What is the economic meaning of the powers of K and L? Briefly explain. What is the level of output ? produced when the economy in long-run equilibrium.
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What is the economic meaning of the powers of K and L? Briefly explain.
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What is the level of output ? produced when the economy in long-run equilibrium.
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- 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?The economy of Ouratricot has 50 units of labor and 30 units of capital. Ouratricot has a production unit that produces knitted goods with a technology described by the production function QT=min{2KT,LT} where QT is the quantity of knitted goods produced, KT is the quantity of capital used in the knitted goods production unit, and LT is the quantity of labor used in the knitted goods production unit. Ouratricot has a production unit that produces Ouras with a technology described by the production functionQO=min{KO,LO} where QO is the quantity of Ouras produced, KO is the quantity of capital used in the production unit of Ouras, and LO is the quantity of labor used in the production unit of Ouras. Find all of the capital and wage allocations between the two production units that are likely to be part of an optimal allocation in the sense of Pareto in the economy of Ouratricot. Justify your answer with precision and clarity.Consider three inputs of production: labour, physical capital and natural resources, and an economy with decreasing returns to scale. If you increase all three inputs x times then the total gross domestic product (GDP) in the economy will increase exactly x times, but GDP per capita will decrease
- Which is an example of the aggregate production function, Y = F(K, N), that exhibits constant returns to scale? Y= 2 K N Y = 3 K N Y = K/N Y= 2K + 3 NSuppose the economy's production function is Y = AK0.3N0.7. If K = 2000, N = 100 and A=1 then Y = 246. If K and N both rise by 20% and A is unchanged, by how much does Y increase?Assume that digital revolution popularizes the use of artificial intelligence (computers) in the workplace. The production function becomes: Y = 0.25 K(2/5)(ACN)(3/5) where C stands for the number of computers.: a) Use growth accounting to predict the increase in total output in response to an increase in the number of computers by 10 percent. b) The nominal interest rate on government bonds equals 9 percent and inflation equals percent. The rate of GDP growth is equal to the result obtained in (a). Use the debt dynamics equation and graph to explain whether or not the level of public debt in percent of GDP can be stabilized if the government runs a primary deficit. c) Use the neoclassical investment model (equation and graphs) to assess the impact of a decrease in the number of computers on investment (in traditional physical capital K).
- 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.(1) In one country, its production function of national output is Y = F(K, L) = A * K(3/4) * L(1/5). Does the production function have a constant return to scale, an increasing return to scale or a decreasing return to scale? And why? (show your work)Question1. 1. Suppose the economy's production function is Y = AKO.3N0.7. If K = 2000, N = 100, and A = 1, then Y= 246. If K rises by 10%, and A and N are unchanged, by how much does Y increase?
- Suppose 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!6. Consider a hypothetical economy that has the production function Y = = F (K, LE) = K¹/3 (LE) 2/3, where Y is output, K is capital, and LE is the number of effective workers. Suppose the saving rate is 20%, the capital depreciates by 3%, the population grows at the rate of 1%, and the rate of labor-augmenting technological change is 1%. a. Solve for the per-effective-worker production function.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?