1. Suppose that the production function of an economy is characterized by the followingCobb-Douglas production technology Y = Ka L*1, where Y is the aggregate output, Kis the capital stock, L is the labor and 0< a <1.a Assuming dosed economy with no govemment, labor growth rate being constant(gs) and depreciation rate is positive ô > 0, show the step-by-step derivation ofthe fundamental equation of growth (using per worker capital, k). Hint: Firstderive per worker production function.b. Find the steady-state values of capital per labor (k), output per labor(), and consumption per labor (c). Hint: use the fact: k= 0.What would be the effect of changes in s, gs and a on kf2. Recall that general form of fundamental equation of growth in Solow model isdescribed as follows:k = s - f(k.) – (gs + 6)kaNoting that at steady-state kss = 0 and hencea Using the fact kes= 0, show the steady-state graphically and provide economicinterpretation of the steady-state condition s- f(k s) = (gs + 6)k *b Using the same graph you draw in part (a) explain the transitional dynamics ofthe Solow. Hint: Defime what happens if k. k s-3. Assume that production fumction takes the form Y = (K'0.5) + L'as)E, Show ifthis production function obeys neoclassical assumptions.4. Lets assume that the time derivative of a continuous variable Xa is defmed asX = M+Nwhere, M: and N: are also continuous variables defined by following functions:N: = ekt & M, = et and k is a constant. Find the grow th rate of x at the steady statein terms of k.

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1. Suppose that the production fumction of an economy is characterized by the foll owing Cobb-Douglas production technology Y = Ka L*•i, where Y is the aggregate output, K is the capital stock, Lis the labor and 0 0, show the step-by-step derivation of the fundamental equation of growth (using per worker capital, k). Hint: First derive per worker production function. a Find the steady-state values of capital per labor (k), output per labor (). and consumption per labor (c). Hint: use the fact k= 0. c What would be the effect of changes in s, g; and a on kf

1. Suppose that the production fumction of an economy is characterized by the foll owing Cobb-Douglas production technology Y = Ka L*•i, where Y is the aggregate output, K is the capital stock, Lis the labor and 0 0, show the step-by-step derivation of the fundamental equation of growth (using per worker capital, k). Hint: First derive per worker production function. a Find the steady-state values of capital per labor (k), output per labor (). and consumption per labor (c). Hint: use the fact k= 0. c What would be the effect of changes in s, g; and a on kf

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

Chapter20: Economic Growth

Section: Chapter Questions

Problem 9SCQ: Would the following events usually lead to capital deepening? Why or why not? A weak economy in...

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How is the concept of technology, as defined with the aggregate production function, different from our everyday use of the word?
Why dues productivity growth in high-income economies not slow down as it runs into diminishing returns from additional investments in physical capital and human capital? Does this show one area where the theory of diminishing returns fails to apply? Why or why not?
What do the growth accounting studies conclude are the determinants of growth? Which is more important, the determinants or how they am combined?
Would the following events usually lead to capital deepening? Why or why not? A weak economy in which businesses become reluctant to make long-term investments in physical capital. A rise in international trade. A trend in which many more adults participate in continuing education courses through their employers and at colleges and universities.
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.
1. Country A and B both have the production functionY = F (K, L) = K ½L ½or Y = K0.5 L0.5 a) What is the per-worker production function, y= f (k)? Please make sure to write specificfunctional form of the per-worker production function. b) Assume that neither country experiences population growth nor technological progressand that 4 percent of capital depreciates each year. Assume further that country A saves 24percent of output each year and country B saves 16 percent of output each year. Using youranswer from part a) and the steady-state condition, find the steady-state level of capital perworker for each country. Then find the steady-state levels of income per worker for eachcountry and steady-state level of consumption per worker for each country.
asap Suppose the economy's production function is Y = AKO.3NO.7. If K=2000, N = 100, and A = 1, then Y=246. If K and N both rise by 20%, and A is unchanged, by how much does Y increase?
Suppose an economy begins in steady state. By what proportion does per capita GDP change in the long run in reponse to each of the following changes? Production function is Y=AK^1/3L^2/3 a. Investment rate doubles b. depreciation rate falls by 10% c. Productivity level rises by 10% d. Earthquake destrys 75% of the capital stock e. Generous immigration policy lead the population to double
Question 3Consider an economy described by the production function:Y = F(K, L) = K0.3 L0.7 a. What is the per-worker production function?b. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.c. Assume that the depreciation rate is 10 percent per year. Make a table showing steadystate capital per worker, output per worker, and consumption per worker for saving ratesof 0 percent, 10 percent, 20 percent, 30 percent, and so on. (You will need a calculator with an exponent key for this.) What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?
suppose the production formula is given by yt= kt ^1/3 where y is the output per worker and k is the capital per worker. futhermore assume that the saving rate is exogenous and the capital deprecitates at delta rate. if the sum of both deprectiation rate and saving rate equals 1, answer the questions below 1. find the steady state values of capital, output, investments and consumption as functions of the saving rate only? 2. in a diagram show the steady state value values in a part (a)?
I have worked on 1-3, but am stuck on 4-6, could you please assist? Suppose that the economy is summarized by the following: Technology (Production Function): Yt = 10 (Kt)0.3 (Lte)0.7 Consumption function: Ct = 0.8Yt Depreciation rate: 8% (i.e. δ= 0.08) Population growth: 2% (i.e. n = 0.02) Technological growth: 4% (i.e. g = 0.04) QUESTIONS: Find the steady state (long run) equilibrium values of kte, yet, and cet. Show graphically what would be the effect of a increase of the saving rate to s=0.4? Show graphically what would be the effect of an increase in population growth to 0.04? Assuming that in 2013 the US economy is in the steady state and L2013 = Le2013 = 8, what is the value of ke2014, ye2014, ce2014 , k2014, y2014, and c2014 ? Use your answer to e) to calculate the growth rate of ket, yet, cet , kt, yt, and ct Based on your answers to the previous questions and on your knowledge of how the Solow growth model works, explain what policies should a less-developed country…
2. An economy has a production function:Yt = 3(squaredKt)(squaredLt). The economy has a saving rate of 24 percent, a depreciation rate of 3 percent,and Lt = 1 for all period (no population growth). There is no technologicalprogress. (a) What is the per-worker production function, yt = f(kt)? Define yt =YtLtand kt =KtLt.(b) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (c) Find the long-run growth rate of output per worker. Now the economy has the following production function:Yt = 3Kt but savings rate, depreciation rate, and population remain the same. (d) What is the per-worker production function, yt = f(kt)? Define yt =Yt/Lt (e) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (f) Find the long-run growth rate of output per worker. (g) Explain why the economy with production function (2) explain persistent growth without the assumption of exogenous technologicalprogress. How does this differ from the economy…