1(b) Assume that the production function for an economy in the Solow Growth Model is given by: Y = K 1/3 (L x E) 2/3 (where Y = Total output; K = Capital stock; L = Labour force; E = advances in technology, which are measure as improvements in the efficiency of labour). The savings rate in the economy is 0.4, the depreciatio rate is 0.1, the growth in the labour force is 0.05 and technology advances at a rate of 0.05 (each of these
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- In the Solow Growth Model, a country's production function is defined by the following: Y = F (K/L) = kºs Where K is capital and I. labour; labour grows at a rate (n), and the economy faces depreciation at a rate (8) The initial Capital Stock per worker: k, = 9 units The savings rate: s = 0.20 and the rate of depreciation: a = 0.1 Using equations and identities from the Solow Growth Model, calculate the level of capital k, Output y, Consumption c, depreciation and change in capital from the equation of motion for periods 1, 2 and 3. Comment on the accumulation of capital and output over the three periods.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…Consider an economy described by the Solow model with the following production function: Y = F(K, L) = K“ (L)'-« L grows at the rate n, the depreciation rate is 8, and the country saves a constant fraction s of its income. The change in capital per-worker is given by Ak = sy – (n+ 8)k. (a) Derive the per-worker production function. (b) Assuming population growth equals n and the depreciation rate equals 8, find the steady state level of capital per worker. It will depend on a, s, n and 8. Imagine the economy begins at the steady state you found in part b. Then there is a war that destroys a substantial amount of the economy's capital. The war does not affect the size of the labor force, population growth, the depreciation rate, or the saving rate. c) What is the immediate effect of the war on output per worker? Explain. d) After the war, is the growth rate of output per worker higher or lower than it was in steady state? Explain. e) How does the war affect steady state output per…
- Consider the basic Solow growth model. Let the aggregate production function be defined as Y = F(K, L) = K0.5 L0.5 where Y is output, K is capital, and L is labor. Furthermore, let the saving rate be 48%, population growth be 2%, and depreciation rate be 10%. a. Find the steady-state levels of capital per worker k and output per worker y.. %. b. Now assume that, because of the proliferation of financial technologies, the saving rate increases suddenly to 54% after one year. The steady-state level of capital will increase by ____%, and the steady-state level of output will increase by_Problem 2: Growth Models Solow Growth Model: Assume there is an imaginary country where output is produced according to the following constant returns to scale production function that lies at the heart of the standard Solow growth model: Y = 10K0.5 L0.5 Also assume that the savings rate is 13% (s = 0.13), the population grows at a rate of 2% per year (n 0.02), and capital depreciates at a rate of 2% per year (d = .02). (a) Which of the following is an expression of the production function in per-capita terms y expressed as a function of capital per worker k: i. Y = k0.5 ii. Y = 10k0.5| iii. y = k0.5 iv. y = 10k0.5 (b) What is the steady state level of capital per worker? (c) What is the steady state level of output per worker? (d) Suppose that the populist leader of our imaginary country increases the savings rate from 13% to 15%, i.e., (s = 0.15), what is the new steady state level of capital per worker? [Note: Assume that the other parameters n and d remain unchanged.] (e) [TRUE or…Question 1 1(a) In the Solow Growth Model the output function for the economy is given by: Y = K 1/3 (L x E) 2/3 (Y = output; K = capital stock; L = labour force; E = efficiency of labour so that L x E = labour force measured in efficiency units) The depreciation rate (8) is 0.05, the growth rate of the population (n) is 0.03 and the rate of advance in technology (g) is 0.07. Use mathematical analysis to calculate the golden rule steady state capital stock per efficiency unit of labour (k*gold). 1(b) Create a schedule that confirms that the result in part (a) is correct. The schedule should include the following seven columns: the savings rate, the steady state capital stock per efficiency unit of labour, the steady state output per efficiency unit of labour, the sum of the depreciation rate, population growth rate and the rate of advance in technology all with respect to the steady state capital stock per efficiency unit of labour, the steady state consumption per efficiency unit of…
- Consider the Solow model with no technological progress and population growth rate of n. The production function in intensive form is given by y = f(k) = Bk"B. (a) Find the expression for the steady-state value of per capita capital stock (k*). [Hint: s.f(k*) = (n+ 8).k*] (b) Now suppose the population growth rate and the depreciation rate is each equal to 1 percent (n=0.01, 8 = 0.01). Calculate the steady-state value of per capita capital stock given the exogenous rate of saving rate of s = 0!2 and a = 0.5 & ß = 0.4.Consider a standard Solow growth model. Denote capital stock as K, population as N, capital depreciation rate as d, saving rate as s, output as Y. Output is produced by a representative firm according to the production function Y=zF(K, N), where z is current total factor productivity. The law motion for capital is K' = (1 - d)K + I, where K' is the future capital stock. Population grows at a constant rate n, that is N' = (1 + n)N, and household supply labor inelastically, so population equals labor force. (a) In a graph, show the steady state level of capital per worker. Use lower case letters to denote per-capita terms and use * to denote steady state.(b) Suppose a country is initially at a steady state, then a war destroyed some of its capital stock. Determine the long run effects on the quantity of capital per worker and on output per worker in the steady state. Show by a graph. (C)Define golden rule saving rate. What does it maximize? Determine the effects of a decrease in the…3). Let's consider the Solow Model without technology advancement. Y(t)=2K(t)^(1/2)*L(t)^(1/2) The population growth rate=0.02 Capital accumulation is s*Y(t)-d*K_ s=0.2, d=0.03 d is the capital depreciation rate. In the steady state, please calculate the following measurements. (b)Marginal product of capital (Hint: The first derivative of Y with respect to K) А. 1 В. 1/2 С. 1/4 D. 1/8 E. 1/16 F. None of the above
- Consider the Solow Growth Model studied in Chapter 5 with the following information: The production function is: Y₁ = AK₁¹/³L2/3 Amount of labor (Lt) = 1000 Investment rate (s) = 0.1 Depreciation rate (d) = 0.4 Productivity (A) = 1 Find the numerical value of the steady-state level of output per person.1. Consider Avataria, which can be described by the Solow model with the population growth. Its production function Y(K,L) = 2K¹2 L¹/2 Its investment rate is 40%, its depreciation rate is 10%, and its population growth rate is 10%. Calculate the capital-labor ratio, output per worker, and consumption per worker in the steady state. Assume that now the population growth slows down to 4%. What happens with the output per worker and consumption per worker in the new steady state? Calculate the exact values. (a) (b)Consider the Solow model with a production function Y(t) = A*K(t)^α*L(t)^(1-α), Where A is a fixed technological parameter. Explicitly solve for the steady-state value of the per capita capital stock and per capita income. How do these values change in response to a rise in (a) the technological parameter A, (b) the rate of saving s, (c) α , (d) δ, the depreciation rate, and (e) the population growth rate n?