In the Solow model, suppose the per worker production function is y = 6 k0.5 Suppose s = 0.08, n = 0.04, and d = 0.08. Calculate the steady-state equilibrium capital-labor ratio. k= (Round to two decimal places.)
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- Q1] Consider the Solow model with no technological progress and population growth rate of n. The production function in intensive form is given by y = f(k) = Ak“. a) Find the expression for the steady-state value of per capita capital stock (k*). [Hint: sf(k*) = (n+ d)k*] b) Find the expression for steady-state qutput.In the Solow model, suppose the per worker production function is y = 5 k0.5 Suppose s = 0.11, n = 0.07, and d = 0.08 Calculate the steady-state equilibrium capital-labor ratio. (Round to two decimal places.) k =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 to
- Consider 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…Consider the Solow model with a production function Y(t) = A*K(t)^α*L(t)^(1-α), Where A is a fixed technological parameter. Explicitly solve for the steady-state value of the per capita capital stock and per capita income. How do these values change in response to a rise in (a) the technological parameter A, (b) the rate of saving s, (c) α , (d) δ, the depreciation rate, and (e) the population growth rate n?Assume that a closed economy has a production function of the form Y = z.F (K,N) = z.KaN¹-a where Y=output, z is total factor productivity, K is capital, N is employment=population. 13. a) Use the Solow Model, assuming a constant saving rate s, constant population growth rate, n, and depreciation rate d, to show that in steady state capital per worker k=K/N is given by K-( ) k S.Z |1–α n+d b) Contrast the sho term and long-term impacts of a permanent rise in s and a permanent rise in z, on capital per worker, output per worker, consumption per worker and the return on capital (where relevant you may refer to your answer to part a) c) Explain how your answers to parts a) and b) illustrate the role of total factor productivity in i) long-run growth ii) sustained differences in income between countries.
- an economy is described by the Solow-Swan model with the following variables, E(t)=1 The saving rate is 0.41 per year. Labor's share of income is 0.44. The growth rate of labor efficiency is 0.03 per year. The growth rate of the labor force is 0.02 per year Depreciation is 0.09 per year. calculate the steady-state value of the capital-to-labor ratio, K/L Enter your answer to two places after the decimal.Consider 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!!Consider the basic Solow model. Assume that Country A has a production function as following. Y = A√K Where A represents the technology available in the country and & the aggregate capital. Let the national saving rate be equal to 30%, s = 0.3. Also, assume that capital depreciates at a constant rate of 3%, delta = 0.03. a) Now, the economy experiences a positive shock to the idea/technology and A becomes 2 which was originally 1. Relative to the previous steady state level of capital and output, what will happen?
- Consider the Solow growth model with labour-augmenting aggregate production function, Y = F(K, AL), where Y is output, K is the capital stock, and L is the labour force. The labour force (assumed equal to population) grows at a constant rate n > 0. Technological level A grows at a constant rate a > 0. С5. Prove analytically, that for the production function in the intensive form y = f (k) the expression for MPL = ƏY takes the form MPL = A[f(k) – kf'(k)]. Find the growth rate of real wage w = W /P for every moment in time and on the balanced growth path.K1/3 L2/3, where K is = Suppose that the production function in the Solow-Swan model is Y capital and L is the population size. Which of the following is TRUE? There is no steady state The lower the per capita capital stock, the slower the growth of per capita income If per capita capital is below its steady state, it increases towards the steady state None of the aboveQ5 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?