(Production function) A technological breakthrough raises a country’s A ̄ by 10%, but capital and laborare all unchanged. Assuming the country’s production function is given by Y = A ̄K1/2L1/2.(a) Figure out what impact this breakthrough will have on the MPK and MPL in that country.(b) Draw a picture Y of against K holding L fixed. 1(c) Redraw the picture with A ̄ increased to 1.1A ̄ but L fixed at same level as before. (Production function) For the production function Y = K1/3L2/3(a) find the function for output per capita(b) What is the growth rate of per capita for this function in terms of the growth rate of K, gK, andthe growth rate of L, n.

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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(Production function) A technological breakthrough raises a country’s A ̄ by 10%, but capital and labor

are all unchanged. Assuming the country’s production function is given by Y = A ̄K1/2L1/2.
(a) Figure out what impact this breakthrough will have on the MPK and MPL in that country.

(b) Draw a picture Y of against K holding L fixed. 1

(Production function) For the production function Y = K1/3L2/3

(a) find the function for output per capita
(b) What is the growth rate of per capita for this function in terms of the growth rate of K, gK, and

the growth rate of L, n.

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