Macroeconomics
10th Edition
ISBN: 9780134896441
Author: ABEL, Andrew B., BERNANKE, Ben, CROUSHORE, Dean Darrell
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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b. Repeat Part (a) but assume now that the production function is Y=K0.3 Nº.8
2. (This is problem 3, page 239 of the textbook.) This problem adds the
government to the Solow model. Suppose that a government purchases goods
in the amount of g per worker every year; with Nt workers in year t, total
government purchases are gNt. The government has a balanced budget so that
its tax revenue in year t, Tt, equals total government purchases. Total national
saving, St, is St=s (Yt - Tt), where Yt is total output and s is the saving rate.
a. Graphically show the steady state for the initial level of government purchases
per worker.
b. Suppose that the government permanently increases its purchases per worker.
What are the effects on the steady-state levels of capital per worker, output per
worker, and consumption per worker? Does your result imply that the optimal
level of government purchases is zero?
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…
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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
- an 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_forwardConsider 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_forward
- Assume that in the Solow model the aggregate production function takes the Cobb-Douglas form: Y = 8K“ (AL)'-a where Y is output, K is capital input, L is labour input, and A is the level of labour- augmenting technical progress. Capital grows through investment but also decays due to wear and tear at a constant rate per period. Assume that A is growing at the exogenous rate g, that L is growing at the exogenous raten, and that households save a constant proportion s of their income. There is perfect competition in the markets for output and the inputs. a. Find the steady-state level of output per unit of labour in terms of A and the parameters of the model. What is the growth rate of total factor productivity (TFP) in terms of the parameters of the model? b. Find the steady state level of the capital-output ratio (k/y) in terms of the parameters of the model. c. Write down an expression for consumption per effective labour (c*) in the long run and show how it is affected by an increase…arrow_forwardIn the Solow model with technological progress, suppose that the rate of depreciation is 10% per year, the population growth rate is 2% per year, and the growth rate of technology is 3% per year. Which of the following represents the level of investment needed to maintain a constant capital stock (K) in this economy? 0.02K 0.03K 0.05K 0.10Karrow_forwardProblem 4 Consider a Solow-Swan economy with a Cobb-Douglas production function. Imagine that the savings rate "s" is an increasing function of capital and it has the following functional form: for low values of k the savings rate is constant at some low level. For intermediate levels of k, the savings rate increases rapidly. For high values of k the savings rate is constant again. In other words, the savings rate looks like: Does a steady state necessarily exist? Will the steady state be necessarily unique? Will the steady state(s) be stable? Will there be a "poverty trap"? (define poverty trap) а. b. С. d. How can this model be used (and how has this model been used) to justify large increases in foreign development aid? Discuss THREE potential flaws of the "savings poverty trap" model. е. f.arrow_forward
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