Definition: The cost function is a function of input prices and output quantity. Its value is the cost of making that output given those input prices.
A common form:
c(w1, w2, y) is the cost of making output quantity y using inputs that cost w1 and w2 per unit.
A common form:
c(w1, w2, y) is the cost of making output quantity y using inputs that cost w1 and w2 per unit.
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