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- The aggregate production function is Y = 3KL. If there are 20 units of capital and 50 units of labor, what is aggregate output? Group of answer choices 600 1000 150 3000A 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)∗?The aggregate production function is Y = 5KL. If there are 18 units of capital and 50 units of labor, the capital productivity is ___________.
- Economies production function is Y = AK0.3N0.7. If K = 2000, N = 100, and A= 1, then Y = ?Please no written by hand and graph Consider a small world that consists of two different countries, a developed and a developing country. In both countries, assume that the production function takes the following form: Y = F (K, LE) = K¹/4 (LE) 3/4, where Y is output, K is capital stock, L is total employment and E is labour augmenting technology. (a) Does this production function exhibit constant returns to scale in K and L? Explain. (b) Express the above production function in its intensive form (i.e., output per-effective worker y as a function of capital per effective worker k). (c) Solve for the steady-state value of y as a function of saving rate s, population growth rate n, technological progress g, and capital depreciation rate 6. (d) The developed country has a savings rate of 30% and a population growth rate of 2% per year. Meanwhile, the developing country has a savings rate of 15% and population growth rate of 5% a year. Technology evolves at the rate of 8% and 2% in…The term capital, as used by economists, refers to a money b the physical space in which production occurs c the time allocated to producing goods and services d financial securities such as stocks and bonds e machinery and equipment that is not used up during the production process
- Suppose that the production function is Y=K^((1)/(3))(EL)^((2)/(3)) where E is the efficiency of labor. (a) Derive the per-efficiency-unit-of-labor production function. (i.e., y=f(k)= Y//EL) (b) Solve for the steady state value of y as a function of s,n,g, and d (c) A developed country has a savings rate of 28% and a population growth rate of 1% per year. A less-developed country has a saving rate of 10% and a population growth of 4% per year. In both countries, g=0.02 and d=0.04. Find the steady state valueAKL The Suppose the production function takes the form F(K, L) = K+L capital share is equal to: 3 L L+K ĀK K+LGiven the following aggregate production function: Y = K0.25 (AL) 0.75, where technology A grows at a fixed rate: = g> 0 (a) Obtain the marginal product of capital algebraically, also discussing the second derivative. (b) Transform the production function into efficiency-worker terms, showing how =ỹ depends AL on =k. K AL
- Suppose the production function for widgets is given by KL – 0.5K2 – 0.1 L2 , where q represents the annual quantity of widgets produced, K represents annual capital input, and L represents annual labor input. (a). Suppose K=5; what is the average productivity of labor (Average product of Labor, MPL) (b). Suppose K=10; at what level of labor input does the total output reach the maximum?Consider the simple (one period) production model. The production function is Cobb Douglas, exhibits constant returns to scale, and the exponent on capital equal to 0.25.Are there key differences between an increase in the capital stock and an improvement in the level of technology?