In slide 22, I believe "x" denotes an input, whereas "y" denotes outputs. Therefore, we're interested in minimizing the cost given a certain price and a certain amount of fixed output, thus, we're interested in c(w, y). Inputs, however, may vary according to V(y), the set of requirements of inputs that could be used to produce an output of y. Thus, the quantities of all the x-es, unlike y, are not fixed amounts. In short, c(w, y) would pertain to the minimum of the sum of w1x1 + w2x2 + ... + wnxn, such that it satisfies V(y), a set of inputs required to produce y.
Does anyone know why the cost function is c(w, y) but not c(w, x)?
In slide 22, I believe "x" denotes an input, whereas "y" denotes outputs. Therefore, we're interested in minimizing the cost given a certain price and a certain amount of fixed output, thus, we're interested in c(w, y).
Inputs, however, may vary according to V(y), the set of requirements of inputs that could be used to produce an output of y. Thus, the quantities of all the x-es, unlike y, are not fixed amounts.
In short, c(w, y) would pertain to the minimum of the sum of w1x1 + w2x2 + ... + wnxn, such that it satisfies V(y), a set of inputs required to produce y.
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