3. Consider the production function Y, = Kª (AL¿)1-a In 2013, the capital stock Kt increased by 4%, total factor productivity A increased by 2%, and labor Lt increased by 3%. What is the growth rate of output per worker in 2013? a. (a – 1)% b. (1– a)% c. (5a + 2)% d. (2 – a)%

3. Consider the production function Y, = Kª (AL¿)1-a In 2013, the capital stock Kt increased by 4%, total factor productivity A increased by 2%, and labor Lt increased by 3%. What is the growth rate of output per worker in 2013? a. (a – 1)% b. (1– a)% c. (5a + 2)% d. (2 – a)%

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

Chapter20: Economic Growth

Section: Chapter Questions

Problem 20RQ: For a high-income economy like the United States, what aggregate production function elements are...

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Y - K"(LE) The economy has a capital share of 0.20, a saving rate of 45 percent, a depreciation rate of 3.75 percent, a rate of population growth of 5.00 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k"), output per elffective worker (y"), and the marginal product of capital. k' - y* = marginal product of capital =
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].
J 7 Given a production function Yt = AKt1 /3L2 /3 , if K0=8, A = 2, L = 4, s = 0.2, and d = 0.05: (a) Calculate the steady-state level of capital and output. (b) Calculate K1 , I 1 , Y1 and C1 .
2. An economy has a production function:Yt = 3(squaredKt)(squaredLt). The economy has a saving rate of 24 percent, a depreciation rate of 3 percent,and Lt = 1 for all period (no population growth). There is no technologicalprogress. (a) What is the per-worker production function, yt = f(kt)? Define yt =YtLtand kt =KtLt.(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:Yt = 3Kt but savings rate, depreciation rate, and population remain the same. (d) What is the per-worker production function, yt = f(kt)? Define yt =Yt/Lt (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 persistent growth without the assumption of exogenous technologicalprogress. How does this differ from the economy…
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Q4) Production Functions and Growth (a) Time is continuous and the production function of the economy is given by (1) Y¢ = ( K¢ )ª( A¿N; )1-« Total factor productivity evolves according to (2) A = egt Ao such that A where the growth rate of technological progress g is exogenous. Population grows at an exogenous rate n according to (3) N{ = ent No with No = 1 such that = n Find an expression for the growth rate of (i) output per capita (Yt / Ni) and (ii) output per effective worker ( Yt/ (A:N:) ). When is the growth rate of (ii) equal to zero?
5. Suppose that the economy's production function is Y = √KVLA where K is capital, L is labor, and A is the state of technology. Suppose that the saving rate (s) is equal to 2.4%, the rate of depreciation of capital (6) is equal to 3%, the number of workers grow at 0.7% per year and the rate of technological progress is 3%. (a) Find the steady state values of: iv. v. growth rate of output growth rate of output per worker (b) Suppose that the growth rate of workers decreases. What is its short-run and the long-run effect on the growth rate of output per worker ?
4. If the production function is given by Y=K2L'3 and the saving rate saving rate (s) equals the depreciation rate (8). Find the numerical values of the steady state capital and output?
72) According to new growth theory, the accumulation of ________ capital is subject to diminishing returns at the ________ level, but not at the level of the economy as a whole. A) physical; firm B) technological; personal C) knowledge; firm D) physical; production 73) Because knowledge capital is nonexcludable and nonrival, firms have an incentive to ________ the research and development of other firms. A) make bids on B) not use C) ignore D) free ride on 74) When firms benefit from the results of research and development they didn't pay for, we say firms A) are litigious. B) free ride. C) invest in knowledge capital. D) maintain a level playing field. 75) For how long does a patent give a firm the exclusive legal right to a product? A) 10 years B) 17 years C) 20 years D) 50 years 76) A copyright grants the creator of a book, film, or piece of software exclusive legal rights to use the creation for how long? A) 10 years B)…
Regard x and y as continuous variables. If x grows at 3% rate and y grows at 2% rate, what is the growth rate of z = x2y2? a. 0.5% b. 1.5% c. 2.5% d. None of above.
1. Consider an economy where the production function is Y = K0.5 (LE)0.5 The depreciation rate is = 0.04, the savings rate is s = 0.2, the popula- tion growth rate is n = 0.03 and technology growth rate is g = 0.03. (a) What is the 'per effective worker' production function? (b) Find the steady state levels of capital per effective worker (k*), in- come per effective worker (y*), investment per effective worker (¿*) and consumption per effective worker (c"). (c) Find the golden rule levels of capital per effective worker (kg), income per effective worker (y), investment per effective worker (it) and consumption per effective worker (c2). Also find sg, that is the level of the savings rate that would lead the economy to the golden rule steady state. (d) Suppose the government pursues policies that change the savings rate from s = 0.2 to sg. What is the immediate effect on income per effective worker and consumption per effective worker? What is the long run effect on income per…
1. Consider the following Romer model of economic growth: Y₁ = A₁Lyt AA, = ZA,L, Lat = Lyt= = L Lat = lL (a) If 4₁ = 100, ē = 0.1,ī = 1/3,000, [= 1,000, and what is the growth rate of knowledge in this economy? (b) What is the growth rate of per capita output in this economy? (c) Using the information from year 1, what is the level of per capita output in this economy in year 5?