Use the simple Solow model, with no population growth. The formula for steady-state consumption per worker (c*) as a function of output per worker and investment per worker is: c * = f(k*) - δk* c * = f(k*) + δk * c * = f(k*) ÷ nk* c * = k* - f(k)*
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5. Use the simple Solow model, with no population growth. The formula for steady-state consumption per worker (c*) as a function of output per worker and investment per worker is:
-
- c * = f(k*) - δk*
- c * = f(k*) + δk *
- c * = f(k*) ÷ nk*
- c * = k* - f(k)*
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- In 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 0.10KIn the Solow model, if investment per-worker initially exceeds saving per-worker, how isthe steady-state capital per worker reached? Draw a graph to support your answerPopulation Growth and Technological Progress-Work It Out An economy has a Cobb-Douglas production function: Y = K (LE)¹- The economy has a capital share of 0.20, a saving rate of 49 percent, a depreciation rate of 4.00 percent, a rate of population growth of 1.50 percent, and a rate of labor-augmenting technological change of 4.0 percent. It is in steady state. a. At what rates do total output and output per worker grow? Total output growth rate: Output per effective worker is constant in the steady state and does not change. increases in the steady state. declines in the steady state. % Output per worker growth rate: %
- 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 %3D 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?9) 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<04. Suppose that the Indonesian economy can be explained by the Solow model using the following production function: Y = K (LE) ² , where E is the efficiency of labor. a. Derive the production function reflecting per-efficiency-unit-of-labor (in this case; y = fik) = Y/EL). b. Use the answer in (a) to find the steady-state value of y as a function of s, n , g, and d. c. Now suppose that the Malaysian economy also has the above production functions, but they have different parameter values. Indonesia has a savings rate of 28 percent and a population growth of 1 percent per year. While Malaysia has a savings rate of 10 percent and a population growth of 4 percent per year. Both Indonesia and Malaysia have g = 0.02 and d = 0.04. Determine the steady-state values of y in the two states.
- Suppose a Solow economy is initially at its steady state k∗, and suddenly is hit by a decrease in the depreciation rate δ, from δ to δ1. This change does not alter any of the other exogenous parameters in the model Depict this situation in a graph What happens to steady state level of capital per capita in this situation? What happens to the level of capital per capita over time? Depict this in a graph and explain intuitively.Problem 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) a. 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.Problem 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.
- Sweden and Norway are two neighboring countries in Northern Europe with similar savings rates, population growth rates, technology growth rates, and depreciation rates. However, Norway differs from Sweden in that Norway has large deposits of oil all along its coast, which makes it very easy for Norway to produce large quantities of crude oil every year with relatively little capital and labor. a) Draw a Solow Growth diagram that compares Sweden and Norway. What is the main difference between the two countries in the diagram? b) According to the Solow Growth Model, which country would have a higher standard of living in the long run? Which country would have a higher growth rate of its standard of living in the long run? c) Suppose now that, in the long run, oil becomes obsolete and has no value because it is uneconomical relative to renewable energy sources like solar and wind power. What would this do to your Solow Growth diagram in part a? How would the standard of living in Norway…In a standard Solow growth model that is calibrated in per-worker terms, what happens to the level of output when the saving rate (“s”) rises? How does the increase in “s” impact long-term output growth? How does the level of consumption change initially when savings rates rise? What happens to consumption over time?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…