Final answer:
Graphically, long-run profits for a firm in a perfectly competitive market are represented where price equals average cost at the lowest point of the curve, indicating zero economic profits. This point of long-run equilibrium is reached as new firm entry and existing firm exits eventually balance out, leaving no incentive for movement in or out of the market.
Step-by-step explanation:
To show graphically the long run profits for a firm in a perfectly competitive market, we need to consider a scenario where the market reaches a long-run equilibrium. In this equilibrium, firms earn zero economic profits, as the price (P) they receive for their product equals average cost (AC) and also equals marginal cost (MC) at the output level where P = MR = MC. There is no incentive for firms to enter or leave the market.
In the short run, if product demand increases, causing the market price to rise, firms will increase production until P = MR = MC. However, in the long run, the entry of new firms due to positive economic profits, or exit of firms facing losses, will drive the market back to a point where economic profits are zero. The average cost curve intersects the market price at the lowest point on the curve, indicating no economic profit or loss for the firm, establishing long-run equilibrium.
Ultimately, perfectly competitive markets attain long-run equilibrium when there is no further incentive for new firms to enter or existing firms to exit, as all firms are earning a zero profit.