Question 1The Mankiw-Romer-Weil (1992) model.Assume the production function is given byY = KaH³(AL)¹-a-Bwhere a and B are constants between zero and one whose sum is also between zero and one. Physical capital isaccumulated asK = SKY dkwhere SK is the constant share of output invested in physical capital. And human capital is accumulated just likephysical capital:Н = SHY dHwhere SH is the constant share of output invested in human capital.The labor force grows at rate n, and the technological progress occurs at rate g. Solve the model for the path ofoutput per worker y=Y/L along the balanced growth path as a function of SK SH, n, g, d, a and B.(Hint: Define state variables such as y/A, h/A, and k/A.)

Production functionY=KαHβ(AL)1-α-β α and β are constant between 0 &1Physical capital…

The Mankiw-Romer-Weil (1992) model. Assume the production function is given by KaH³(AL) ¹-a-B where a and B are constants between zero and one whose sum is also between zero and one. Physical capital is accumulated as = K = SKY - dk where SK is the constant share of output invested in physical capital. And human capital is accumulated just like physical capital:

The Mankiw-Romer-Weil (1992) model. Assume the production function is given by KaH³(AL) ¹-a-B where a and B are constants between zero and one whose sum is also between zero and one. Physical capital is accumulated as = K = SKY - dk where SK is the constant share of output invested in physical capital. And human capital is accumulated just like physical capital:

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

Chapter20: Economic Growth

Section: Chapter Questions

Problem 9SCQ: Would the following events usually lead to capital deepening? Why or why not? A weak economy in...

