Macroeconomics (Fourth Edition)
4th Edition
ISBN: 9780393603767
Author: Charles I. Jones
Publisher: W. W. Norton & Company
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Chapter 5, Problem 11E
(a)
To determine
The projection of the relative per capita steady state GDP of countries.
(b)
To determine
The projection of the relative per capita steady state GDP of countries.
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Consider the Solow Growth Model studied in Chapter 5 with the
following information:
The production function is: Y₁ = AK₁¹/³L2/3
Amount of labor (Lt) = 1000
Investment rate (s) = 0.1
Depreciation rate (d) = 0.4
Productivity (A) = 1
Find the numerical value of the steady-state level of output per
person.
Q5 Suppose in a Solow model, we have the following parameter values: n = 0, s = 0.5, a = 0.3. There
is no growth in the total factor productivity so that A, = A = 1. Moreover, we know that at time 0,
the economy is at a steady state so that k = k, =1. Now imagine that a foreign power invaded this
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country. 1% of the population was killed and another 14% of the population fleeded the country to
avoid violence. Moreover, 15% of capital stocks were destroyed. All of this happens in period t=1.
After that, the war ended and there was no more destruction of capital or loss of population (but the
refugee permanently settled outside of the country and will never return0. What is the growth rate of
per-capita output in period t =4?
Consider the Solow growth model in which population evolves according to: N′ = (1 + n)N where N is the population (labor force) in the current period, N′ is the population (labor force) in the future period, and n is the population growth rate. There are public health expenditures that takes the form of government spending, G = gN, where G is the current period government spending on health care, g is the per-capita health spending in the current period. The production technology is given by Y = zKαN1−α where Y is the output of the consumption good, z is the total factor productivity, K is the current period capital stock, aN is the labour input, and 0 < α < 1 is a parameter. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1.
(a) Suppose that the economic is hit by a pandemic (e.g. Covid-19). The government responds to the pandemic by raising the public health spending per person (e.g spending on vaccination) temporarily (i.e. one-period…
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- Consider the Solow growth model in which population evolves according to: N′ = (1 + n)N where N is the population (labor force) in the current period, N′ is the population (labor force) in the future period, and n is the population growth rate. There are public health expenditures that takes the form of government spending, G = gN, where G is the current period government spending on health care, g is the per-capita health spending in the current period. The production technology is given by Y = zKαN1−α where Y is the output of the consumption good, z is the total factor productivity, K is the current period capital stock, aN is the labour input, and 0 < α < 1 is a parameter. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. Suppose that the economic is hit by a pandemic (e.g. Covid-19) which causes a temporary decrease in total factor productivity, z, as certain sectors in the economy (e.g. entertainment, travel etc.) cannot deliver…arrow_forwardConsider the Solow growth model in which population evolves according to: N′ = (1 + n)N where N is the population (labor force) in the current period, N′ is the population (labor force) in the future period, and n is the population growth rate. There are public health expenditures that takes the form of government spending, G = gN, where G is the current period government spending on health care, g is the per-capita health spending in the current period. The production technology is given by Y = zKαN1−α where Y is the output of the consumption good, z is the total factor productivity, K is the current period capital stock, aN is the labour input, and 0 < α < 1 is a parameter. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. (a) Suppose that the economic is hit by a pandemic (e.g. Covid-19). The government responds to the pandemic by raising the public health spending per person (e.g spending on vaccination) temporarily (i.e. one-period…arrow_forwardConsider the Solow growth model. Suppose that F(K, N) = zK^a N^1-a,where a = 0.3. Also, assume that capital depreciation rate is 10% (that is d = 0.1), savings rateis 25% (that is s = 0.25), populations growth rate is 2% (that is n = 0.02), and z = 2.• First, determine capital per worker, income per capita, and consumption per capita in thesteady state.• Second, assume that the savings rate has increased to 40% but the total factor productivitydecreases to 1. Discuss the effect of savings and productivity on the steady state level ofconsumption per worker. PLEASE SHOW ALL HAND WRITEN STEPS!!arrow_forward
