− − ⩾ In other words, the sign of the change in the maximizing x is the same as the sign of the change in p. If replaces in (1), then the sign of the change in x is the opposite of the sign of the change in ⩽ ⩾ p. For minimization rather than maximization the sign of the efect is reversed. Proof : By definition of maximization, we have

q = 196 = 49. profit-maximizing level of production i 1 If mπ = mr – mc = 0, then mr = mc. This is known as the first-order condition for a profit maximum. Second, find the firm’s profit-maximizing price p by substituting q* = 49 into the inverse demand function (Equation 4): = 200 49 = 200 − 98

All firms are maximizing profits. No firm has incentive to enter or exit, because all firms are earning zero economic profit. Note that economic profits include opportunity costs Thus, zero economic profit includes the value of your next best option -- what would you be earning if you weren't in your current business? Price is such that QS = QD.

In this module we ask the question: what quantity of output would maximize the producer’s profit? First we will find the profit-maximizing quantity by calculating the total profit at each quantity for comparison.

The profit-maximizing output is found by setting marginal revenue equal to marginal cost. Given a linear demand curve in inverse form, P = 100 - 0.01Q, we know that the marginal revenue curve will have twice the slope of the demand curve.