Help (a)Consider the following data on the fictional countries of Sylvania and Freedonia.The production function is y = Akah¹-a, where a = 0.5.Sylvania FreedoniaOutput per Worker, y100200Physical Capital per Worker, k100100Human Capital per Worker, h2564(b) Calculate the level of productivity, A, in each country.(c)(d)Calculate the countries' relative levels of output if all differences in output were theresult of productivity.Calculate the countries' relative levels of output if all differences in output were theresult of factor accumulation.

a) To calculate the level of productivity, A, in each country, we can use the production function…

Answered: (a) Consider the following data on the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider an economy that exhibits both population growth (L grows at rate n) and technological progress (A grows at rate a) described by the production function, Y = F(K,AL) = Kª(AL)¹-α| Here K is capital and Y is output. (a) Show that this production function exhibits constant returns to scale. What is the per-effective-worker production function? (c) Find expressions for the steady-state capital-output ratio, capital stock per effective worker, and output per effective worker, as a function of the saving rate (s), the depreciation rate (8), the population growth rate (n), the rate of technological progress (a), and the coefficient a. (You may assume the condition that capital per effective worker evolves according to Ak = sf (k) − (a +n+8)k.) (d) Show that at the Golden Rule steady state the saving rate for this economy is equal to the parameter a.
1. Over a period of 10,000 years, the population of Brobdingnag is estimated to have increased from 4 million to 170 million. Assuming that the level of income per worker was constant, there are only two factors of production, Land (X) and Labour (L), and the exponent on land in the production function is one-third, what was the annual growth rate of productivity, A? a) 0.17% b) 0.42% c) 0.03% d) 0.01%
Assume the following production function for maize: Q=3K^1.2 L^0.5, where Q is the number of bags of maize produced, K is the units of capital used and L the units of the labour employed. (a) Derive the MRTS of K and L. (b) Estimate the factor intensity of the production function and interpret results. (c) Is the above production function characterized by decreasing returns of scale? Explain
Assume the rate of technological progress is constant in a SSGM with Cobb- Douglas production function. Show that a steady-state cannot be identifiede if the technological progress is capital augmented, i.e. F(K, L) = [A(t)K(t)]*L(t)'_ª, where A(t) is the efficiency term growinge with a constant rate g.t
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…
Some less-developed nations are unable to devote resources to various research and development projects. Attempting to increase their economic growth, sometimes they acquire pharmaceutical or technological goods and reverse engineer them to determine how they’re made, then sell them in domestic markets. Is it ethical and/or necessary to produce and sell a product without having developed it and not having a patent for the product? What could be the short run and long run consequences of such an action?
1. Country A has a capital-labor ratio that is initially twice as big as that of country B, but neither is yet in a steady state. Both countries have the same production function: f(k) = 6k^1/2 Country A has a 10% saving rate, 10% population growth rate, and 5% depreciation rate, while country B has a 20% saving rate, 10% population growth rate, and 20% depreciation rate. a. Calculate the steady-state capital-labor ratio for each country. Does the initial capital-labor ratio affect your results? b. Calculate output per worker and consumption per worker for each country. Which country has the highest output per worker? The highest consumption per worker?
For a production function q= f(K, L) = K^1/3 L^1/3 and factor prices w=8 and r=1, answer the following questions: (a) Explain what returns to scale mean and its implication for the cost function. What returns to scale does this production function exhibit? (b) optimal mix and equation of the expansion path. What does it show? (c) Minimized cost function for the technology. (d) Why are the short-run cost curves different from the long-run cost curves? Your answer must include the terms expansion path and optimal input mix.
(a) Assuming that the production function is of the form y = Ak1/3, where y and k denote GDP and capital per capita, fill in the missing entries of the table. (b) Comment on the results that you find.
Please no written by hand and graph Consider a small world that consists of two different countries, a developed and a developing country. In both countries, assume that the production function takes the following form: Y = F (K, LE) = K¹/4 (LE) 3/4, where Y is output, K is capital stock, L is total employment and E is labour augmenting technology. (a) Does this production function exhibit constant returns to scale in K and L? Explain. (b) Express the above production function in its intensive form (i.e., output per-effective worker y as a function of capital per effective worker k). (c) Solve for the steady-state value of y as a function of saving rate s, population growth rate n, technological progress g, and capital depreciation rate 6. (d) The developed country has a savings rate of 30% and a population growth rate of 2% per year. Meanwhile, the developing country has a savings rate of 15% and population growth rate of 5% a year. Technology evolves at the rate of 8% and 2% in…
In our one country model of technology growth, y = A(1- γA). Suppose that the country temporarily raises its level of γA. (a) Draw two graphs, one for y and one for A, showing how the time paths of output per worker (y) and productivity (A) will compare under this scenario with what would have happened if there had been no change in γA Please do fast ASAP fast
The aggregate production function is Y = 3KL. If there are 20 units of capital and 50 units of labor, what is capital productivity? Group of answer choices 300 1000 600 150

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