10. Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for conve- nience, and that there is labor-augmenting tech- nological progress, with a production function Y = F(K, bN), where b denotes the number of units of "human capital" per worker, and bN is “efficiency units" of labor. Letting b' denote future human capital per worker, assume that b' = (1+f)b, where f is the growth rate in human capital. (a) Show that the long-run equilibrium has the K property that k** what rate does aggregate output, aggregate consumption, aggregate investment, and per capita income grow in this steady state? Explain. is a constant. At bN

10. Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for conve- nience, and that there is labor-augmenting tech- nological progress, with a production function Y = F(K, bN), where b denotes the number of units of "human capital" per worker, and bN is “efficiency units" of labor. Letting b' denote future human capital per worker, assume that b' = (1+f)b, where f is the growth rate in human capital. (a) Show that the long-run equilibrium has the K property that k** what rate does aggregate output, aggregate consumption, aggregate investment, and per capita income grow in this steady state? Explain. is a constant. At bN

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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In the Solow growth model:1. Write the expression for consumption per capita in the steady-state equilibrium, asa function of capital per capita.2. What is the golden rule quantity of capital per capita ? Specifically, tell me thedefinition of this concept, and then relate it to the equation for the equilibriumconsumption per capita whose expression answers question (1) above.23. How do we find the golden rule savings rate, once we know the golden rule quantityof capital per capita?
4. Suppose that we have a standard Solow model with a Cobb-Douglas production function. The central equation of the model is as follows:kt+1 = sAkαt + (1 − δ)kt.Consumption per worker is given by:ct = (1 − s)Akαt.(a) Solve for an expression for the steady state capital stock per worker. Indoing so, assume that the level of productivity is fixed at some value A.(b) Use your answer on the previous part to solve for an expression forsteady state consumption per worker.(c) Use calculus to derive an expression for the s which maximizes steadystate consumption per worker.
Assume that Economyland’s production function is Y = F (K, L) = K 0.5 L 0.5Where Y is output level, K is the amount of capital input, and L is the amount of laborinput. a) What is the per-worker production function, y= f (k) for Economyland? b) Assume that 10 percent of capital depreciates each year and savings rate is 20 percent,find the steady-state level of capital per worker for Economyland. Then find the steady-state levelof income per worker and steady-state level of consumption per worker. c) Is it possible to save too much? Why?
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.
2. Solow-Swan Model (a) You will demonstrate the importance of diminishing returns to capital in the Solow-Swanmodel. Draw a Solow-Swan diagram in which there are constant returns to capital. Thiswould happen if the production function were Yt= AKt, where A = 1. Furthermore,assume that the sum of population growth and the depreciation rate is greater than thesaving rate. Does the economy converge to a steady state in this case? To answer thisquestion, you should draw a Solow-Swan diagram in terms of output per person, as we didin class. Use this diagram to explain why the economy converges to a steady state or doesnot. (b) Assume, instead, that the sum of population growth and the depreciation rate is equal tothe saving rate. In this case, are there any steady states? If yes, describe the steady-statelevels of capital per person. If no, explain why not. (Note: Diagram is not needed for thispart.)
Consider the Solow Model with no population or technological growth. Suppose that two countriesare identical except that in Country A the depreciation rate is greater than the depreciation rate inCountry B.a. How do you compare the steady state level of capital per worker in these countries? Illustrategraphically. Explain the economic intuition for the di erences in capital per worker in steadystate.b. Which country a higher output per worker in steady state? What about investment per workerin steady state? Explain carefully.
4 Explain the central paradox at the heart of the Solow model, with constant and exogenous technologies. Given this paradox, why is the Solow model still relevant?
which statement \s are true. use graphs to exlain a. In the Solow growth model, the saving rate is a crucial determinant of the economy's long-run growth rate of output per worker. b. In the endogenous growth model , the representative firm sets the wage so that the demand and supply of efficiency units of labour are equal. c. In the endogenous growth model , there is no steady state of the economy as human capital will always continue to grow forever. d. The assumption of Constant Returns to Scale technology implies that the marginal product of factor imput is always decreasing.
Consider the Solow growth model in which we allow for long-run techno- logical progress. Assume N′ = (1 + n)N where N is the population (labor force) in the current period, N′ is the population (labor force) in the future period, and n is the pop- ulation growth rate. Assume that z = 1 for simplicity, and there is labour-augmenting technological progress. The production technology is given by Y = F(k,bN) where Y is the output of the consumption good, K is the current period capital stock, b denotes the number of units of “human capital” per worker, and bN is the “efficiency units” of labour. Assume that b′ = (1 + β)b where β > 0 is the growth rate in human capital. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. The production function F exhibits constant returns to scale. (a) Define a variable k as the quantity of capital per efficieny units of labor (as opposed to quantity of capital per labour). Using equilibrium conditions derive the…
Consider the Solow growth model with concave production function as studied in class. Supposethe economy is initially in the picture below, and currently has the level of capital stock of K0. What wouldhappen to the dynamics of capital accumulations when depreciation rate increases? Graphically denote thedirection and the speed of change/accumulation/decumulation of the capital stock, then verbally explain whythey move like so.
B. The rate of technological progress rises. 2. Describe how, if at all, each of the following developments affects the break-even and actual investment lines in our basic diagram for the Solow model: a. The rate of population growth falls. B. The rate of technological progress rises. C. The production function is Cobb-Douglas, F(K,AL) = K" (AL)1-" , and capital"s share, ", rises. D. Workers exert more effort, so that output per unit of effective labor for a given value of capital per unit of effective labor is higher than before.
Consider a one time change in immigration policy that immediately and permanently increases the level of the labour force in an economy. Suppose it rises permanently from L to L 0 . Assuming 2 the economy starts in its initial steady state, use the Solow model to explain what happens to the economy over time (transition dynamics) and in the long run (steady state). In particular, discuss what happens to the levels of capital, capital per worker, GDP and GDP per worker both at the new steady state as well as during the transition to the new steady state. You are not required to discuss how growth rates change over time (this is tricky). To answer this question use both the Solow diagram with total output, and diagrams with time on the horizontal axis and each of these variables on the vertical axis. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.