This question aims to explore some of the points discussed about the Solow-Swan model Consider an economy with the general Cobb-Douglas production function YAKL The equation describing capital dynamics is Where d is a constant parameter that captures the depreciation rate. Investment follows a behavioural equation as discussed in class, ie, a constant Y traction of output is invested in every period. Answer the following questions assuming that labour grows at the rate n-0 and adopting the assumptions ma Assume:s 0.60. d - 0.10, a - 0.5. Le 1and A 1. de in lecture.

This question aims to explore some of the points discussed about the Solow-Swan model Consider an economy with the general Cobb-Douglas production function YAKL The equation describing capital dynamics is Where d is a constant parameter that captures the depreciation rate. Investment follows a behavioural equation as discussed in class, ie, a constant Y traction of output is invested in every period. Answer the following questions assuming that labour grows at the rate n-0 and adopting the assumptions ma Assume:s 0.60. d - 0.10, a - 0.5. Le 1and A 1. de in lecture.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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This model states that output depends on the economy’s initial endowment of capital and labor. Y = f (K,L)a. Harrod-Domar Modelb. Rostow’s Stages of Growth Modelc. Solow Modeld. Power-Balance Model
This model begins from the assumption that savings is a constant proportion of income.a. Harrod-Domar Modelb. Rostow’s Stages of Growth Modelc. Solow Modeld. Power Balance Model
Consider the Solow model without technological progress and an economy with the following production function, Y=A[Kα+Gα]1/α where α<1, K is private capital and G is public capital that is used freely and provided by the government. The level of technology A is fixed and assumed to be equal to 1. A. Does this production function feature constant returns to scale? Explain. In order to finance public capital, the government taxes all investment on private capital at the rate 0<τ<1. So, the revenue raised by the government in each period is sKYt(1−τ) where sK is the private savings rate so that sKYt is pre-tax private savings. Public investment towards public capital is a constant fraction sG of total revenue. Then, the accumulation equations for private and public capital, respectively, are, Kt+1−Kt=sKYt(1−τ)−δKt Gt+1−Gt=sG(sKYtτ)−δGt where δ is the common depreciation rate B. Consider a balanced growth path where the growth rates of private capital is equal to the growth…
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.
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(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…
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