- Consider the model you developed in Question 1, where labor growth at a constant rate. Suppose that F(K, L) = K0.5 L0.5 with d = 0.1, s = 0.2, n = 0.01, and A = 1, and take a period to be a year. Question 2 Part a Determine capital per worker, income per capita, and consumption per capita in the steady state. Question 2 Part b Now, suppose that the economy is initially in the steady state that you calcu- lated in Part a. Then, s increases to 0.4 Question 2 Part b1 Determine capital per worker, income per capita, and consumption per capita in each of the 10 years following increase in the savings rate Question 2 Part b2 Determine capital per worker, income per capita, and consumption per capita in the new steady state. Question 2 Part b3 Discuss your results, in particular, comment on the speed of adjustment to the new steady state after the change in the savings rate, and the paths followed by capital per worker, income per capita, and consumption per capita.arrow_forwardIn the Solow Growth Model, a country's production function is defined by the following: Y = F (K/L) = kºs Where K is capital and I. labour; labour grows at a rate (n), and the economy faces depreciation at a rate (8) The initial Capital Stock per worker: k, = 9 units The savings rate: s = 0.20 and the rate of depreciation: a = 0.1 Using equations and identities from the Solow Growth Model, calculate the level of capital k, Output y, Consumption c, depreciation and change in capital from the equation of motion for periods 1, 2 and 3. Comment on the accumulation of capital and output over the three periods.arrow_forwardConsider the following numerical examples for the Solow Growth Model: Economy A z=1 s=0.5 F(K,N)=K0.3N0.7 n=0.01 d=0.1 Economy B z=1 s=0.2 F(K,N)=K0.3N0.7 n=0.01 d=0.1 In which economy is Consumption per capita higher in steady state? O Economy A O Economy B Not enough Informationarrow_forward
- Consider the following numerical examples for the Solow Growth Model: Economy A z=1 s=0.5 F(K,N)=K0.3N0.7 n=0.01 d=0.1 Economy B z=1 s=0.2 F(K,N)=K0.3N0.7 n=0.01 d=0.1 In which economy is GDP per capita higher in steady state? O Economy A O Economy B O Not enough Informationarrow_forwardIn class we assumed that the rate of population growth "n" was a constant. This was true for the Solow-Swan growth model as well as for the AK model. Imagine now that the rate of population growth is a function of k. Do you think fertility should be a function of k? An increasing or decreasing function of k? (Think of the costs and benefits of having children, and the reasons that lead people to purchase and produce kids) In the real world, do rich societies have larger or smaller fertility rates? Do you think mortality should be a function of k? An increasing or decreasing function of k? In the real world, do rich societies have larger or smaller mortality rates? Do you think net migration is a function of k? An increasing or decreasing function of k? In the real world, do rich societies tend to receive or to send migrants? а. b. C.arrow_forwardAll values are 2005 dollars. Part a) Calculate the growth of GDP/capita in each column. Part b) Calculate the average annual growth in GDP/capita for japan, uk, and USA from 1980 to 2010 using the growth formula in the image. In the growth function, t is the current time period, t-j is the original time period, and g is the annual growth rate. Part c) In parts a and b, are the calculated values for nominal gdp/capita or real gdp/capita. Explain why.arrow_forward
- Consider two countries in a Solow economy with growth in population but no growth in technological change. Assume both start from below their steady-state k∗, but one starts further below than the other, and all parameters are identical. On the same diagram, plot transition paths for each country.arrow_forwardProblem 2 In class we assumed that the rate of population growth "n" was a constant. This was true for the Solow-Swan growth model as well as for the AK model. Imagine now that the rate of population growth is a function of k. Do you think fertility should be a function of k? An increasing or decreasing function of k? (Think of the costs and benefits of having children, and the reasons that lead people to purchase and produce kids) In the real world, do rich а. societies have larger or smaller fertility rates? Do you think mortality should be a function of k? An increasing or decreasing function of k? In the real world, do rich b. societies have larger or smaller mortality rates? Do you think net migration is a function of k? An increasing or decreasing function of k? In the real world, do rich societies tend to receive or to send migrants? С. Imagine that n is a DECREASING function of k. Draw the savings and depreciation lines in the Solow-Swan models. d. In class we showed that, with…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
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