3.By using the same production function in question 2: Assume the followings:ParametersEquationss=0,20marginal propensity to saveY = WK" L1-rProduction Functionu=0,02Population growth rateK = s. f(k) – aKCapital Accumulationb=0,04Technological growth ratePopulation Growth= 1.a=0,05Depreciation rateTechnological Progress=bWS = s. f(k)SavingsFind steady-state level of capital per effective labor: kDraw a graph and show output function, actual investment and breakeven investmenta.b.lines.с.Assume that in this economy, people start spending more and therefore marginalpropensity to save decline permanently. What will happen to variables in the model(steady-state level capital per effective labor; output growth etc.).Instead of reduction in saving assume this time that we face lower fertility rate in thed.country. What will happen to variables in the model (steady-state level capital pereffective labor; output growth etc.).

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3. By using the same prođuction function in question 2: Assume the followings: Parameters Equations s=0,20 marginal propensity to save Y = WK" L1-r Production Function %3! v=0,02 Population growth rate K = s. f(k) – aK Capital Accumulation b=0,04 Technological growth rate Population Growth = U a=0,05 Depreciation rate Technological Progress =b S = s.f(k) Savings Find steady-state level of capital per effective labor: k a. b. Draw a graph and show output function, actual investment and breakeven investment lines. с. Assume that in this economy, people start spending more and therefore marginal propensity to save decline permanently. What will happen to variables in the model d. (steady-state level capital per effective labor; output growth etc.). Instead of reduction in saving assume this time that we face lower fertility rate in the country. What will happen to variables in the mođel (steady-state level capital per effective labor; output growth etc.).

3. By using the same prođuction function in question 2: Assume the followings: Parameters Equations s=0,20 marginal propensity to save Y = WK" L1-r Production Function %3! v=0,02 Population growth rate K = s. f(k) – aK Capital Accumulation b=0,04 Technological growth rate Population Growth = U a=0,05 Depreciation rate Technological Progress =b S = s.f(k) Savings Find steady-state level of capital per effective labor: k a. b. Draw a graph and show output function, actual investment and breakeven investment lines. с. Assume that in this economy, people start spending more and therefore marginal propensity to save decline permanently. What will happen to variables in the model d. (steady-state level capital per effective labor; output growth etc.). Instead of reduction in saving assume this time that we face lower fertility rate in the country. What will happen to variables in the mođel (steady-state level capital per effective labor; output growth etc.).

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 5SCQ: What do the growth accounting studies conclude are the determinants of growth? Which is more...

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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?
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.
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)?
2. Solow-Swan Model (a) You will demonstrate the importance of diminishing returns to capital in the Solow-Swanmodel. Draw a Solow-Swan diagram in which there are constant returns to capital. Thiswould happen if the production function were Yt= AKt, where A = 1. Furthermore,assume that the sum of population growth and the depreciation rate is greater than thesaving rate. Does the economy converge to a steady state in this case? To answer thisquestion, you should draw a Solow-Swan diagram in terms of output per person, as we didin class. Use this diagram to explain why the economy converges to a steady state or doesnot. (b) Assume, instead, that the sum of population growth and the depreciation rate is equal tothe saving rate. In this case, are there any steady states? If yes, describe the steady-statelevels of capital per person. If no, explain why not. (Note: Diagram is not needed for thispart.)
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
(50 points) Consider the two-period economy with investment discussed in class. Forthe sake of simplicity, assume that the utility is time separable and that the per-periodutility is equal to:u(C) = log CAssume also that the technology to produce the consumption goods has constant returns to scale. Moreover, capital is the only input to production. Hence the currentperiod technology can be represented as:Y = zK1where Y , K, and z stand for output, capital and total factor productivity in the currentperiod. The future period technology is akin to the current period technology. There isno government expenditure in the current and future period so that G = 0 and G0 = 0.Finally there is full capital depreciation, namely δ = 1.(a) (10 points) Write down the social planner’s problem. State the variables withrespect to which the social planner maximises.(b) (10 points) Derive the first order conditions to the planner problem. Rearrangethere condition to find the conditions characterising the…
One of your clients, a mining company with operations in the Democratic Republic of Congo and Zambia, is concerned withthe current macroeconomic environment’s impact on their operations. Among their worries is the slowdown in global growth, which is expected to moderate from 5.9 in 2021 to 4.4 percent in 2022—half a percentage point lower for 2022 than in the October World Economic Outlook.You are required to critically discuss some of the major factors that drove the global growth trajectoryi) Pre-Covid-19 pandemic ii) at the height of the pandemic iii) going into 2022 and beyond.
Consider an economy in which production is characterized by the neoclassical productionfunction:Y = K0.5N0.5Suppose that it has a saving rate (s) of 0.1, a population growth rate (n) of 0.02, and an average depreciationrate (d) of 0.03.a) Write this production function in per capita form, and find the steady-state values of per capitacapital k and per capita output y.b) At the steady-state value of k, is there more or less capital than at the golden-rule level?c) Determine what saving rate would yield the golden-rule level of capital in this model.
4. Suppose that we have a standard Solow model with a Cobb-Douglas production function. The central equation of the model is as follows:kt+1 = sAkαt + (1 − δ)kt.Consumption per worker is given by:ct = (1 − s)Akαt.(a) Solve for an expression for the steady state capital stock per worker. Indoing so, assume that the level of productivity is fixed at some value A.(b) Use your answer on the previous part to solve for an expression forsteady state consumption per worker.(c) Use calculus to derive an expression for the s which maximizes steadystate consumption per worker.
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) 1. 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 ?
(a) Consider an economy that is initially in a steady state equilibrium. Assume that in this equilibrium it has a saving rate of 50 per cent and a depreciation rate of 2 per cent. Further assume that the population growth rate is 3% and that the level of output produced can be represented by the following production function: = where A = 1 and = 0.5. Use the Solow-Swan model to determine the level of capital per worker and output per worker in this economy. (1 mark) (b) Now suppose the government introduces a set of policies to improve the institutional set up as well as better production technique which increases total factor productivity by double. What is the new steady state level of capital per worker and output per worker? (1 mark) (c) Use a Solow-Swan diagram to show the qualitative effects of this new government policy upon steady state output per worker and capital per worker. Briefly describe the intuition behind this result. (1 mark) (d) Now suppose, population growth rate…
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…