See similar textbooks

Similar questions

Show that, when using a traditional economic production function,doubling our population can double our output if capital stocks alsodouble. Use the production function: Q = AK L , where A representstechnology in an economy, K capital, and L labor. Double K and L andshow that Q also doubles, assuming α=β=1/2. Now show that, when we incorporate natural capital into thediscussion, doubling the population does not increase output in thesame way (since natural capital cannot also grow). Use theproduction function: Q = AK L N , where N is natural capital. DoubleK and L and show that Q less than doubles, assuming α=β=γ=1/3.
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 CamScanner
Some resource-rich countries have succeeded in converting resource wealth into longterm and equitable economic development, while many others have not. Naturalresources have played a fundamental role in the growth of several industrializedeconomies, including Germany and the United Kingdom, where coal and iron ore depositswere a precondition for the Industrial Revolution. The United States was the world’sleading mineral economy from the mid-nineteenth to the mid-twentieth century and in thesame period became the world’s leader in manufacturing (van der Ploeg 2011). Morerecently, countries such as Botswana, Chile, and Norway have used abundant oil andmineral resources as the foundation for economic growth. However, in many othercountries, resource extraction appears to have undermined governance, fed corruptionand capital flight, and increased inequality.Required:(a) Discuss the main challenges posed by resource revenues; and(b) Discuss the special fiscal institutions and mechanisms…
Why Capital does not Flow from Rich to Emerging Countries? We assume that the production function in country i is 1 1 2 Yi = A ² k², (1) where y, and ki are output and capital per capita, respectively, in country i, and A is a measure of technology in country i. (a) Calculate the marginal product of capital (MPK) denoted by Ri in country i. (b) Express the MPK in terms of output per capita, yi, i.e., eliminate ki from Ri by using the production function (1). (c) We consider two countries, indexed by i 1 and i 2, whose production function is described by (1). Both are assumed to have the same level of productivity, i.e., A₁ A2. We assume y2 50y₁. Calculate the ratio R₁/R₂. (d) We keep assuming that y2 50y1, but now we assume that A2 educational attainment is higher in country 2. Calculate the ratio R₁/R₂ under 10A₁ because these assumptions. FX = - (e) We keep assuming y2 50y₁ but now we consider that technology in country 1 is a function of technology of the more advanced country 2,…
Consider the Human Capital Accumulation model with a production function given by Y = AK0.5 H0.5, saving rates sã 0.16 and SH 1. Which of the following is false? 8 - 0.05 and A = = - = 0.09, a common depreciation rate is the long-run intensity of human capital relative to physical capital will fall when SH falls the long run growth rate of physical capital will fall when SH falls the long-run intensity of human capital relative to physical capital is 9/16 the long-run growth rate of physical capital is 0.12
Consider the Solow model (Y-AK1/4L3/4). Suppose that the productivity parameter is A=500, the depreciation rate is d=1/10, the savings (investment) rate is s=0.30, and the labor force is constant and equal to 2 million. ÊÊWhat is the steady state capital stock (K)? Please choose the closest answer." a. b. 48200 million C. 34341 million d. 15930 million 18340 million
YIN CN Next question Suppose that the production function is given by Y- 05VR N 454 where Y is output, Kis capital, and N is the number of workers 4 Suppose that 60 05 With your favonte spreadsheet software, compute steady-state output per worker and steady-state consumption per worker for s 0, 801, a02, s1 Graph the steady-state level of output per worker and the steady-state level of consumption per worker as a function of the saving rate 25 1) Using the multipoint curve drawing tool, drawa curve showing the relationship between YIN and the saving rate. Properly label your curve 15 2) Using the multipoint curve drawing tool, draw a curve showing the relationship between CIN and the saving rate. Properly label your curve 0.5 Although the control ponts for your multpownt curves do not have to be exact try to plot them as accurately as possible 01 02 03 a'4 os o6 07 os 09 Saving rate, At what saving rates are YIN and CIN maximized? After plotting the final point of your multipoint curve…
The “per person” versions of production functions: Write each productionfunction given below in terms of output per person y ; Y/L and capital perperson k ; K/L. Show what these “per person” versions look like in a graphwith k on the horizontal axis and y on the vertical axis. (Assume A is somefxed positive number.)(a) Y = K 1/3L2/3 and Y = K 3/4L1/4 (on the same graph) (b) Y = K(c) Y = K + AL(d) Y = K − AL
In the Saul model, if the per capita production function is y=k^0.7, the savings rate is 0.2, and the depreciation rate(8) is 0.1, then the steady-state level of capital per worker (k') equals O O O A. B. C. D. 4.85 8.05 10.08. 11.12
da qaoudon Suppose that the production function is given by Y=05/K √N, where Y is output, K is capital, and N is the number of workers. The steady-state level of capital per worker in terms of the saving rate, s, and the depreciation rate, 6, is KIN= (Property format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g. a superscript can be created with the character.) The steady-state level of output per worker in terms of the saving rate, s, and the depreciation rate, 6, is VIN= (Property format your expression using the tools in the palette.) The equation for steady-state consumption per worker in terms of the saving rate, s, and the depreciation rate, 6, is CIN=(Property format your expression using the tools in the palette.)
1. Country A and B both have the production functionY = F (K, L) = K ½L ½or Y = K0.5 L0.5 a) What is the per-worker production function, y= f (k)? Please make sure to write specificfunctional form of the per-worker production function. b) Assume that neither country experiences population growth nor technological progressand that 4 percent of capital depreciates each year. Assume further that country A saves 24percent of output each year and country B saves 16 percent of output each year. Using youranswer from part a) and the steady-state condition, find the steady-state level of capital perworker for each country. Then find the steady-state levels of income per worker for eachcountry and steady-state level of consumption per worker for each country.
An increase in the initial stock of knowledge: Suppose we have two economies—let’s call them Earth and Mars—that are identical, except that one begins with astock of ideas that is twice as large as the other: A Earth 0 = 2 × A Mars0 Te two economies are so far apart that they don’t share ideas, and each evolves as a sepa-rate Romer economy. On a single graph (with a ratio scale), plot the behavior of per capita GDP on Earth and Mars over time. What is the efect of starting outwith more knowledge?