(This is problem 7, page 239 of the textbook.) An economy has a per-capita production function y = Akªh¹-ª, where A and a are fixed parameters, y is per- worker output, k is the capital-labor ratio, and h is human capital per worker, a measure of the skills and training of the average worker. The production function implies that, for a given capital-labor ratio, increases in average human capital raise output per worker. The economy's saving rate is s, and all saving is used to create physical capital, which depreciates at rate d. Workers acquire skills on the job by working with capital; the more capital with which they have to work, the more skills they acquire. We capture this idea by assuming that human capital per worker is always proportional to the amount of physical capital per worker, or h = Bk, where B is a fixed parameter.

(This is problem 7, page 239 of the textbook.) An economy has a per-capita production function y = Akªh¹-ª, where A and a are fixed parameters, y is per- worker output, k is the capital-labor ratio, and h is human capital per worker, a measure of the skills and training of the average worker. The production function implies that, for a given capital-labor ratio, increases in average human capital raise output per worker. The economy's saving rate is s, and all saving is used to create physical capital, which depreciates at rate d. Workers acquire skills on the job by working with capital; the more capital with which they have to work, the more skills they acquire. We capture this idea by assuming that human capital per worker is always proportional to the amount of physical capital per worker, or h = Bk, where B is a fixed parameter.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose an economy uses only two inputs in production: capital and labour. The following table describes a production function, where y stands for output per worker and k is capital per worker.Suppose there are two countries, A and B. The economies of the two countries can be described by this production function. If Country A has initially a capital–labour ratio k = 0.167 and Country B has k = 0.412, show that an equal increase in capital produces more extra output in country A than in Country B. Explain with words (computations) + graph y k 0.000 0.000 0.173 0.030 0.302 0.091 0.408 0.167 0.480 0.231 0.535 0.286 0.577 0.333 0.612 0.375 0.642 0.412 0.667 0.444 0.688 0.474 0.707 0.500 0.724 0.524 0.739 0.545
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