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The steady occurs when the economy is in equilibrium. Specifically, the steady state refers to the situation where K/N and Y/N are constant. K/N will not change when investment per worker equals
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- The economy does not grow once it reaches a steady state. This result is based on the assumption that output depends on capital and labor there is no saving. there is no depreciation. output depends on technologiesAn economy has production function Y = K¹/2L¹/2, a savings rate of 60 percent. There is no technological progress or labour force growth. The depreciation rate initially 10 percent, increases to 40 percent. There are 400 workers in this economy. When the depreciation rate is 40 percent, output will be equal to dollars.In Wonderland production per worker (y) depends on capital per worker() such the y=10vk. Every year 15% of the capital stock depreciates, while workers in Wonderland save 10% of their income. Every year the population grows ratas te of 3% (c) The country of Neverland is identical to Wonderland in terms of output per worker, the savings rate, the depreciation rate and population growth. They differ in one respect: Wonderland has capital per worker of 10, whereas Neverland has capital per worker of 20. Which country experiences a higher growth rate of output per worker and how will their growth rates evolve over time?
- (Assume that L =>1 and K=>1) a) Verify that this change represents technological progress.Which one of the following statements is FALSE? Group of answer choices If investment per worker is less than depreciation per worker, then capital per worker decreases. If investment per worker exceeds depreciation per worker, then capital per worker increases. In steady-state, investment equals to depreciation. In steady-state, capital per worker keeps growing steadily.Suppose that the economy's production function is: Y = (K) 0.5 (AN) 0.5, that the savings rate s is equal to 16%, and that the rate of depreciation d is equal to 10%. Suppose further that the number of workers grows at 2% per year and that the rate of technological progress is 4% per year. a) Find the steady state values of the variables listed below: i) The capital stock per effective worker. ii) Output per effective worker. iii) The growth rate of output per effective worker. iv) The growth rate of output per worker. v) The growth rate of output. b) Suppose that the rate of technological progress doubles to 8% per year. Recompute the answers in part a). Explain the differences. c) Now suppose that the rate of technological progress is still equal to 4% per year, but the number of workers now grows at 6% per year. Recompute the answer to part a). Are people better off in part a) or c)? Explain.
- 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= 2/3The production function for an economy is Y; = 1.5 Kª L(1«), where Y; is total output, K; is total capital, and L; is total labor. Total savings for the economy is given by S; = 0.2 Y. The rate of population growth, n, is 5% and the rate of depreciation, 8, is 10%. Write down the per capita production function. (a) (b) Write down the fundamental equation of Solow-Swan. (c) Imagine that a=0.7. In the long run, what is the growth rate of per capita output, y?? In the long run, what is the growth rate of total output, Y;? (d) In the long run, is there a constant level of capital per person, output per person and consumption per person? If so what are they? If not, why not? (e) Imagine that the depreciation rate increases from 10% to 12%. If the economy is initially in steady state, what are the effects on the levels and growth rates of k, y, and c? () Imagine that a=1. In the long run, what is the growth rate of per capita output, y.? In the long run, what is the growth rate of total…Consider an economy that has access to a production technology Y = AKαL1−α 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 δ = 0). The x˙ population growth rate is n. (Throughout, gx = x , where x can be any of the variables in the model.) (a) Assume that technology is determined by A = BKφ What sort of endogenous growth model is this? Find K/K in terms of the K, L, and other parameters of the model.
- Assume the per-worker production function is y = 2k05 The saving and depreciation rates are 0.2 and 0.04 respectively. Calculate the value for output per worker (y) at the steady state, assuming no population growth. Answer:Suppose a Solow economy is initially at its steady state k∗, and suddenly is hit by a decrease in the depreciation rate δ, from δ to δ1. This change does not alter any of the other exogenous parameters in the model Depict this situation in a graph What happens to steady state level of capital per capita in this situation? What happens to the level of capital per capita over time? Depict this in a graph and explain intuitively.An increase in research productivity: Suppose the economy is on a balanced growth path in the Romer model, and then, in the year 2030, research pro-ductivity z rises immediately and permanently to the new level z r. (a) Solve for the new growth rate of knowledge and yt.(b) Make a graph of yt over time using a ratio scale.