Question 3b. Let the aggregate production function of a national economy be given by Y = F(K,L) = AK0.3510.65 Explain what variables Y, A, K and L denote. What does this production function imply about the income distribution in the economy? What is the Solow residual and how is it related to the production function?
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- 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)∗?Question 27Refer to Figure 1. Suppose the per-worker production function in the figure above represents the production function for the U.S. economy. If the United States decided to double its support of university research, this would cause a movement fromn.Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = Ka.Lb a. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or or y' or dy/dk ? c. Briefly explain why y'>0 or dy/dk > 0 . Is it possible that dy/dk < 0 ? Why? d. Briefly explain why y'' ≤ 0 . e. Find the elasticity of substitution between K and L. What does expansion path look like?
- Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=Ka.Lba. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or y- or dy/dk ? c. Briefly explain why y’>0 or =dy/dk >0 . Is it possible that dy/dk>0 ? Why? d. Briefly explain y’’ < 0 e. Find the elasticity of substitution between K and L. What does expansion path look like?Suppose the economy of Utopia has a labor force of 600 workers, 100 units of capital and 400 hectares of land. It produces manufactured goods (M) which use labor (LM) and capital (K) in production and agricultural goods (A) which use labor (LA) and land (T) in production. The production functions are given by: QM = VR/LM %3D And Ly + LA = L = 600 In autarky, PA = PM = 10. %3D Suppose Utopia engages in trade and the price of manufactured goods, PM = 20. What happens to: 1. The workforce and output of manufactured goods? Of agricultural goods? 2. The nominal and real wage in Utopia? 3. The real return to capital and to land in Utopia? 4. Will everyone support trade?The production function for an economy can be expressed as Y= F(K,L), where Y is real GDP, K is the quantity of capital in the economy, and L is the quantity of labor in the economy. If Y = K0.5 L0.5, what is real GDP if the quantity of capital is 900 and the quantity of labor is а. 400? b. What is/are the endogenous variable(s) in this model? What is/are the exogenous variable(s) in this model? с.
- e here to search ? 2 2 3 S 1. Consider the following production function: Y=F(K, L) = A(2K + 3L) Does this production function exhibit constant returns to scale? 2. Suppose the table represents the production function of both Mexico and Spain. Use the following information to answer the next question. K = Capital (trillions) Y = Output (trillions) Country L = Population (millions) Mexico 3 Spain E D 105 3. Calculate per capita income for both countries. 4 45 2. Calculate total factor productivity for both countries using Equation 3. Equation 3: Y = F(KL) = AK0.3 L0.7 R 4. Explain the difference in per capita income. % 0.18 0.74 5 6 hip & T Y 1 G H a 00 1.0 W 1.7 39 FocusSuppose a country has a population of 120 people, a working-age population of 100 people, its labor force participation rate is 0.5 (50%), and the quantity of output is 60 units. Suppose that the production function of the economy is given by Y=2N, where Y represents the quantity of output and N represents the number of workers needed to produce the output. I know the answer is 0.4 but I don't understand how to get it. Thank you!Give only typing answer with explanation and conclusion The production function in an economy is given by Y = K0.4L0.6, where Y is output level, K is capital input, and L is labour input. The saving rate is 24%, the annual population growth rate is 4%, and annual depreciation rate is 2%.
- Given the following production function Y=X+4X^2-0.2X^3. At what level of X does the Total physical product (TPP) reach its maximum?Suppose that the aggregate production function takes the form y= A(5ON -0.1N), where Y is output, A is productivity, and N is total hours worked. Let's suppose A-1.0. Assuming that the supply of labor is given by ys = 100 + 10w where w is the wage rate. What is the equilibrium level of output and hours worked? (Hint: use the labor market equilibirum condition to find w) OA N-150, Y-2,350 OB. N-200, Y-6000 OC N-200, Y-5,000 OD. N-50, Y-3,750Hello I need help to find the answer for my econ 101 hw for a question as follows: Assume that the production function for a country is given by ?=√K and annual investment is given by the function ?=?×? where γ=0.270, and that the yearly depreciation rate is 4.50%. Suppose that this year, the output in the country is 1, and a neighbor country's output is 50% higher. Calculate the time it would take for the country's output to catch up with its neighbor's output. Assume the neighbor country's economy is neither growing nor shrinking. I will be also attaching the original problem for your reference as I just need to find the time that it would take the country's output to catch up with its neighbor's output. Thank You and please refer to the image to further assist with the question that I want answered.