Where the firm produces just a single output, it is common to distinguish output from inputs. To do this, we reserve p for the price of the output, and let the vector or list w = (w1; w2; . . . ; wn) denote the prices of the inputs. Using this convention, define the profit function for a profit maximizing competitive firm producing a single output.
The following exercise shows the importance of allowing the value function to take infinite values.