of the K, L, and other parameters of the model. ii. Write an expression for gy in terms of gk and g₁. What must be true for a balanced growth path to exist in this model? Solve for the balanced growth path value of gy and gy,…
- 8) Suppose that z; = (1.01)'zo and x = (1.05)'xo. Let y be given by y = (z/x). Assume that the growth rates of z and x are constant. Approximately how many years will it take for the level of y to double? Α. 17.5 В. 280 С. 35. D. It will never double Answer:1. Using the solow growth model, given y(K) = k^0.4, S=0.20, depreciation rate=0.04 and n=1%, a. What is the steady-state level of capital per worker? b. What is the steady-state of output per worker? c. What is the steady-state level of consumption per worker? 2. Now assume population growth is instead-0.5% (approximately the growth rate when every couple has 1.7 children), but that all other parameters stay the same. a. What is the new steady-state output per worker? Is it higher or lower than with faster population growth? [A numerical answer and a 1 sentence response is fine.] b. What is the new steady- state of consumption per worker? Is it higher or lower than with faster population growth? [A numerical answer and 1 sentence response is fine].Sweden and Norway are two neighboring countries in Northern Europe with similar savings rates, population growth rates, technology growth rates, and depreciation rates. However, Norway differs from Sweden in that Norway has large deposits of oil all along its coast, which makes it very easy for Norway to produce large quantities of crude oil every year with relatively little capital and labor. a) Draw a Solow Growth diagram that compares Sweden and Norway. What is the main difference between the two countries in the diagram? b) According to the Solow Growth Model, which country would have a higher standard of living in the long run? Which country would have a higher growth rate of its standard of living in the long run? c) Suppose now that, in the long run, oil becomes obsolete and has no value because it is uneconomical relative to renewable energy sources like solar and wind power. What would this do to your Solow Growth diagram in part a? How would the standard of living in Norway…