Consider the following production function: Y; = AKSH}-«L; where Kris capital, He is human capital, Ltis the amount of workers and A is the (constant) level of technology. • (i) Does this production function satisfy all the neoclassical properties. Discuss the meaning of each property INTUITIVELY.
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- Problem 4 Consider the following production function: Y, = AKÇH!-"L where Kr is capital, H;is human capital, Leis the amount of workers and A is the (constant) level of technology. • (1) Does this production function satisfy all the neoclassical properties. Discuss the meaning of each property INTUITIVELY. Imagine that parents invest in the human capital of their children up to the point where the MARGINAL PRODUCT OF PHYSICAL CAPITAL, K, is equal to the MARGINAL PRODUCT OF HUMAN CAPITAL, H:. 2 • (ii) What is the relation between K:and H:? Use this relation to write down total output as a function of Kronly. Imagine that the number of people in this economy, Nr, is different from the number of workers because some people do not work. Let l =4 be the number of workers per capita (the fraction of the population that works). Let y; ミ be output per capita and be capital per capita. Finally, let n be the rate of population growth and y, be the growth rate of labor. (ii) Using the "effective…Problem 4 Consider the following production function: Y, = AKÇH!-"L where Kr is capital, H;is human capital, Leis the amount of workers and A is the (constant) level of technology. • (1) Does this production function satisfy all the neoclassical properties. Discuss the meaning of each property INTUITIVELY. Imagine that parents invest in the human capital of their children up to the point where the MARGINAL PRODUCT OF PHYSICAL CAPITAL, K, is equal to the MARGINAL PRODUCT OF HUMAN CAPITAL, H:. 2 • (ii) What is the relation between K:and H:? Use this relation to write down total output as a function of Kronly. Imagine that the number of people in this economy, Nr, is different from the number of workers because some people do not work. Let l =4 be the number of workers per capita (the fraction of the population that works). Let y; be output per capita and Kt be capital per capita. Finally, let n be the rate of population growth and y, be the growth rate of labor. (iii) Using the…(ii) What is the relation between Kt and Ht? Use this relation to write down total output as a function of Ktonly. Imagine that the number of people in this economy, Nt, is different from the number of workers because some people do not work. Lt Let lt - be the number of workers per capita (the fraction of the population that works). Let y Nt Yt be output per capita and Nt Kt kt be capital per capita. Finally, let n be the rate of population growth and y, be the growth rate of labor. Nt (iii) Using the "effective production function" you derived in (b), write down output per capita, yt, as a function of capital per capita, kt, labor per capita, lt, the level of population Nt, and the level of technology, A. Following Solow and Swan, assume there is no government and no net exports, that the depreciation rate of capital is the constant 8 > 0 and the savings rate is constant 0 < s < 1. (iv) DERIVE the fundamental equation of Solow-Swan. How does the growth rate of capital depend on…
- (a) Explain the characteristics of the production function used in the Heckscher-Ohlin (H-O)model. (b) Explain with the help of a graph how we can determine the specific combination oftwo goods that can be produced in the economy in the H-O model.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.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.
- Economics, physical capital represents the uildings or machines used by a business to produce product. The marginal product of physical capital presents the rate of change of output product with spect to physical capital (informally, if you increase e size of your factory a little, how much more Foduct can you create?). articular model tells us that the output product Y is given, a function of capital K, by Y = AKªL'-a ere A is a constant, L is units of labor (assumed to be stant), and a is a constant between 0 and 1. Determine marginal product of physical capital predicted by this del. ned with CamScannerTrue or False A production function in "economics" summarizes the technological relationship between inputs and outputs.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.
- Indicate whether the following statement is TRUE or FALSE and explain your answer: ‘Consider threeinputs of production: labour, physical capital and natural resources, and an economy with decreasingreturns to scale. If you increase all three inputs x times then the total gross domestic product (GDP) inthe economy will increase exactly x times, but GDP per capita will decrease.’please asnwer the question in the image Some economists believe that the U.S. economy as awhole can be modeled with the following productionfunction, called the Cobb–Douglas production function:Y 5 AK1/3L2/3,where Y is the amount of output, K is the amount ofcapital, L is the amount of labor, and A is a parameterthat measures the state of technology. For this productionfunction, the marginal product of labor isMPL 5 (2/3) A(K/L)1/3.Suppose that the price of output P is 2, A is 3, K is1,000,000, and L is 1,000. The labor market is competitive,so labor is paid the value of its marginal product.a. Calculate the amount of output produced Y and thedollar value of output PY.b. Calculate the wage W and the real wage W/P. (Note:The wage is labor compensation measured in dollars,whereas the real wage is labor compensationmeasured in units of output.)c. Calculate the labor share (the fraction of the value ofoutput that is paid to labor), which is (WL)/(PY).d. Calculate what happens to output Y,…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).
