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 3AP
a
To determine
To plot: The graphical representation of steady state for initial level of government purchase.
b)
To determine
To find: The effects on the steady state levels of capital per worker, output per worker, consumption per worker.
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Take the Solow model without technological change. Assume there is a government
that taxes consumer's income at the tax rate t. The government uses the tax receipts to
buy some of output. Assume that individuals save a fixed fraction, s, of their after tax
income so St=s(1-t)Yt. (In this case, the government spending, g = TY). Show
graphically that an increase in the tax rate will lower the steady state capital stock of an
economy. Solve algebraically for the steady state capital stock.
Use the Solow model below to answer the question.
Y 3
Y ₂
2
Y₁
K₁
K₂
K3
Y = Af (K, H)
dk
SY
K
Suppose that Y₁ is 1,436, Y₂ is 6,076, and Y3 is 11,238. The savings rate for this economy is 11%
and the depreciation rate is 5.1%.
If this economy is currently at a GDP of 1,436, what is the smallest amount of foreign aid which
would move the economy up to a GDP of 11,238?
Assume that all foreign aid becomes investment. Round your final answer to two decimal places.
Suppose the economy of an island behaves as the Solow model (Y=AK1/2L1/2), version 1.0 (constant population). Suppose that the productivity parameter is A=90, the depreciation rate is d=1/10, the savings (investment) rate is s=0.10, and the labor force is equal to 2 million (and constant over time).
1-Due to climate change, from 2011 onward, every year the island is hit by hurricanes of increasing force that destroy capital. As a result, the depreciation rate doubles. What will be the new long-run (steady state) value for income per worker (Y/L)? Pick the closest value. Also label the new steady-state GDP as point C in the diagram.
Between 75 and 85
None of the other options
Between 4,500 and 5,200
Between 8,000 and 8,500
Between 44 and 49
2-In year 2021 investors recognize that the depreciation rate is higher than a decade earlier. They also recognize that the actual returns to their investments in physical capital over the previous decade have consistently fallen below their…
Chapter 6 Solutions
Macroeconomics (9th Edition)
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- 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).arrow_forwardUse the Solow model below to answer the question. Y Y3 Y₂ Y₁ K₁₁ K₂ K3 Y = Af(K,H) dk SY K Suppose that Y₁ is 1,475, Y₂ is 6,184, and Y3 is 10,992. The savings rate for this economy is 30% and the depreciation rate is 8.2%. If this economy is currently at a GDP of 1,475, what is the smallest amount of foreign aid which would move the economy up to a GDP of 10,992? Assume that all foreign aid becomes investment. Round your final answer to two decimal places.arrow_forwardPart 2. Multiple equilibria in the Solow Model Consider again the economy of Avataria, which can be described by the Solow model. Avataria has the old depreciation rate of 8% and the production function as in part (d), Y(K,L)=10(K)¹/2 (L) 1/2, and its investment rate is equal to its saving rate. However, now Avataria has two saving rates: saving rate is equal to 8%, if the income per capita is below 160, saving rate is equal to 16%, if the income per capita is above 160. (e) What will be the steady-state output per capita in Avataria, if its initial capital- labor ratio is 200? Calculate the exact value. ● ● (f) What will be the steady-state output per capita in Avataria, if its initial capital- labor ratio is 361? Calculate the exact value. (g) In which case, (e) or (f), do you expect Avataria to have a faster initial growth rate? Explain.arrow_forward
- Consider an economy described by the textbook Solow model with the following Cobb-Douglas production function: Y = ÅK°L*. %3D where a The economy is producing 100 units of output and the productivity parameter is equal to 1. the depreciation rate is 6%, the investment rate is 24%, and there are 64 workers, the growth rate of total output Y, is positive and the economy is converging to to its steady-state output per capita of 100 units. Question 6 total depreciation exceeds gross investment, the economy is below its steady state and outout per person is growing at a positve rate Question 7 Starting from steady state a permanent decrease in the rate of depreciation in the Solow model causes output per capita to Select) in the short nun in the long run the growth rate of the economy Sekectarrow_forward9) In the basic Solow model, suppose that Y = AK"N'-a,without population growth and technological progress. In this economy, long run growth in the level of GDP is possible if a) a > 0 and sA-d>0 b) a = 0 and sA-d>0 c) a = 1 and sA-d>0 d) a =1 and sA-d<0arrow_forwardDo not type in dollar signs or round any of your answers. Solow Model. Suppose a country's production function is Y = K1/2L/2. If capital depreciates at the rate of 4 percent each year and the population grows at the rate of 1 percent each year, calculate the savings rate that would lead to a steady-state equilibrium value for aggregate output (Y) equal to 900 assuming the labor force is equal to 150 workers: savings rate = percent Given the savings rate calculated above, steady-state capital per worker (k*) is equal to output per worker (y*) is equal to , and consumption per worker (c*) is equal toarrow_forward
- Consider an economy described by the Solow model with the following production function: Y = F(K, L) = K“ (L)'-« L grows at the rate n, the depreciation rate is 8, and the country saves a constant fraction s of its income. The change in capital per-worker is given by Ak = sy – (n+ 8)k. (a) Derive the per-worker production function. (b) Assuming population growth equals n and the depreciation rate equals 8, find the steady state level of capital per worker. It will depend on a, s, n and 8. Imagine the economy begins at the steady state you found in part b. Then there is a war that destroys a substantial amount of the economy's capital. The war does not affect the size of the labor force, population growth, the depreciation rate, or the saving rate. c) What is the immediate effect of the war on output per worker? Explain. d) After the war, is the growth rate of output per worker higher or lower than it was in steady state? Explain. e) How does the war affect steady state output per…arrow_forwardan 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.arrow_forwardConsider the Solow-Swan growth model, with a savings rate, s, a depreciation rate,8, and a population growth rate, n. The production function is given by: Y = AK + BK¹/2 H¹/4L¹/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb-Douglas production function. (a) Express output per person, y =Y/L, as a function of capital per person, k =K/L.arrow_forward
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