Consider the Cobb-Douglas production function y-AKO.3N0,7, where y is output, A is total factor productivity, is capital and y is employment. In the Solow growth model, by how much (in percent terms) would the steady-state output per worker grow in response to a 21.1% increase in total factor productivity? (Submit your answer with up to two decimals, i.e., 10.22 for 10.22% and 11.44 for 11.442%.)
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- Suppose we started out at the steady state capital stock in the basic Solow growth model (see graph a few questions ago). If there subsequently were an increase in the demand for loanable funds due to more favorable tax treatment of business investment, ceteris paribus (i.e., holding other factors constant, including no shift in the supply of loanable funds), then as we move to the new steady state over time we would expect to see Group of answer choices A) economic growth rates turn negative as we move toward the new steady state and the nation’s capital stock to decrease from its current level. B) economic growth rates turn positive as we move toward the new steady state and the nation’s capital stock to decrease from its current level. C) economic growth rates turn positive as we move toward the new steady state and the nation’s capital stock to grow from its current level. D) economic growth rates turn negative as we move toward the new steady state and the nation’s…Suppose an economy described by the Solow model is in a steady state with population growth n of 1.8 percent per year and technological progress g of 1.8 percent per year. Total output and total capital grow at 3.6 percent per year. Suppose further that the capital share of output is 1/3. If you used the growth-accounting equation to divide output growth into three sources—capital, labor, and total factor productivity—how much would you attribute to each source?Show how an economy described by the Solow model with total factor productivity converges to its steady state values of output per effective worker (Hint: substitute A}¬- a = A) using an excel simulation. Set parameters to the following values: 0.4 15% a 4.5% 8% 25% 10 ko
- Production function is given by Y = Ka(AN)'¯ª, where a=2/3. Initially, the saving rate was equal to s and the economy was in the steady state. Use the Solow growth model to answer the following questions. (Please fill in numbers; use a yomma as a decimal separator: 10,5) 1. In order to increase capital per unit of effective labor in the steady state by a factor of 27 (i.e. to make it 27 times larger), the rate of saving needs to increase by a factor of 2. In order to increase output per unit of effective labor in the steady state by a factor of 4 (i.e. to make it 4 times larger), the rate of saving needs to increase by a factor of 3. Suppose that s=25 percent, the rate of depreciation of capital is equal to 5 percent, the rate of technological progress is equal to 1 percent, and the rate of population growth is equal to 0,25 percent, a=2/3. The steady state level of investment per unit of effective labor is equal toQ5 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?Consider an economy with a Cobb-Douglas production function with α = 1/3 that begins in steady state with a growth rate of technological progress of g of 2 percent. Consider what happens when g increases to 3 percent. (a) What is the growth rate of output per worker before the change? What happens to this growth rate in the long run? (b) Perform a growth accounting exercise for the economy, decomposing the growth rate in output per capita into components contributed by capital per capita growth and technology growth. What is the contribution of the change in g to output per capita growth according to this formula? (c) In what sense is the growth accounting result in part b producing a misleading picture of this experiment? Explain why this is the case.
- In the Solow model, population growth leads to steadystate growth in total output, but not in output per worker. Do you think this would still be true if the production function exhibited increasin g or decreasing returns to scale? Explain.Suppose an economy described by the Solow model is in steady state with population growth n of 1.8 percent per year and technological progress g of 1.8 percent per year. total output and total capital grow at 3.6 percent per year. suppose further that the capital share of output is 1/3. if you used the growth accounting equation to divide output growth into three sources- capital, labor, and total factor productivity- how much would you attribute to each source? compare your results to the figures we found for the united states in tables 9-2.. This part considers a modified version of the Solow growth model. Suppose the production function is given by F(K,bN) = K°(bN)1-a where b is the labour augmenting technology, which grows at a rate f, i.e., b+1 = (1+ f)b. For simplicity, assume that the total factor productivity z = 1, and the population is constant, i.e., N, = N for all t. The rest of the model is the same as in the standard Solow model in the textbook. Especially, the aggregate capital stock evolves according to Kt+1 = I4 + (1 – d)Kt. And assume that the economy is still closed, and there is no government. For any aggregate variable X, let the lower case letter a be the variable per effective unit of worker; that is a = *. Show that the production technology specified above satisfies the assumption of con- stant returns to scale.
- Suppose in a Solow model, we have the following parameter values: n = 0, s = 0.2, a = 0.33. 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 deadly pandemic hits the economy at time t=1. As a result, the population at time t =1 is 10% lower than the population at time t=0. The pandemic is a one-time shock so that population growth rate remains the same, i.e., from t-2 onward, the population remains the same as the population at time t=1. The total capital stock, however, is unchanged so that K, Ko. What is the growth rate of per-capita capital in percentage (rounded to the 2 decimal places, e.g., answer 1.08 if your calculation shows the growth rate is 0.01079) at time t=3 from time t=2? %3!This part considers a modified version of the Solow growth model. Suppose the production function is given by F(K,bN) = Kª(bN)!-ª where b is the labour augmenting technology, which grows at a rate f, i.e., bt+1 = (1+ f)bt. For simplicity, assume that the total factor productivity z = 1, and the population is constant, i.e., N, = N for all t. The rest of the model is the same as in the standard Solow model in the textbook. Especially, the aggregate capital stock evolves according to K++1 = It + (1 – d)Kį. And assume that the economy is still closed, and there is no government. For any aggregate variable X, let the lower case letter a be the variable per effective unit of worker; that is x = *. Show that the production technology specified above satisfies the assumption of con- stant returns to scale. List all the equilibrium conditions of this model. Using the equilibrium conditions you listed above, write down an expression that describes the evolution of the aggregate capital stock,…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.