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 0 where B > 0 is a constant. Aggregate output is the sum of the...

Extracted 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.