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.
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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text: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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