Assume an economy in which there are i = 1,2, .., M identical firms, each withthe following production function:Yt = A K“ L;1-a, 0< a <1Notice that A is the same for all firms and are given for the whole economy as afunction of the aggregate capital/labor ratio:(KYA = B (),Y > 0where B > 0 is a constant. Aggregate output is the sum of the outputs of each ofthe firms so that:Mdi=1in terms of the capital per worker k; and A.(a) Obtain the per capita production function for each firm.b) Argue why all firms would choose the same capital/labor (k) and find theaggregate per capita production function of the economy.

(a) The way per capita income is calculated by dividing the total income from the population of the…

Answered: a) Obtain the per capita production…

a) Obtain the per capita production function for each firm. b) Argue why all firms would choose the same capital/labor (k) and find th aggregate per capita production function of the economy.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Assume an economy in which there are i = 1,2, .., M identical firms, each with
the following production function:
Yt = A K“ L;1-a, 0< a <1
Notice that A is the same for all firms and are given for the whole economy as a
function of the aggregate capital/labor ratio:
(KY
A = B (),
Y > 0
where B > 0 is a constant. Aggregate output is the sum of the outputs of each of
the firms so that:
M
di=1
in terms of the capital per worker k; and A.
(a) Obtain the per capita production function for each firm.
b) Argue why all firms would choose the same capital/labor (k) and find the
aggregate per capita production function of the economy.

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