In the Solow model with population growth and labor augmenting technological progress, with depreciation rate 8, population growth rate n, and technological growth rate g, the number of effective workers grows at the rate of: O a. n+g. b. O c. n+ 8. O d. n-g. n+g+8.
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- In a Solow economy with technological progress, the production function is given by: Y = KO.5(LE)0.5. Furthermore, the saving rate of this economy is 0.2. The population growth rate is 0.03. The depreciation rate is 0.01. The technological progress is given by g which is equal to 0.01. Define y = Y/LE and k = K/LE. a) Find out the steady state values of k (i.e.: k*) and y (i.e.: y"). 2. Ay Ak AY ΔΚ b) Find out the values of and in the steady state. K y'k'YConsider the basic Solow growth model. Let the aggregate production function be defined as Y = F(K, L) = K0.5 L0.5 where Y is output, K is capital, and L is labor. Furthermore, let the saving rate be 48%, population growth be 2%, and depreciation rate be 10%. a. Find the steady-state levels of capital per worker k and output per worker y.. %. b. Now assume that, because of the proliferation of financial technologies, the saving rate increases suddenly to 54% after one year. The steady-state level of capital will increase by ____%, and the steady-state level of output will increase by_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,…
- Production function is given by Y= (1/2)K^a(AN)^(1-a), where a=2/3. The rate of depreciation of capital is equal to 15 percent, the rate of technological progress is equal to 3 percent, and the rate of population growth is equal to 2 percent. The economy was in the steady state at time tand the level of technology was equal to A=80. Use the Solow growth model to answer the following questions. 1. If the saving rate s=80 percent, the steady state level of output per unit of effective labor at time tis equal to ... 2. If the saving rate s=80 percent, the steady state level of consumption per unit of effective labor at time tis equal to ... 3. If the saving rate s=80 percent, the steady state level of consumption per worker at time tis equal to ... 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.Consider the Solow growth model with a Cobb-Douglas production function with capital share a, a constant savings rate s, a constant depreciation rate 8, and a constant population growth rate n (0 0. 1. Derive the law of motion of capital per capita. 2. Derive the steady state levels of capital and output per capita. 3. Explain intuitively why there is a steady state. Now suppose that productivity increases by 10% to A2. 4. Derive the new steady state levels of capital and output per capita. Compare them to the old ones. 5. In three separate figures, draw the evolution through time of productivity A, capital per capita Kit, and output per capita Yit. Make sure to include several periods of the pre-shock steady state, the time of the shock, the transition to the final steady state, and several periods of the final steady state. Discuss the differences between the two figures. 6. Suppose that the economy has converged to its new steady state. Do a growth accounting exercise on output per…
- Suppose a country has a capital-output ratio equal to 10, a savings rate equal to 20% of GDP, capital that lasts on average 100 years and population growth of 1% per year. If we assume the country is at its steady state and production is given by the Solow model with labor-augmenting technological change, so Y = K^a(EL)^(1 – a), then the growth rate of technology as measured by the growth rate of efficiency workers is 0% 1% 3% 2% 4%Explain the Solow Model when there is an improvement of technologyIn the Solow growth model, suppose that the per-worker production function is given by y = zk 0.4 with s = 0.15, d = 0.1, and n = 0.02. a. Suppose in country A that z= 1. Calculate the steady-state capital per worker and income per capita in country A. The steady-state capital per worker is (Round to two decimal places as needed.) The steady-state income per capita is. (Round to two decimal places as needed.) b. Suppose in country B that z = 2. Calculate the steady-state capital per worker and income per capita in country B. The steady-state capital per worker is|. (Round to two decimal places as needed.) The steady-state income per capita is (Round to two decimal places as needed.) c. As measured by GDP per capita, how much richer is country B than country A? What does this tell us about the potential differences in total factor productivity to explain differences in standards of living across countries? Country B is times richer than country A, as measured by GDP per capita. This…
- Consider the following Solow growth model in which households save a constant fraction of their income. Let N be the population (also the labor force) in the current period. Assume that the population follows N′ = (1+n)N where N′ is the population in the future period, and n is the net population growth rate. Assume that the output is produced according to the production function Y = zF(K, N), where z is the total factor productivity, K is capital stock, and F(K, N) exhibits constant returns to scale. Capital depreciates at the rate d where 0 < d < 1. The capital stock changes over time according to K′ = (1 − d)K + I where I is the investment level. (a) Derive the equation that determines the future capital-per-worker in competitive equilibrium. Here is some additional information for parts (5b), (5c), and (5d). Suppose that the economy is initially in steady state, and experiences a natural disaster (e.g. the recent quake and tsunami in Japan in 2011) that destroys some of the…In the Solow growth model with population growth, if the per-worker production function is given by y = √k, the saving rate is 0. 3, the depreciation rate is 0. 1, and the population growth rate n is 0.05, then the steady-state capital stock per worker (*) is: a) 6 Ob) 4 O c) 5 d) 2We presented two versions of the Solow growth model. (1) In the simple version, there is no technological progress. Show in this simple version that at the steady state output per worker (GDP per worker) depends positively on the saving rate, and negatively on the population growth rate. What’s the growth rate of GDP at the steady state? What’s the growth rate of GDP per worker at the steady state? (2) In the version of the model with technological progress, what’s the growth rate of GDP at the steady state? What’s the growth rate of capital per worker at the steady state? What’s the growth rate of GDP per worker at the steady state? Show your steps