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- Consider an economy described by the production function: Y = F(K, L) = K^0,3L^0,7 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.Consider an economy described by the production function Y=F(K, L)=?^0.4?^0.6 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.The output of an economy is characterized by a Cobb-Douglas production function with constant return to scale and an output elasticity with respect to capital equal to 0.3. Also given are the following parameters: 30% saving rate, 5% depreciation rate, 2% population growth rate, and the technology factor is 2. a). Find the capital-labour ratio, and also the output, consumption and investment on a per capita basis in the steady state equilibrium. b). Is a government policy that raises the saving rate to 40% socially desirable? Explain your answer with reference to a comparison of this new steady state equilibrium and the initial steady state equilibrium in a) above. c). If the initial capital-labour ratio is 30, is the economy operating efficiently in the sense that welfare cannot be improved? Explain concisely. What if the initial capital-labour ratio is 15? Again explain concisely.
- 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 2 Its production function is 2 times the square root of k (the same as 2k1/2) and its depreciation rate is 3 percent. Its population grows at a rate of 4 percent per year, and technology is advancing at a rate of 1 percent annually. Its residents consume 90% of each additional dollar of income. Find the economy's steady state level of capital (k*), carefully following all numeric instructions.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?
- Say an economy begins with an initial level of capital per worker, k0, that is above its steady state level of capital per worker, k*. All else equal, what will happen to output per worker and capital per worker?If we have an aggregate production function of the form Y = AK, at what capital-labor ratio can a steady-state equilibrium be reached?Suppose an economy begins in steady state. By what proportion does per capita GDP change in the long run in response to each of the following changes? (a) The investment rate doubles (b) the depreciation rate falls by 10% (c) The productivity level rises by 10% (d) an earthquake destroys 75% of the capital stock (e) A more generous immigration policy leads the population to double.
- Q)If the economy is in a steady state, then A. both consumption per worker and capital per worker are decreasing. B. both consumption per worker and capital per worker are constant. C. consumption per worker is decreasing but capital per worker is constant. D. consumption per worker is constant but capital per worker is decreasing.A CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H: where 0 a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?Assume a hypothetical society that decides to reduce consumption (production of consumption goods) and increase investment (production of capital goods). How would this change affect economic growth? What groups in society would benefit from this change? What groups might be hurt?