1. Consider the Solow model with total factor productivity A, constantly growing at rate g>0. a. Determine the a) instantaneous impact on GDP per capita, b) instantaneous impact on consumption per capita, c) long-run impact on GDP per capita (i.e. compare the level of GDP per capita with and without the parameter change, in the long-run), d) long-run impact on consumption per capita (i.e. compare the level of consumption per capita with and without the parameter change, in the long-run), and e) impact on long-run GDP per capita growth rate of a one-time and instantaneous increase (jump) in productivity At, through a significant and non- repeatable invention, after which At immediately resumes growth at rate g. Assume the country begins at its "steady state value" of k* before this event occurs. Justify your answer by use of graph and/or equation. [Hint: this is not a change in g, since productivity resumes growth at rate g after the one-time jump; it is a one-time jump in At.] b. Graph the path of ln(yt) and ln(c) against time for the event analyzed in part a. c. Repeat parts a&b for a permanent, instantaneous increase in the growth rate of productivity, g. Treat this simply as an increase in trend growth with no change in the "steady
1. Consider the Solow model with total factor productivity A, constantly growing at rate g>0. a. Determine the a) instantaneous impact on GDP per capita, b) instantaneous impact on consumption per capita, c) long-run impact on GDP per capita (i.e. compare the level of GDP per capita with and without the parameter change, in the long-run), d) long-run impact on consumption per capita (i.e. compare the level of consumption per capita with and without the parameter change, in the long-run), and e) impact on long-run GDP per capita growth rate of a one-time and instantaneous increase (jump) in productivity At, through a significant and non- repeatable invention, after which At immediately resumes growth at rate g. Assume the country begins at its "steady state value" of k* before this event occurs. Justify your answer by use of graph and/or equation. [Hint: this is not a change in g, since productivity resumes growth at rate g after the one-time jump; it is a one-time jump in At.] b. Graph the path of ln(yt) and ln(c) against time for the event analyzed in part a. c. Repeat parts a&b for a permanent, instantaneous increase in the growth rate of productivity, g. Treat this simply as an increase in trend growth with no change in the "steady
Chapter1: Making Economics Decisions
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![1. Consider the Solow model with total factor productivity At constantly growing at rate g>0.
a. Determine the a) instantaneous impact on GDP per capita, b) instantaneous impact on
consumption per capita, c) long-run impact on GDP per capita (i.e. compare the level of GDP per
capita with and without the parameter change, in the long-run), d) long-run impact on
consumption per capita (i.e. compare the level of consumption per capita with and without the
parameter change, in the long-run), and e) impact on long-run GDP per capita growth rate of a
one-time and instantaneous increase (jump) in productivity At, through a significant and non-
repeatable invention, after which At immediately resumes growth at rate g. Assume the country
begins at its "steady state value” of k* before this event occurs. Justify your answer by use of
graph and/or equation. [Hint: this is not a change in g, since productivity resumes growth at rate
g after the one-time jump; it is a one-time jump in At.]
b. Graph the path of ln(y+) and ln(c+) against time for the event analyzed in part a.
c. Repeat parts a&b for a permanent, instantaneous increase in the growth rate of
productivity, g. Treat this simply as an increase in trend growth with no change in the “steady
state" value of k or y. It may help to do the graphs against time first, and use those to answer the
a)-e) impacts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F144161ac-559f-4b1a-80a0-0fffa7827db1%2F68cb300a-2fbb-4903-9ad1-2ed9dcc6b017%2Fmat1u9e_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the Solow model with total factor productivity At constantly growing at rate g>0.
a. Determine the a) instantaneous impact on GDP per capita, b) instantaneous impact on
consumption per capita, c) long-run impact on GDP per capita (i.e. compare the level of GDP per
capita with and without the parameter change, in the long-run), d) long-run impact on
consumption per capita (i.e. compare the level of consumption per capita with and without the
parameter change, in the long-run), and e) impact on long-run GDP per capita growth rate of a
one-time and instantaneous increase (jump) in productivity At, through a significant and non-
repeatable invention, after which At immediately resumes growth at rate g. Assume the country
begins at its "steady state value” of k* before this event occurs. Justify your answer by use of
graph and/or equation. [Hint: this is not a change in g, since productivity resumes growth at rate
g after the one-time jump; it is a one-time jump in At.]
b. Graph the path of ln(y+) and ln(c+) against time for the event analyzed in part a.
c. Repeat parts a&b for a permanent, instantaneous increase in the growth rate of
productivity, g. Treat this simply as an increase in trend growth with no change in the “steady
state" value of k or y. It may help to do the graphs against time first, and use those to answer the
a)-e) impacts.
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