If the production function of a competitive firm is homogeneous of degree one, then the cost function

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If the production function of a competitive firm is homogeneous of degree one, then the cost function c(w,y). is homogeneous of degree one in y, that is,
c(w, y) = yc(w, 1)
where c(w, 1). is the cost of producing one unit (unit cost).
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