Suppose еcohomy eхperiene positive population growth (8» ) and technological progress (8a ). The capital depreciation rate is . The saving rate is exogenously given as s. » Draw a diagram with variables in per effective worker terms to show how a steady state level of capital per effective worker (K/AN) is determined. Also explain your answers in words. We further assume that the aggregate production function is given by Y-K"(AN)*“ , where 0

Suppose еcohomy eхperiene positive population growth (8» ) and technological progress (8a ). The capital depreciation rate is . The saving rate is exogenously given as s. » Draw a diagram with variables in per effective worker terms to show how a steady state level of capital per effective worker (K/AN) is determined. Also explain your answers in words. We further assume that the aggregate production function is given by Y-K"(AN)*“ , where 0

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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…
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.)
Assume that a E (0, 1). Draw a diagram that describes the evolution of kt, and show that there exists a unique steady state, k* > 0. Label properly. Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. , Now, assume that α = 1. Draw a diagram that describes the evolution of kt, and show that income per worker can grow indefinitely in this case. Label properly.
J 7 Given a production function Yt = AKt1 /3L2 /3 , if K0=8, A = 2, L = 4, s = 0.2, and d = 0.05: (a) Calculate the steady-state level of capital and output. (b) Calculate K1 , I 1 , Y1 and C1 .
4. Assume an endogenous growth model with a production function that in per capita terms can be written as y = 0.8k. If the savings rate is s = 0.3, the rate of growth of population is n = 0.03, and the rate of depreciation is d = 0.1, how high is the rate of growth of output per capita? A. 14% B. 17% C. 13% D. 11% E. There is not enough information to calculate it.
6. Using the Solow Model, determine graphically, the steady state for capital and output when there is an: (a) a permanent decrease in the savings rate (b) a permanent decrease in A (c) a permanent increase in the depreciation rate.
a.Assume that α(0, 1). Draw a diagram that describes the evolution of kt, and show that there exists a unique steady state, k* > 0. Label properly. also Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. , b.Now, assume that α = 1. Draw a diagram that describes the evolution of kt, and show that income per worker can grow indefinitely in this case. Label properly. c.Discuss the key difference(s) between the scenario in a and b as much as you want.
estion 30 A country with neither population growth nor technological progress is nitaly in the golden-rule steady state. Carefuly ilustrate this situation using a graph with output per worker, investment per worker, and depreciation per worker on the vertical axis and capital per worker on the horizontal axis. Now suppose climate change increases the depreciation rate. If the country adjusts its saving rate to reach the new golden- rule steady state, is it possible to determine how output per worker and consumption per worker in the new steady state compare to their levels in the initial steady state? Explain.
Let the production function be Q = K0.®L0.2 Solow's assumptions are K = sQ – 6K The symbols s represents a (constant) marginal propensity to save, n, a (constant) rate of growth of labor and 8 constant depreciation rate. (a) Derive the fundamental equation of Solow growth model for given production function. (b) Sketch graph of with k on the vertical axis and k on the horizontal take n = 0.01, s = 0.3, 8 = 0.1.
Assume that a country's per-worker production is y = k1/2, where y is output per worker and kis capital per worker. Assume also that 10 percent of capital depreciates per year (= 0.10) 2 andthere is no population growth or technological change.a. If the saving rate (s) is 0.4, what are capital per worker, production per worker, andconsumption per worker in the steady state?b. Solve for steady-state capital per worker, production per worker, and consumption perworker with s = 0.6.c. Solve for steady-state capital per worker, production per worker, and consumption perworker with s = 0.8.d. Is it possible to save too much? Why?
5. Consider the Solow growth model. The production function is: Y = Kª(AN)!-«, the is the capital depreciation rate is & per year, the population and technology savıng rate grow at annual rates of n and g respectively. Calculate K/N, K/(AN), Y /N and Y/(AN) in the steady state. Does the change in s affect the growth rate? Explain. S, 6. Suppose that the model of the economy is given by Y = C +I+G + X 99 sunny hp 10 f8 144 14 is & 6. 7. 8. 24
Solow-Swan Model Assume an economy with a production function that exhibits constant returns to capital.1 Ineach of the following cases, draw a Solow-Swan diagram and use is to explain whether andhow the economy converges to a steady state. Clearly identify any steady state(s) or otherwiseexplain why there is no steady state. (i) Assume the sum of population growth and the depreciation rate is greater than the savingrate.(ii) Instead assume the sum of population growth and the depreciation rate is less than thesaving rate.(iii) Instead assume that the sum of population growth and the depreciation rate is equal tothe saving rate. What is the importance of diminishing returns to capital in the Solow-Swan model?