Suppose that a country's production function is Y = K1/2L1/2. If capital depreciates atthe rate of 8 percent, consumption per worker will first[[ Select ]v and then [ Select ]as the rateof savings increases from 0 to 100 percent. For this production function, the GoldenRule savings rate is equal to [ Select ]so the steady-statevalues are:capital per worker =[ Select ]%3Doutput per worker = [Select ]consumption per worker =[ Select ]assuming no population growth or technological change.In the steady state, if the labor force is equal to 640 workers, aggregate output isequal to[ Select ]. As long as the labor force is constant andthere is no technological change, aggregate output I Select ]change once the steady state is reached.>

The production function is, Y = K^(1/2)*L^(1/2) y = k^(1/2) y = f(k) where, y = Y/L = output per…

Answered: ings rate is equal to [ Select ] re: er…

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ings rate is equal to [ Select ] re: er worker = [ Select ] [ Select er worker = [ Select ]

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 1:- Suppose a country has a gross savings rate of 25%, a depreciation rate of 2%, and an incremental capital output ratio (lCOR) of 2.2. Using the Harrod-Domar growth model, a) find the implied rate of growth of total GDP in the country. b) How much would the rate of savings have to increase to raise the growth rate of total GDP to 10%? c) Is your answer consistent with the Harrod-Domar model? Explain.
Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is yt = 2.2kt^0.5, where y is output per worker and k is capital per worker. The depreciation rate of capital is 10% per year a- Households initially consume 80% of income and save the remaining 20% of income. There is no government spending. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker? b-Suppose saving rate decreases to 10% permanently. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker?
Question 3Consider an economy described by the production function:Y = F(K, L) = K0.3 L0.7 a. What is the per-worker production function?b. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.c. Assume that the depreciation rate is 10 percent per year. Make a table showing steadystate capital per worker, output per worker, and consumption per worker for saving ratesof 0 percent, 10 percent, 20 percent, 30 percent, and so on. (You will need a calculator with an exponent key for this.) What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?
7 Assume a Cobb-Douglas production function, where © =0.5 and A = 1. If AN/N = 0.06, d = 0.04, and s = 0.2, what is the steady state value of capital per capita ??
An economy has the per-worker production function yt=f(kt)=4kt)0.4, where yt is the output per worker and kt is the capital-labor ratio. The depreciation rate is 0.15, and the population growth rate is 0.04. Saving is St=0.5Yt, where St is total national saving and Yt is total output. The slope of the per worker production function is given by f' (kt)=1.6kt-0.6 . What is the steady state value of capital-labor ratio, k*? Round your answer to at least 2 decimal places.
Suppose that the economy is summarized by the following: Technology (Production Function): Yt = 10 (Kt)0.3 (Lte)0.7 Consumption function: Ct = 0.8Yt Depreciation rate: 8% (i.e. δ= 0.08) Population growth: 2% (i.e. n = 0.02) Technological growth: 4% (i.e. g = 0.04) 1. Assuming that in 2013 the US economy is in the steady state and L2013 = Le2013 = 8, what is the value of ke2014, ye2014, ce2014 , k2014, y2014, and c2014 ?
Consider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.
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?
3 Assume a closed economy, perfectly elastic labor supply, and linear technology. Suppose the incremental capital-output ratio (ICOR) is 3, the depreciation rate is 3%, and the gross savings rate is 10%. Use the Harrod-Domar growth equation to determine the rate of growth. What would the gross savings rate have to be to achieve 5% growth? Assuming a perfectly elastic labour supply, state one criticism of this model from an exogenous growth theory viewpoint and another criticism of this model from an endogenous growth theory viewpoint.
Suppose that two countries are exactly alike in every respect except that capital depreciates at afaster rate in Country A than in Country B due to harsh climate conditions. In which country willthe Golden Rule level of capital per worker be higher? Illustrate graphically.
Y2 Assume that neither country experiences population growth or technological progress and that 4 percent of capital depreciates each year. Assume further that country A saves 14 percent of output each year and country B saves 26 percent of output each year. Using your answer from part b and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker (?∗)(k∗), income per worker (?∗)(y∗), and consumption per worker (?∗)(c∗) for each country. For Country A and For Country B ?∗k∗ for Country A: ?∗k∗ for Country B: ?∗y∗ for Country A: ?∗y∗ for Country B: ?∗c∗ for Country A: ?∗c∗ for Country B:
Exercise 4: Growth and capital over-accumulationSuppose two countries, A and B, with the same production function Y = KαL1−α. Thevalue of α is 0.30, the growth rate of population is 2% and the depreciation rate is 5%.a) Show that with price-taking firms the share of labor must be 1 − α.b) Compute the stock of capital, output and consumption per unit of labor in the steadystate if the savings rates were 25% for country A and 35% for country B.c) Compare both economies to the Golden Rule.d) Explain what would happen to both countries if suddenly their savings rate becamethe Golden Rule savings rate.