1. Consider the Solow growth model with depreciation of capital and labour-force growth. The fundamental equation of the Solow model is: Ak = s f(k) - (n+ô) k rate of labour, and ô = the rate of depreciation of capital. a) Show the steady state value of k in a diagram. What happens to the steady-state value of k when s increases? where s= MPS=APS, k = capital per worker, n= growth b) Other things being the same, what happens to the steady-state value of k as n declines. Show this in a diagram.

1. Consider the Solow growth model with depreciation of capital and labour-force growth. The fundamental equation of the Solow model is: Ak = s f(k) - (n+ô) k rate of labour, and ô = the rate of depreciation of capital. a) Show the steady state value of k in a diagram. What happens to the steady-state value of k when s increases? where s= MPS=APS, k = capital per worker, n= growth b) Other things being the same, what happens to the steady-state value of k as n declines. Show this in a diagram.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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QUESTION 1 (10 marks) Consider the Solow growth model without population growth or technological change. The parameters of the model are given by s = 0.2 (savings rate) and δ = 0.05 (depreciation rate). Let k denote capital per worker; y output per worker; c consumption per worker; i investment per worker. a. Rewrite production function per-worker terms. b. Find the steady-state level of the capital stock, kss
3. Consider the Basic Solow growth model with a Cobb-Douglas production function and no technological change for the economy china. In this island economy, capital’s share α= 0.3, the annual depreciation rate on capital δ = 0.08 and the annual population growth rate n = 0.02. Suppose that this is the year 2017, and the economy is in the steady-state with GDP (Y) = 200 bananas, and capital stock K = 400 bananas. [Feel free to use any form of exponentiation that works best for you] Project the equilibrium level of GDP for 2050. Calculate the market value of fixed capital (K) in 2050 on a gross basis. Using the steady-state conditions, solve for the saving rate (s*) that is consistent with a stable steady-state.
i need part C,D,E,F,G In the Solow growth model, output Y is produced using capital K and labour L.Assume the production function is Y =√K√L, which has total factor productivityconstant over time. The change over time in the capital stock is ∆K = I−δK, whereI is investment and δ is the depreciation rate. The labour force L is constant overtime. Investment I is equal to saving S, which is a fraction s of income.Let k = K/L and y = Y/L denote capital per worker and output per worker. In thisquestion, assume that δ = 1. Capital can be used for production and generates anincome for its owner before it depreciates.(a) Show that y =√k and ∆k = s√k − k, and solve for the steady-statevalues of k and y where ∆k = 0.(b) Using a diagram, explain intuitively why there is a steady statewhere growth in output per worker is zero, and why the economy convergesto this steady state in the long run.Total consumption divided by the number of workers is given by c = (1 − s)y.(c) Using your answer…
2) Assume that two countries are identical in every respect, except Country A initially has more capital per worker than Country B (i.e. they have the same saving rate (s), labor supply growth rate (n), depreciation rate (d), total factor productivity (A), and elasticity of output with respect to capital (a)). A) According to the Solow model, which country has greater income per worker initially? B) According to the Solow model, which country will grow faster in the short-run? What about the long-run? Explain your answer. C) Compare Country A’s steady-state output per worker with Country B’s in the Solow model. Explain.
Q) Suppose that the depreciation rate increase. In the Solow growth model, determine the effects of this on the quantity of capital per worker (k) and on output per worker (y) in the steady state. Show with graphs Note:- copy paste answer not provided. Give me your own words and correctly explains.
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?
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.
Hello, please help me to solve these questions.Consider the Solow growth model with technological progress at the rate g, population growth at the rate n, and capital depreciation rate at the rate δ. The savings rate is denoted by s and the production function is given by:Y = Kα (AL)1-α , 0 < α < 1.Y is aggregate output, K is aggregate capital, L is aggregate labour, A is technology and AL is effective labour. (a) Let ݇k = K/AL which denotes capital per unit of effective labour. Obtain the production function in terms of capital per unit of effective labour. Explain the properties this production function satisfies. (b) Derive the key equation that governs the evolution of capital per unit of effective labour in this Solow model. Provide the steady state value of capital and output in per unit of effective labour terms. What are the growth rates of capital per unit of labour and output per unit of labour in the steady state? (c) Analyse the effect of a decrease in the…
Question 3 Consider the steady state of the Solow model with population growth and technological progress. (a) Use a graph to show what happens to steady-state capital per effective worker and output per effective worker in response to a decrease in the depreciation rate (?). Explain your answer. (b) Use a graph to show what happens to steady-state capital per effective worker and output per effective worker in response to a decrease in the population growth rate (?). Explain your answer. (c) Briefly explain any differences between the growth rate of output per worker (?⁄?) in the steady state when comparing your answers to parts (a) and (b). Define the steady state.
10.In the Solow model of economic growth, a country with a higher rate of capital depreciation will, ceteris paribus, have a steady-state equilibrium withA. lower output per worker.B. higher capital to labour ratio.C. the same capital to labour ratio.D. more investment. PROVIDE A BRIEF WRITTEN EXPLANATION JUSTIFYING YOUR CHOICE.
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.
1. Carefully draw a graph depicting steady state conditions within the Solow Growth Model framework. Carefully explain, making reference to depreciation rates and savings rates, how the steady state level of capital is determined. Now, demonstrate how the economy can grow from this point forward (in separate analyses) assuming: (a.) widespread improvements in production technology, and (b.) increases in savings rates. For each analysis show and carefully describe how the new steady state level of capital is attained.