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Consider N firms each with the constant-returns-to-scale production function Y = F (K,AL), or (using the intensive form) Y = ALf (k). Assume f (•) > 0, f (•) < 0.=”” assume=”” that=”” all=”” firms=”” can=”” hire=”” labor=”” at=”” wage=”” wa=”” and=”” rent=”” capital=”” at=”” cost=”” r,=”” and=”” that=”” all=”” firms=”” have=”” the=”” same=”” value=”” of=””> (a) Consider the problem of a firm trying to produce Y units of output at minimum cost. Show that the cost-minimizing level of k is uniquely defined and is independent of Y, and that all firms therefore choose the same value of k. (b) Show that the total output of the N cost-minimizing firms equals the output that a single firm with the same production function has if it uses all the labor and capital used by the N firms.



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