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 () 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 labour, the marginal product of capital and finally the difference between the marginal product of capital and the sum of the depreciation rate, population growth rate and the rate of advance in technology.

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 () 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 labour, the marginal product of capital and finally the difference between the marginal product of capital and the sum of the depreciation rate, population growth rate and the rate of advance in technology.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. Consider an economy that operates under competitive markets and meets the assumptions of the Solow model. The production function is given as follows: Y(t) = K (t) 0.3 (A(t)L(t)) ⁰.7 Assume a saving rate of 15%, labor force growth rate of 2% and depreciation rate of 5% and effectiveness of labor growth rate of 8%. a. Show that the production function exhibit constant return to scale? b. Derive the production function for output per capita. c. Derive the production function for output per effective unit of labor. d. Find equilibrium real wage as a function of capital per unit of effective labor and effectiveness of labor. e. Find equilibrium real rental price of capital as a function of capital per unit of effective labor and effectiveness of labor. f. Solve for steady state level of capital per unit of effective labor. g. Find steady state level of output per unit of effective labor. h. Find growth rate of output and output per worker on the balanced growth path. i. Which one would…
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
Draw a graph with the following elements: A Solow growth (Y) function where Y= square root of K An investment (I) function where I = % * Y A depreciation (D) function where D = % * K
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1) In the steady state of the Solow model with technological progress, which of the following variables is not constant? (a) capital per effective worker (b) the real rental price of capital (c) the real wage (d) the capital-output ratio
Consider the Swan-Solow model of economic growth. [Hint: Question (e) below goes beyond the subject matter discussed in the lecture and requires you to think independently.] c) Draw a typical Depreciation curve into the diagram. Briefly explain how you came up with the curve and what you need to know to exactly pin it down.
The Solow Growth Model is a model that is often used to explain the theoretical relationship between several factors that determine a country's economic growthcountry.(a) Explain what you know about the Solow Growth Model and what are the most important determinants of a country's long-term growth rate?(b) Within the framework of the Solow Growth Model, how does population growth affect a country's economic growth rate?(c) Still within the framework of the Solow Growth Model, how does technological progress affect a country's growth rate?
Suppose that the economy of Santa Cruz County follows the equations of the Solow model. It has an investment rate of 0.6 and a depreciation rate of 0.2, and an aggregate production function Y=4K(1/4) In the year 2019 the economy is in steady state. But in 2020 the CZU wildfire destroys 50% of the capital stock (so K2020= 0.5 K2019). Assuming the economy returns to its usual growth dynamics after that, what would the growth rate of GDP from 2020 to 2021? Write your answer in percentage points and round to 1 decimal place (e.g. 4.2 would mean 4.2% growth from 2020 to 2021).
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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 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 a version of the Solow growth model in which output is determined by the production function Y = z(¾½³K + ¾½N) where z = 1. The depreciation rate and the savings rate are given by d = 0.13 and s 0.3. Assume that population N grows at a rate of n = 0.02. Calculate the = steady-state output per capita and consumption per capita, y* and c*, respectively. O (y*, c*) = (0.2, 0.06) ○ (y*, c*) = (0.5, 0.35) ○ (y*, c*) = (0.5, 0.21) ○ (y*, c*) = (1.0, 0.70)