The depreciation rate of capital in the US is 8 = 0.043 and the population growth rate is g₁ = 0.007. Moreover, Y/K is around 0.35 on average over the last 60 years in the US (see the graph. below). If the saving rate is s= 0.2 in the US, then find the long-run growth rate of average income in the US according to the Solow's model. (Note: To cross-check Compare your theoretical result with the actual growth rate of average income in the US which is 2%.)

The depreciation rate of capital in the US is 8 = 0.043 and the population growth rate is g₁ = 0.007. Moreover, Y/K is around 0.35 on average over the last 60 years in the US (see the graph. below). If the saving rate is s= 0.2 in the US, then find the long-run growth rate of average income in the US according to the Solow's model. (Note: To cross-check Compare your theoretical result with the actual growth rate of average income in the US which is 2%.)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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In the Solow growth model with no population growth and no technological change, the output per worker increases when investment per worker is greater than depreciation of capital per worker. Select one: True False
Consider an economy that exhibits both population growth (L grows at rate n) and technological progress (A grows at rate a) described by the production function, Y = F(K,AL) = Kª(AL)¹-α| Here K is capital and Y is output. (a) Show that this production function exhibits constant returns to scale. What is the per-effective-worker production function? (c) Find expressions for the steady-state capital-output ratio, capital stock per effective worker, and output per effective worker, as a function of the saving rate (s), the depreciation rate (8), the population growth rate (n), the rate of technological progress (a), and the coefficient a. (You may assume the condition that capital per effective worker evolves according to Ak = sf (k) − (a +n+8)k.) (d) Show that at the Golden Rule steady state the saving rate for this economy is equal to the parameter a.
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. (a)Capital per capita A. 16 В. 24 С. 36 D. 48 Е. 64 F. None of the above (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
an economy is described by the Solow-Swan model with the following variables, E(t)=1 The saving rate is 0.41 per year. Labor's share of income is 0.44. The growth rate of labor efficiency is 0.03 per year. The growth rate of the labor force is 0.02 per year Depreciation is 0.09 per year. calculate the steady-state value of the capital-to-labor ratio, K/L Enter your answer to two places after the decimal.
The following will decrease the steady state of the capital to labor ratio in the Solow Growth Model. an increase in the savings rate an increase in Total Factor productivity. a decrease in the population growth rate. an increase in the depreciation rate. none of the above.
All values are 2005 dollars. Part a) Calculate the growth of GDP/capita in each column. Part b) Calculate the average annual growth in GDP/capita for japan, uk, and USA from 1980 to 2010 using the growth formula in the image. In the growth function, t is the current time period, t-j is the original time period, and g is the annual growth rate. Part c) In parts a and b, are the calculated values for nominal gdp/capita or real gdp/capita. Explain why.
= 2. Consider a Solow growth model in which the production function is Yt AK²N₁¹/2, where A = 1. Moreover, assume that the depreciation rate is d = 0.02, the rate of population growth is n = 0.02, and the saving rate is s = = 0.2. a. Compute the value of the capital stock per worker in steady state. b. Draw a graph that represents the steady-state equilibrium of the model. c. Suppose that the capital-labor ration in year t is 90. What will the level of the capital- labor ratio be in year t+1? Will it increase or decrease in future periods? Explain. d. Compute the rate of change of the capital labor ratio between time t and t + 1. How does it compare to the rate of growth of the capital-labor ratio in steady state?
Suppose that the per hour worked form of the production function for an economy is given by y = 10k03 The depreciation rate is 11%, the saving rate is 21%, and the growth rate of labor hours is 7%. The steady-state capital-labor ratio for this economy is (Round your response to two decimal places.)
Consider the Solow growth model in which population evolves according to: 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 population growth rate. There are public health expenditures that takes the form of government spending, G = gN, where G is the current period government spending on health care, g is the per-capita health spending in the current period. The production technology is given by Y = zKαN1−α where Y is the output of the consumption good, z is the total factor productivity, K is the current period capital stock, aN is the labour input, and 0 < α < 1 is a parameter. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. Suppose that the economic is hit by a pandemic (e.g. Covid-19) which causes a temporary decrease in total factor productivity, z, as certain sectors in the economy (e.g. entertainment, travel etc.) cannot deliver…
Consider the Solow model with a production function Y(t) = A*K(t)αL(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 the population growth rate n?
Consider a Solow-Swan model with saving rate s - 0.4, labour force growth g, - 0.05. constant productivity A = 1, and depreciation = 0.05. If output per worker is y = Y/L = 200 and capital per worker is k = K/L = 800, which of the following is true? O Efective depreciation per worker is 60, saving per worker is 80 and k will decrease towards the steady state Effective depreciation per worker is 80, saving per worker is 80 and k is at the steady state O Efective depreciation per worker is 60, saving per worker is 80 and k will increase towards the steady state O Effective depreciation per worker is 80, saving per worker is 60 and k will decrease towards the steady state
. This part considers a modified version of the Solow growth model. Suppose the production function is given by F(K,bN) = K°(bN)1-a where b is the labour augmenting technology, which grows at a rate f, i.e., b+1 = (1+ f)b. For simplicity, assume that the total factor productivity z = 1, and the population is constant, i.e., N, = N for all t. The rest of the model is the same as in the standard Solow model in the textbook. Especially, the aggregate capital stock evolves according to Kt+1 = I4 + (1 – d)Kt. And assume that the economy is still closed, and there is no government. For any aggregate variable X, let the lower case letter a be the variable per effective unit of worker; that is a = *. Show that the production technology specified above satisfies the assumption of con- stant returns to scale.