Assume that a production function is given by Y = AK³L²/³. IfĀ = 2 and [ = 1, and if the steady-state capital stock is 8.0, the steady-state level of output is about: Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a b 8.0. 4.0.
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- Consider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is yt = 2.2kt^0.5, where y is output per worker and k is capital per worker. The depreciation rate of capital is 10% per year a- Households initially consume 80% of income and save the remaining 20% of income. There is no government spending. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker? b-Suppose saving rate decreases to 10% permanently. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker?Consider an economy A described by the production function: Y = F(K, L) = K0.3L0.7. In economy B, everything is similar to economy A, except, saving rate is 40%. Explain how steady state output per worker, consumption per worker and golden rule level of capital stock will differ from those of country A
- Question 3Consider an economy described by the production function:Y = F(K, L) = K0.3 L0.7 a. What is the per-worker production function?b. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.c. Assume that the depreciation rate is 10 percent per year. Make a table showing steadystate capital per worker, output per worker, and consumption per worker for saving ratesof 0 percent, 10 percent, 20 percent, 30 percent, and so on. (You will need a calculator with an exponent key for this.) What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?Suppose that the economy is summarized by the following: Technology (Production Function): Yt = 10 (Kt)0.3 (Lte)0.7 Consumption function: Ct = 0.8Yt Depreciation rate: 8% (i.e. δ= 0.08) Population growth: 2% (i.e. n = 0.02) Technological growth: 4% (i.e. g = 0.04) 1. Assuming that in 2013 the US economy is in the steady state and L2013 = Le2013 = 8, what is the value of ke2014, ye2014, ce2014 , k2014, y2014, and c2014 ?Given a saving rate of 6%, a depreciation rate of 1%, and a production function in which y = k0.5 where y is output per worker and k is capital per worker, calculate the steady state values for capital per worker, output per worker, consumption per worker, and Calculate the golden rule steady state level of capital Assuming an economy is at steady state, with the use of an appropriate diagram with descriptions illustrate the impact of a reduction in the saving rate on capital per worker and output per worker. In the context of the Solow model, illustrate with appropriate descriptions the impact of increased migrant workers on capital per worker and output per worker in an economy.
- Using the law of motion for physical capital accumulation (K), what is the amount of capital for the next period if the amount of physical capital today is 20 and Investment is 15 (Assume a depreciation rate of 10%) a) 23 b) 33 c) 34 d) 35 3- Using the law of motion for physical capital accumulation (K), what is the steady state level of capital when investment is 10? (Assume a depreciation rate of 10% and remember that physical capital is constant at the steady state) a) 100 b) 50 c) 120 d) 123 4- What is the key difference between catching up growth and cutting edge growth? a) Cutting edge growth is based on capital accumulation while catching up growth is based on technological advances b) Cutting edge growth is based exclusively on natural resources unique to every country c) Cutting edge growth is based on innovation, new ideas. Catching up growth is based on physical capital accumulation d) None of the above7. 1. Consider a neoclassical growth economy described by the following.•Yt = K0.3t ·L0.7t (aggregate production function)•s = 0.35 (saving rate)•δ = 0.10 (depreciation rate)•n = 0.01 (population growth rate)•L1 = 120 (initial population)•K1 = 160 (initial capital stock)•g = 0 (technological growth rate)Compute K, Y , k, y, and c for the first three periods. Please report numerical answersto two decimal points. (a) K1 = ; Y1 = ; k1 = ; y1 = ; c1 =(b) K2 = ; Y2 = ; k2 = ; y2 = ; c2 =(c) K3 = ; Y3 = ; k3 = ; y3 = ; c3 =Exercise 4: Growth and capital over-accumulationSuppose two countries, A and B, with the same production function Y = KαL1−α. Thevalue of α is 0.30, the growth rate of population is 2% and the depreciation rate is 5%.a) Show that with price-taking firms the share of labor must be 1 − α.b) Compute the stock of capital, output and consumption per unit of labor in the steadystate if the savings rates were 25% for country A and 35% for country B.c) Compare both economies to the Golden Rule.d) Explain what would happen to both countries if suddenly their savings rate becamethe Golden Rule savings rate.
- Consider an economy in which production is characterized by the neoclassical productionfunction:Y = K0.5N0.5Suppose that it has a saving rate (s) of 0.1, a population growth rate (n) of 0.02, and an average depreciationrate (d) of 0.03.a) Write this production function in per capita form, and find the steady-state values of per capitacapital k and per capita output y.b) At the steady-state value of k, is there more or less capital than at the golden-rule level?c) Determine what saving rate would yield the golden-rule level of capital in this model.Suppose that K(t+3)/N > K(t+1)/N, where K(t+3) is capital in period t+3 and K(t+1) is capital in period t+1. The economy will reach or reached a steady-state (long-run equilibrium) in period __ (choose the best one, given the information available). t+5 t-2. t-1. tCountry A and B each have a production function Y = A ̄K1/2L1/2. Assume A ̄ = 1, d ̄ = 0.05, and L ̄ = 100 in each country but investment rate differs, s ̄A = 0.1 in country A and s ̄B = 0.2 in country B. Each country starts off with an initial K of 200. (a) What happens to capital and output in each country in the long run? (b) Does country B overtake country A? (c) Suppose an earthquake hits country A so its initial K (instead of being 2) is now reduced to 1. There is no effect on country B. How does the long run output compare with your answer in (a).