Do not type in dollar signs or round any of your answers. Suppose a country's production function is Y = K1/2L1/2. If capital depreciates at the rate of 5 percent each year and the population grows at the rate of 1 percent each year, calculate the savings rate that would lead to a steady-state equilibrium value for capital per worker of 100 machines: savings rate = percent In this steady-state equilibrium, output per worker is and consumption per worker is

Do not type in dollar signs or round any of your answers. Suppose a country's production function is Y = K1/2L1/2. If capital depreciates at the rate of 5 percent each year and the population grows at the rate of 1 percent each year, calculate the savings rate that would lead to a steady-state equilibrium value for capital per worker of 100 machines: savings rate = percent In this steady-state equilibrium, output per worker is and consumption per worker is

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The output of an economy is characterized by a Cobb-Douglas production function with constant return to scale and an output elasticity with respect to capital equal to 0.3. Also given are the following parameters: 30% saving rate, 5% depreciation rate, 2% population growth rate, and the technology factor is 2. a). Find the capital-labour ratio, and also the output, consumption and investment on a per capita basis in the steady state equilibrium. b). Is a government policy that raises the saving rate to 40% socially desirable? Explain your answer with reference to a comparison of this new steady state equilibrium and the initial steady state equilibrium in a) above. c). If the initial capital-labour ratio is 30, is the economy operating efficiently in the sense that welfare cannot be improved? Explain concisely. What if the initial capital-labour ratio is 15? Again explain concisely.
Exercise 4: Growth and capital over-accumulation = Suppose two countries, A and B, with the same production function Y KaL¹-a. The value of a 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 a. b) Compute the stock of capital, output and consumption per unit of labor in the steady state 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 became the Golden Rule savings rate.
Assume the economy is initially in its balanced growth state. Suppose policymakers pursue policies that would increase the saving rate to s1=0.3. Draw a carefully-labelled diagram to illustrate the effect of the change in the saving rate on the economy in the long run. Explain the effect of the change in saving rate on steady-state capital per effective worker and steady-state consumption per effective worker?
Consider an economy described by the textbook Solow model with the following Cobb-Douglas production function: Y = ÅK°L*. %3D where a The economy is producing 100 units of output and the productivity parameter is equal to 1. the depreciation rate is 6%, the investment rate is 24%, and there are 64 workers, the growth rate of total output Y, is positive and the economy is converging to to its steady-state output per capita of 100 units. Question 6 total depreciation exceeds gross investment, the economy is below its steady state and outout per person is growing at a positve rate Question 7 Starting from steady state a permanent decrease in the rate of depreciation in the Solow model causes output per capita to Select) in the short nun in the long run the growth rate of the economy Sekect
1. Consider Avataria, which can be described by the Solow model with the population growth. Its production function Y(K,L) = 2K¹2 L¹/2 Its investment rate is 40%, its depreciation rate is 10%, and its population growth rate is 10%. Calculate the capital-labor ratio, output per worker, and consumption per worker in the steady state. Assume that now the population growth slows down to 4%. What happens with the output per worker and consumption per worker in the new steady state? Calculate the exact values. (a) (b)
question 5
Explain why consumption per worker grows at a different rate than in Solow model II (with population growth)
3) Suppose your per capita production function is given as y = k". Capital evolves according to the expression Ak = sy – (n +d)k, and your consumption function is c = (1– s)y. As usual, s is the savings rate, n is the - population growth rate and d is the capital depreciation rate. Imagine a foreign government decides to grant your country an investment subsidy in the form of b, which represents a constant fraction of domestic investment per capita (ia) such that irotal = ia + bia. In per capita terms the expenditure function with the subsidy is y = c + itotal and it is y = c + ia without the subsidy. a) Derive an expression for the steady state capital stock after the subsidy is granted. (Hint: Use the expenditure function with the subsidy to solve for sy then use the expenditure function without the subsidy to solve for domestic investment ia.) b) Use the Solow diagram to show living standards before and after the subsidy is granted. Explain the dynamic process towards the new steady…
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?
Suppose Westeros produces output according to the production function: Y = √K The fraction of output that is saved and invested in new capital is 20%. The depreciation rate is 5%. Use this information to answer the following questions. Macmillan Learning a. What is the steady-state amount of capital (K) in Westeros? b. What is the steady-state amount of output (Y*) in Westeros? c. If Westeros had started out with 25 units of capital, what would the Solow model predict would happen to its output in the long run? O It will decrease, since that is above its steady state level of output of 4 It will decrease, since that is above its steady state level of output of 16 It will increase, since that is below its steady state level of output of 16 It will increase, since that is above its steady state level of output of 41 It will remain at 25, since that is its steady state level of output
In class we argued that if people could accumulate human as well as physical capital, the production function would look like the “AK” production function. • (a) If the production function is AK and the savings rate is constant at rate “s”, and the rates of depreciation and populati on growth are δ and n respectively, what would the growth rate of the economy be? • (b) What would be the macroeconomic consequences of decreasing the savings rate in this economy? • (c) What would be the consequences of an increase in fertility in this economy? • (d) Would the consequences of decreasing fertility be UNAMBIGUOUSLY GOOD? • (e) Can human capital grow without bounds? Explain why or why not (make sure you discuss the physical nature of human capital). • (f) What is the growth rate of the economy (in the absence of technological progress) if human capital cannot grow without bounds?
20) Suppose that the production function is y = k0.25[that is, output per worker is equal to the (1/4th) root of capital per worker], s = 0.36, and lowercase delta (5)[the depreciation rate] = 0.10 and the population growth is 2 percent (n = 0.02). What is (approximately) the per capita steady state %3D consumption in this economy? Select one: а. 5004 b. 1.45 С. 302 d. 0.92