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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- 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…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
- an economy is given by y=k^( 1/3). The depreciation rate is 16%, the saving rate is 26%, the growth rate of the labor force is 4%, and the growth rate of labor-augmenting technological change is 4%. Given these features, this economy's steady-state level of capital per effective worker is (Enter your response rounded to two decimal places.)Consider an economy with the following aggregate production function: Y = 3K1/3(AL)2/3 Capital grows through investment but also decays due to wear and tear at a constant rate δ per period. Assume that A is growing at the exogenous rate g, that L is growing at the exogenous rate n, and that households save a constant proportion s of their income. (a ) Find the steady state level of the capital per effective worker (k*), output per effective worker (y*) and consumption per effective worker (c*) - in terms of the parameters of the model. (B) What is the level of k (k**) that maximizes consumption? (C) Given a depreciation rate of 7%, population growth rate of 2%, technological progress of 1% and a saving rate of 30%, calculate the steady state levels of k, y and c. (D) To move to the level of capital that maximizes consumption, how should the saving rate be changed? Explain. (E) Calculate the saving rate needed to reach the golden rule level of capital per effective worker.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?
- Assume the economy is initially in its balanced growth state. Suppose policymakers pursue policies that would increase the saving rate to s1=0.3. Compute the new steady-state values of (i) capital stock per effective worker, (ii) output per effective worker and (iii) consumption per effective worker.Suppose some of the country's capital is suddenly destroyed. If the depreciation rate, savings rate, and production function remain unchanged, then the real growth rate will _____ in the short run and the steady-state level of capital will _____ increase, decrease, or stay the same?An economy has the per-worker production function yt=f(kt)=4kt)0.4, where yt is the output per worker and kt is the capital-labor ratio. The depreciation rate is 0.15, and the population growth rate is 0.04. Saving is St=0.5Yt, where St is total national saving and Yt is total output. The slope of the per worker production function is given by f' (kt)=1.6kt-0.6 . What is the steady state value of capital-labor ratio, k*? Round your answer to at least 2 decimal places.
- 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…“The Sollow model shows that the saving rate does not affect the growth rate in the long-run, so we should stop worrying about the low US saving rate. Increasing the saving rate wouldn’t have any important effects on the economy.” Explain why you agree or disagree with this statement. Structured response required.