2. An economy has a production function:Y 3KtLt.(1)The economy has a saving rate of 24 percent, a depreciation rate of 3 percent,1 for all period (no population growth).and LtYtLt(a) What is the per-worker production function, ytf(kt)? Define ytКиLtand kt(b) Find the equation for the evolution of capital per worker in terms of ktand kt+1(c) Find the long-run growth rate of output per worker.Now the economy has the following production function:Y 3Kt(2)but savings rate, depreciation rate, and population remain the same YtLtf (kt)? Define yt(d) What is the per-worker production function, yt(e) Find the equation for the evolution of capital per worker in terms of ktand kt+1(f) Find the long-run growth rate of output per worker.(g) Explain why the economy with production function (2) explain per-sistent growth without the assumption of exogenous technologicalprogress. How does this differ from the economy with production func-tion (1)?

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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1. Country A and B both have the production functionY = F (K, L) = K ½L ½or Y = K0.5 L0.5 a) What is the per-worker production function, y= f (k)? Please make sure to write specificfunctional form of the per-worker production function. b) Assume that neither country experiences population growth nor technological progressand that 4 percent of capital depreciates each year. Assume further that country A saves 24percent of output each year and country B saves 16 percent of output each year. Using youranswer from part a) and the steady-state condition, find the steady-state level of capital perworker for each country. Then find the steady-state levels of income per worker for eachcountry and steady-state level of consumption per worker for each country.
A CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H: where 0 a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?
A. Investment in "infrastructure" represents spending on: O roads, bridges, canals, etc. O human capital (education) O government institutions O innovation to physical capital B. Which of the following was not one of Thomas Malthus' assumptions regarding population and economic growth? O Per-capita income would increase. O The economy was agriculturally based O The supply of land was fixed O The population would continue to increase
I am having a problem with these four problems webdav/pid-1221589-dt-content-rid-8618514_1/courses/1678.201780/Assign2.pdf + Automatic Zoom : 19. Technological progress helps increase the productivity of labor, defined as the number of units of output produced per hour of labor. A rise in the productivity of labor in the production process, ceteris paribus, will cause A) the demand for the output to increase. B) the demand for the output to decrease. C) the supply of the output to increase. D) the supply of the output to decrease. E) None of the above is correct. Q Search 20. An economic recession with a decline in household incomes will negatively impact all retail businesses. A) True B) False 21. If we assume that the current equilibrium wage for low-skilled labor is $8 per hour and the minimum wage is increased from $5.75 to $7.25 per hour, then A) unemployment among low-skilled workers will increase. B) unemployment among low-skilled workers will remain unaffected. C) unemployment…
Suppose the per-worker production function is: y = A(1-gA) Where ga is the fraction of all workers that produce technologies. Further, suppose the growth of technology is given by the following equation growth of A = (g//m)(L) Suppose L = 1 and m = 7, and that initially ga = 0.7. If ga fell to 0.8 the level of output per %3D worker would: fall Impossible to say rise stay the same
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.
) The goal is to analyze further the two-sector endogenous growth model. Write down the equation of motion for k, which shows delta k as saving minus break-even investment. (Break-even investment is the amount of investment needed to keep capital per effective worker constant.) Draw a graph that determines the steady-state k. In this economy, what's the steady-state growth rate of output per work? How do the saving rate and fraction of labor force in universities (u) affect this steady-state growth rate?
Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].
In this problem, we distinguish between labor and population in the Solow growth model. A proportion of the population, a, between zero and one, works. The production function is now written as Y = A(K^1/3)[(aL)^2/3] (a) How does an increase in a from 0.3 to 0.6 change steady state GDP? (b) Does it change the steady-state capital? Explain. (c) Suppose a rises steadily over time. How do you think would affect the growth rate of GDP?
Problem 5 A “miraculous" Asian economy has an aggregate wage bill of 300 billion dollars and an aggregate GDP of 500 billion. The annual growth rate of aggregate GDP for this economy over the last 10 years was 7 percent (that is AY/Y=0.07) and the growth rate of labor was 6 percent (AL/L=0.06). Imagine that the production function is given by the standard Cobb-Douglas AK“L“. ,а, 1-а Y What are the "capital share (a)" and the "labor share (1 – a)"? b. Imagine that the government controls the national accounts. In its quest to improve its reputation, the government mistakenly thinks that having "a lot of investment" will make it look good so it "inflates" its growth of capital number to 12% (AK/K=0.12). When researchers estimate the rate of productivity growth (AA/A), what will they find? Is the growth rate of technology positive or negative? Does your result in (b) make sense? d. The actual truth is that the growth rate of capital was one half of what it announced. That is, instead of…
Choose the following opton: 1) In the very long run, across the next fifty years, a country’s economic standard of living as measured by Real GDP Per Person can grow steadily as a result of sustained growth in one of the following two values. The correct focus of growth policy will be to promote: (a) Labor Productivity (b) Total Labor Effort 2) The correct answer to Q#1 is a consequence of which feature of any country’s economy. In the very long run, fifty years and beyond: a) Total Labor Effort (Aggregate Labor Hours) can grow faster than a country’s Population. b) Total Labor Effort (Aggregate Labor Hours) cannot grow faster than a country’s Population.
For this question assume that technological progress does not occur. The rate of saving in Canada has generally been greater than the saving rate in the U.S. Given this information, we know that in the long run A) Canada's growth rate will be greater than the U.S. growth rate. B) capital per worker in Canada will be no different than U.S. capital per worker. C) investment per worker in Canada will be no different than U.S. investment per worker. D) all of these E) none of these

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