Macroeconomics (9th Edition)
9th Edition
ISBN: 9780134167398
Author: Andrew B. Abel, Ben Bernanke, Dean Croushore
Publisher: PEARSON
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Question
Chapter 6, Problem 7NP
a
To determine
To ascertain:An expression for national saving per worker and steady state level of investment per worker, values of capital-labor ratio, output per worker, consumption per worker, investment per worker.
b)
To determine
To ascertain: An expression for national saving per worker and steady state level of investment per worker, values of capital-labor ratio, output per worker, consumption per worker, investment per worker when tax = 0.5%.
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In an economy characterized by a Cobb-Douglas production function (without technical progress), labour’s share of income is 70% and the depreciation rate is 3% per annum. The economy is in a steady state with GDP growth at 4% per year and with a capital output ratio of 2. Find the saving rate and the marginal product of capital. At time t the saving rate in this economy increases to a new constant level, with the outcome that the economy converges to the Golden Rule steady state. What is the new savings rate, capital output ratio and 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].
In Wonderland production per worker (y)
depends on capital per worker() such the
y=10vk. Every year 15% of the capital stock
depreciates, while workers in Wonderland save
10% of their income. Every year the population
grows ratas te of 3%
(c) The country of Neverland is identical to
Wonderland in terms of output per worker, the
savings rate, the depreciation rate and
population growth. They differ in one respect:
Wonderland has capital per worker of 10,
whereas Neverland has capital per worker of 20.
Which country experiences a higher growth rate
of output per worker and how will their growth
rates evolve over time?
Chapter 6 Solutions
Macroeconomics (9th Edition)
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- Suppose there is a country called Solowland whose output (Y) is produced using capital (K), labour (L) according to the following aggregate production function: 13 Y = AK^(1/4) L^(3/4) where A is Total Factor Productivity (TFP). The rate of population growth (n) is 2.5% per year (0.025). The rate of depreciation of capital is 15% per year (0.15). Total factor productivity equals 20 (A=20) and we assume there is no technical progress (growth rate of A is zero).a)Show, analytically, that the production function displays diminishing marginal product of capital and labour and constant returns to scale. Explain your answer. b)If Solowlands savings rate (s) is 20% (0.20), find its steady state capital stock per capita, income per capita, consumption per capita and investment per capita. c)Suppose there is another county, Swanland where output is also produced by a diminishing returns production function using capital, labour, and technology. In this country, population growth is just 0.5%…arrow_forwardSuppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Suppose that now there is labor augmenting technology, the rate of labor-augmenting technological is 2 percent. At what rate does total output, output per worker, and output per effective worker grow?arrow_forwardSuppose that an economy has the following production function: Y = F(K, LE) = K1/2(LE)!/2 Assume that the rate of depreciation is 5 percent per year (d = .05), the rate of population growth is 3 percent per year (n = .03), the rate of labor efficiency growth is 3 percent per year (g=.03) and the saving rate is 60 percent (s = 0.6). Calculate the per effective worker production function, the steady-state levels of capital per effective worker (k*), output per effective worker (y*), consumption per effective worker (c*), and investment per effective worker (i*) %D %3Darrow_forward
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