Assume an economy in which there are i = 1,2, ..., M identical firms, each with the following production function: Yt = AK LF-a, 0 0 is a constant. Aggregate output is the sum of the outputs of each of the firms so that: M Yi i=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