Consider an Economy in steady state, with a Cobb Douglas Production function. They have a savings rate of 45% and a capital share of 2/7. Technological progress is 1%, population growth is 3%, and Depreciation is 5%. 1. Derive the Production function per effective worker and solve for steady state capital, output, and consumption per effective worker. 2. What is MPK in the steady state? Is this country saving too much or too little? How do you know? 3. What should you lower or raise the saving rate to, in order to reach the golden rule steady state
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Consider an Economy in steady state, with a Cobb Douglas Production function. They have a savings rate of 45% and a capital share of 2/7. Technological progress is 1%, population growth is 3%, and
1. Derive the Production function per effective worker and solve for steady state capital, output, and consumption per effective worker.
2. What is MPK in the steady state? Is this country saving too much or too little? How do you know?
3. What should you lower or raise the saving rate to, in order to reach the golden rule steady state
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- Assume that a country's per-worker production is y = k/2, where y is output per worker and k is capital per worker. Assume also that 10 percent of capital depreciates per year (= 0.10) 2 and there is no population growth or technological change. a. If the saving rate (s) is 0.4, what are capital per worker, production per worker, and consumption per worker in the steady state? b. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.6. c. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.8.Population Growth and Technological Progress – Work It Out PLEASE WRITE ANSWERS CLEARLY An economy has a Cobb-Douglas production function: Y = K“(LE)'-a The economy has a capital share of 0.30, a saving rate of 42 percent, a depreciation rate of 4.00 percent, a rate of population growth of 5.25 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital. k* = y* = marginal product of capital =41. Assume that a country's per-worker production is y=1.5k3/4, where y is output per worker and k is capital per worker. Assume also that 10 percent of capital depreciates per year and there is no population growth or technological change. a. If the saving rate (s) is 0.15, what are capital per worker, production per worker, and consumption per worker in the steady state? b. Solve for steady-state capital per worker, production per worker, and consumption per worker with s-0.3. c. Solve for steady-state capital per worker, production per worker, and consumption per worker with s-0.45. d. Is it possible to save too much? Why?
- Population 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: %Q7 An economy has a Cobb–Douglas production function: Y = Kα(LE)1−α The economy has a capital share of 1/3, a saving rate of 24 percent, a depreciation rate of 3 percent, a rate of population growth of 2 percent, and a rate of labor-augmenting technological change of 1 percent. It is in a steady state. a. At what rates do total output, output per worker, and output per effective worker grow?b. Solve for capital per effective worker, output per effective worker, and the marginal product of capital. c. Does the economy have more or less capital than at the Golden Rule steady state? How do you know? To reach the Golden Rule steady state, does the saving rate need to increase or decrease?d. Suppose the change in the saving rate you described in part (c) occurs. During the transition to the Golden Rule steady state, will the growth rate of output per worker be higher or lower than the rate you derived in part (a)? After the economy reaches its new steady state, will the growth rate of…In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about 2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratio is about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has been in a steady state.a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy = (δ + n + g)k.]b. What is the marginal product of capital in the initial steady state?c. Suppose that public policy alters the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal productin the initial steady state. Explain.d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product of…
- In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about 2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratio is about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has been in a steady state.a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy = (δ + n + g)k.]b. What is the marginal product of capital in the initial steady state?c. Suppose that public policy alters the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal productin the initial steady state. Explain.d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product of…An economy's production function as follows Y = 8 (K)¹/2 (EL)¹/2 If depreciation rate is 10%, population growth rate is 4%, tech progress grows 6%, and saving rate is 20%. a. b. C. d. e. f. Write production function in term of per effective worker variables. Find steady state capital per effective worker, output per effective worker, consumption per effective worker, investment per effective worker. Find growth rate of capital per worker and output per worker at steady state. Find growth rate of capital stock and total output at steady state. Propose policies to encourage long run growth of total output and living standard? Draw relevant graph for the above questions.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?
- a. Given a per capita production function ofy= k^0.5, a savings rate of 10%, a depreciation rate of 2%, a technological growth rate of 1%, and a population growth of 3%, what is this economy's steady-state level of output per capita. In a sentence, describe over time what is happening to this economy's level of RGDP when the economy is in a steady state. b. Imagine that the economy described in part a of this problem begins time (tO) with 1 unit of capital per effective worker. Assume that investment demand rises at the same rate as real GDP. Further, assume that by time t1 this economy has achieved the steady-state level of capital. On the left-hand side of the plots below, diagram the movement of the requested variables between time to and time t1.In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about 2 percent per year, the depreciation rate is about 3 percent per year, and the capital-output ratio is about 1.5. Suppose that the production function is Cobb-Douglas and that Ghana has been in a steady state. a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy = (6 + n+ g)k] b. What is the marginal product of capital in the initial steady state? c. Suppose that public policy alters the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal product in the initial steady state. Explain.Economic Growth II- Work It Out Question 1 An economy has a Cobb-Douglas production function: Y = K (LE)¹- The economy has a capital share of 0.35, a saving rate of 45 percent, a depreciation rate of 5.00 percent, a rate of population growth of 5.50 percent, and a rate of labor- augmenting technological change of 4.0 percent. It is in steady state. c. The economy has capital than at the Golden Rule steady state. To achieve the Golden Rule steady state, the saving rate needs to d. Suppose the change in the saving rate you described in part c occurs. During the transition to the Golden Rule steady state, the growth rate of output per worker will be the rate you derived in part a. After the economy reaches its new steady state, the growth rate of output per worker will be