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
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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 (
a. Rewrite production function per-worker terms.
b. Find the steady-state level of the capital stock, kss
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- 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_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…Q5) Solow Growth Model Based on Abel, Bernanke and Croushore, 10th edition, Chapter 6, Numerical Problems No. 5. An economy has the per-worker production function Yt = 3k95 where Yt is output per worker and k, is the capital-labor ratio. The depreciation rate is 8 = 0.1, and the population growth rate is n = 0.05. Saving is St = 0.3Y; where S; is total national saving and Y, is total output. a. Define the steady state of this economy. (Hint: see definition in slides.) b. What are the steady-state values of the capital-labor ratio, output per worker, and consumption per worker? c. Repeat Part (a) for a saving rate of 0.4 instead of 0.3.
- An economy described by the Solow growth model has the following production function: y = Vk A. Solve for the steady-state value of y as a function of s, n, g, and d. B. A developed country has a saving rate of 28 percent and a population growth rate of 1 percent per year. A less developed country has a saving rate of 10 percent and a population growth rate of 4 percent per year. In both countries, g = 0.02 and d= 0.04. Find the steady- state value of y for each country. C. What policies might the less developed country pursue to raise its level of income?Production function is given by Y = 3K"(AN)!-a, where a=2/3. The rate of depreciation of capital is equal to 12 percent, the rate of technological progress is equal to 5 percent, and the rate of population growth is equal to 3 percent. The economy was in the steady state at time t and the level of technology was equal to A:=30. Use the Solow growth model to answer the following questions. (Please fill in numbers; use a comma as a decimal separator: 10,5) 1. If the saving rate s=40 percent, the steady state level of output per unit of effective labor at time t is equal to 2. If the saving rate s=40 percent, the steady state level of consumption per unit of effective labor at time t is equal to 3. If the saving rate s=40 percent, the steady state level of consumption per worker at time t is equal toIn the Solow growth model, suppose that the per-worker production function is given by y=zk2/3 . The saving rate is s, depreciation rate is d, and population growth rate is n. Calculate the per capita capital (k) and output per worker (y) in the steady state.
- Derive the equilibrium law of motion for capital per worker in the Solow growth model (equation 7-19). State which equation you start with, and the operation you perform at each step. 2. Graph this equation in the space of capital tomorrow on the y-axis and capital today on the x-axis, and explain how you identify the steady-state level of capital per capita from the graphConsider our graph of the basic Solow growth model. On the graph above: y represents real output (or income) per worker; y=F(k) is the production function; k is the capital stock per worker; s is the savings rate; δ is the rate of depreciation of capital; ‘i’ represents business investment (purchases of capital) per worker); ‘LF’ stands for Loanable Funds. (For purposed of intuition, think of capital as ‘machines.’) If we started out with a capital (per worker) stock lower than the steady-state stock ( , above), we would expect to see which of the following happen over time? Group of answer choices A) Positive growth rates while the capital stock increases. B) Negative growth rates while the capital stock increases. C) Negative growth rates while the capital stock decreases. D) Positive growth rates while the capital stock stays less than the steady-state level. E) Positive growth rates while the capital stock decreases.Consider the following Solow diagram, indicating two sep-arate savings rates, 0.2 and 0.4: Suppose the savings rate is 0.2. At the steady state, what is capital per worker? What is output per worker? How much is saved per worker? Suppose the population growth rate is equal to the depreciationrate. Solve for n and d.
- Consider a numerical example using the Solow Growth Model. Suppose that F(K,N)=K^0.5N^0.5, with d = 0.1, s = 0.2, n = 0.02, and z = 1, and take a period to be a year. Determine capital per worker, income per capita, and consumption per capita in the steady state. The steady state per work (0.2)(1)k*)^0.5 = (0.02+0.1)k*Consider the Solow growth model. Suppose that F(K, N) = zK^a N^1-a,where a = 0.3. Also, assume that capital depreciation rate is 10% (that is d = 0.1), savings rateis 25% (that is s = 0.25), populations growth rate is 2% (that is n = 0.02), and z = 2.• First, determine capital per worker, income per capita, and consumption per capita in thesteady state.• Second, assume that the savings rate has increased to 40% but the total factor productivitydecreases to 1. Discuss the effect of savings and productivity on the steady state level ofconsumption per worker. PLEASE SHOW ALL HAND WRITEN STEPS!!In a Solow economy with technological progress, the production function is given by: Y = KO.5(LE)0.5. Furthermore, the saving rate of this economy is 0.2. The population growth rate is 0.03. The depreciation rate is 0.01. The technological progress is given by g which is equal to 0.01. Define y = Y/LE and k = K/LE. a) Find out the steady state values of k (i.e.: k*) and y (i.e.: y"). 2. Ay Ak AY ΔΚ b) Find out the values of and in the steady state. K y'k'Y