Given the production function is Y, = ĀK} L}. а. Express the growth rate of per capita GDP as a function of the growth rate of the capital stock. (Hint: You may use the results in Question 4 for previous tutorial. Note that in this question, labour force is fixed.) b. By dividing the capital accumulation equation AK,+1= 5Y, – dK,by K,, we obtain: AK;+1 = S- K; From the capital-output ratio in steady state, we obtain: Y* d Co ombining these results, show that the growth rate of per capita GDP is -1).

Given the production function is Y, = ĀK} L}. а. Express the growth rate of per capita GDP as a function of the growth rate of the capital stock. (Hint: You may use the results in Question 4 for previous tutorial. Note that in this question, labour force is fixed.) b. By dividing the capital accumulation equation AK,+1= 5Y, – dK,by K,, we obtain: AK;+1 = S- K; From the capital-output ratio in steady state, we obtain: Y* d Co ombining these results, show that the growth rate of per capita GDP is -1).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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9. Consider our graph of the basic Solow growth model. steady state dk y=F(() F() (-7' in LF equilibrium) On the graph above: y represents real output (or income) per worker; y-F(k) is the production function; is the capital stock per worker; s is the savings rate; 8 is the rate of depreciation of capital; 'i' represents business investment (purchases of capital) per worker); 'LF' stands for Loanable Funds. (For purposed of intuition, think of capital as 'machines.) If we started out with a capital (per worker) stock higher than the steady-state stock (above), we would expect to see which of the following happen over time? Positive growth rates while the capital stock increases. Positive growth rates while the capital stock stays less than the steady-state level. Negative growth rates while the capital stock increases. Positive growth rates while the capital stock decreases. Negative growth rates while the capital stock decreases.
20) Suppose that the production function is y = k0.25[that is, output per worker is equal to the (1/4th) root of capital per worker], s = 0.36, and lowercase delta (5)[the depreciation rate] = 0.10 and the population growth is 2 percent (n = 0.02). What is (approximately) the per capita steady state %3D consumption in this economy? Select one: а. 5004 b. 1.45 С. 302 d. 0.92
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).
I need help soon a possible I have one and half.
Q1 The steady state Consider the Basic Solow Model without exogenous growth: Y-AKOL-a C= (1-8)Y Y=C+I K' I (1-8)K where labor is constant. Assume the following values for the rest of this question: A=100 a = 0.35 s=0.12 8=0.10 L=25 For each question that follows, if the answer depends on the answer(s) to previous question(s), use unrounded answers in do calculations. If you do not, rounding error will accumulate. Q1.1 Compute steady state capital per worker. Round your answer to at least three decimal places.
Given the following aggregate production function: Y = K0.25 (AL) 0.75, where technology A grows at a fixed rate: A=g>0 (f) Find the steady state solution algebraically for output per efficiency worker, ỹ, where (i = 1,2). Show all workings. (g) Outline and explain the behaviour of per worker variables along the model's balanced growth path.
Consider our graph of the basic Solow growth model. On the graph above: y represents real output (or income) per worker; y=F(k) is the production function; k is the capital stock per worker; s is the savings rate; δ is the rate of depreciation of capital; ‘i’ represents business investment (purchases of capital) per worker); ‘LF’ stands for Loanable Funds. (For purposed of intuition, think of capital as ‘machines.’) If we started out with a capital (per worker) stock lower than the steady-state stock ( , above), we would expect to see which of the following happen over time? Group of answer choices A) Positive growth rates while the capital stock increases. B) Negative growth rates while the capital stock increases. C) Negative growth rates while the capital stock decreases. D) Positive growth rates while the capital stock stays less than the steady-state level. E) Positive growth rates while the capital stock decreases.
You are given the production function Y= AK H14 N 2, where A = 4. The population growth rate n is 0.025, the depreciation rate d is 0.075 (both physical and human capital depreciate at the same rate), and the growth rate of autonomous factors is zero. Investment 1 is the sum of two components, investment in physical capital Ig and investment in human capital Iµ. The fraction of GDP that goes to physical capital investment is SK = 0.05 and the fraction of GDP that goes to human capital investment is SH = 0.05. (i) Convert the production function to a function relating Y/N to both K/N and H/N. (ii) Find the steady-state physical capital-labor ratio and the steady - state human capital - labor ratio. (iii) Find the steady – state per person output. 2.
. This part considers a modified version of the Solow growth model. Suppose the production function is given by F(K,bN) = K°(bN)1-a where b is the labour augmenting technology, which grows at a rate f, i.e., b+1 = (1+ f)b. For simplicity, assume that the total factor productivity z = 1, and the population is constant, i.e., N, = N for all t. The rest of the model is the same as in the standard Solow model in the textbook. Especially, the aggregate capital stock evolves according to Kt+1 = I4 + (1 – d)Kt. And assume that the economy is still closed, and there is no government. For any aggregate variable X, let the lower case letter a be the variable per effective unit of worker; that is a = *. Show that the production technology specified above satisfies the assumption of con- stant returns to scale.