5. The golden rule of saving. Assume that production function is Y = √KL. Depreciation rate in this economy is 10%. What is the steady-state level of capital per worker, output per worker and consumption per worker at different level of saving rates? Solve this exercise by either filling the table below (question a) or solving the steady-state equation (question b). (a) Fill the table below and interpret your findings. saving rate capital per worker output per worker consumption per worker

5. The golden rule of saving. Assume that production function is Y = √KL. Depreciation rate in this economy is 10%. What is the steady-state level of capital per worker, output per worker and consumption per worker at different level of saving rates? Solve this exercise by either filling the table below (question a) or solving the steady-state equation (question b). (a) Fill the table below and interpret your findings. saving rate capital per worker output per worker consumption per worker

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.)
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.
Consider the Production Function: Y=√K√N a) Derive the steady-state levels of output per worker and capital per worker in terms of the saving rate (s) and the depreciation rate.b) Derive the equation for steady-state output per worker and steady-state consumption per worker in terms of the saving rate (s) and the depreciation rate.c) Suppose depreciation is 5% and savings rate is 10%. Calculate the steady-state output per worker.d) Now suppose the savings rate increases to 20%. What is the new steady-state output per worker?
1. Suppose an economy experiences both positive population growth (8 ) and technological progress (84 ). The capital depreciation rate is d . The saving rate is exogenously given as s. (a) 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. (b) We further assume that the aggregate production function is given by Y= K“(AN)™, where o
2. If the production function is given by YFA(KL.)0.5 where Y is the output, A is the technology, L refers to the labor stock, and K is the capital stock. Suppose that the saving rate (s) equals 0.6 and the depreciation rate (d) is 0.3 a. Write the output and capital accumulation equations in terms of the capital per worker? b. Find the steady state capital, output, investment, and consumption? c. What would happen to the steady state capital if the saving rate increased to 0.8 and the depreciation rate increases to 0.4?
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.
4. If the production function is given by Y=K2L'3 and the saving rate saving rate (s) equals the depreciation rate (8). Find the numerical values of the steady state capital and output?
Problem 2 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 population growth are 8 and n respectively, what would the growth rate of the economy be? (b) What would be the macroeconomic consequences of increasing the savings rate in this economy? Explain using the model and intuitively. (c) What would be the consequences of an increase in fertility in this economy? Are these consequences good or bad? Is this answer unambiguous? (d) How are human and physical capital different from one another in the way they evolve from period to period? (e) Does human capital have an upper limit? If it does, what is the resulting production function when this is reached and the growth rate of the economy? If it doesn't have a limit, what is the resulting growth rate of output as it…
1 1 1. Assume that a country's production function is Y = K2L2. Assume there is no population growth or technological change = f(k)? b. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to What is the per-worker production function y а. make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital-labor ratio.) (Ctrl) -
1 1 1. Assume that a country's production function is Y = K2L2. Assume there is no population growth or technological change What is labor productivity computed from the per-worker production function? Is this value the same as labor productivity computed from the original production function а. b. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital-labor ratio.)
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…
1. Consider an economy where the production function is Y = K0.5 (LE)0.5 The depreciation rate is = 0.04, the savings rate is s = 0.2, the popula- tion growth rate is n = 0.03 and technology growth rate is g = 0.03. (a) What is the 'per effective worker' production function? (b) Find the steady state levels of capital per effective worker (k*), in- come per effective worker (y*), investment per effective worker (¿*) and consumption per effective worker (c"). (c) Find the golden rule levels of capital per effective worker (kg), income per effective worker (y), investment per effective worker (it) and consumption per effective worker (c2). Also find sg, that is the level of the savings rate that would lead the economy to the golden rule steady state. (d) Suppose the government pursues policies that change the savings rate from s = 0.2 to sg. What is the immediate effect on income per effective worker and consumption per effective worker? What is the long run effect on income per…