2. Solow Model without Technological Progress (g = 0): Consider an economy which has the following production technology: Y, = zKNa, where 0 < a< 1, K is capital, N is labour, and total factor productivity, z, is constant over time. The growth rate of population is given by: N+1 = (1+n)N, with 0 0) always exist for this model? Explain. (c) Suppose the economy is at its steady state. An earthquake destroys 5% of the economy's capital (K). There is no change in n, d, s, z and a. Using a diagram illustrating the steady state of the economy and time graphs discuss the effects of the earthquake on capital per worker in the short-run and the long-run.

2. Solow Model without Technological Progress (g = 0): Consider an economy which has the following production technology: Y, = zKNa, where 0 < a< 1, K is capital, N is labour, and total factor productivity, z, is constant over time. The growth rate of population is given by: N+1 = (1+n)N, with 0 0) always exist for this model? Explain. (c) Suppose the economy is at its steady state. An earthquake destroys 5% of the economy's capital (K). There is no change in n, d, s, z and a. Using a diagram illustrating the steady state of the economy and time graphs discuss the effects of the earthquake on capital per worker in the short-run and the long-run.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the Solow growth model in which we allow for long-run techno- logical progress. Assume N′ = (1 + n)N where N is the population (labor force) in the current period, N′ is the population (labor force) in the future period, and n is the pop- ulation growth rate. Assume that z = 1 for simplicity, and there is labour-augmenting technological progress. The production technology is given by Y = F(k,bN) where Y is the output of the consumption good, K is the current period capital stock, b denotes the number of units of “human capital” per worker, and bN is the “efficiency units” of labour. Assume that b′ = (1 + β)b where β > 0 is the growth rate in human capital. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. The production function F exhibits constant returns to scale. (a) Define a variable k as the quantity of capital per efficieny units of labor (as opposed to quantity of capital per labour). Using equilibrium conditions derive the…
4 Explain the central paradox at the heart of the Solow model, with constant and exogenous technologies. Given this paradox, why is the Solow model still relevant?
use only equitions and graphs to show correct statement a.The assumption of Constant Returns to Scale technology implies that the marginal product of factor imput is always decreasing. b. In the Solow growth model i the saving rate is a crucial determinant of the economy's long-run growth rate of output per worker. c. In the endogenous growth model , the representative firm sets the wage so that the demand and supply of efficiency units of labour are equal. d. In the endogenous growth model , there is no steady state of the economy as human capital will always continue to grow forever
Please aid in answering the underlined questions in BOLD Question 4:a. Identify two assumptions of the basic Solow Growth Model. b. Why are these assumptions important in supporting the Solow Model? c. You are given the following information about an economy.Y = C + IY = F(K, L)The aggregate production function for this economy exhibits constant returns to scale and the marginal products of labor and capital are both subject to diminishing returns.s = saving rate (assume this is constant) per yearδ= depreciation rate (assume this is a constant) per yeary = Y/Lk = K/Lk* = steady state of capital per worker (K/L) and sf(k) < δk.i. What is sf(k)? ii. What is δk?iii. Interpret the meaning of sf(k) < δk? iv. Graphically illustrate sf(k), δk, and k*. Indicate on your graph where sf(k) < δk.v. Explain what happens in this economy when sf(k) < δk.
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.
which statement \s are true. use graphs to exlain a. In the Solow growth model, the saving rate is a crucial determinant of the economy's long-run growth rate of output per worker. b. In the endogenous growth model , the representative firm sets the wage so that the demand and supply of efficiency units of labour are equal. c. In the endogenous growth model , there is no steady state of the economy as human capital will always continue to grow forever. d. The assumption of Constant Returns to Scale technology implies that the marginal product of factor imput is always decreasing.
4 Consider the context of the Solow model with technical progress in an excess saving scenario, that is,the savings rate is higher than the golden rule savings rate. Imagine that the economy started is in steady state, but at time t0 the saving rate increases suddenly. Elaborate graphs that show the evolution over time of the variables mentioned in the followingparagraphs as a result of the previous event .a) Growth rate of capital per effective workerb) Growth rate of capital per workerc) Capital growth rated) Natural logarithm of capital per effective workere) Natural logarithm of capital per workerf) Natural logarithm of capital
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.
Consider the Solow growth model with concave production function as studied in class. Supposethe economy is initially in the picture below, and currently has the level of capital stock of K0. What wouldhappen to the dynamics of capital accumulations when depreciation rate increases? Graphically denote thedirection and the speed of change/accumulation/decumulation of the capital stock, then verbally explain whythey move like so.
Q1. In the Solow model, suppose s=0.3, delta(depreciation)=0.05, output f(k) = sqrt of k. The economy starts at time t=0 with k=1. Suppose there is expropriation by the government and the entrepreneur only gets to keep 30% out its output. a) What is the capital per worker at time t=1? b) How does this compare with the case of no expropriation?
Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for convenience and that there is labor-augmenting technological progress, with a production function Y =F(K,bN) where b denotes the number of units of "human capital" per worker, and bN is "efficiency units" of labor. Letting b' denote future human capital per worker, assume that b' = (1 + f ) b, where f is the growth rate in human capital. (c) In the real world, we usually consider education level as a proxy to human capital. To examine the theory, what suggestions can you make to growth economists? What are factors other than education can you think of that contribute to human capital?
In the Solow growth model:1. What is the equilibrium effect of an increase in the population growth rate?2. What is the equilibrium effect of an increase in TFP?3. Which of these shocks is better able to generate sustained growth: a decrease in thepopulation growth rate, or an increase in TFP? How does this compare with theresults of the Malthusian model of economic growth?