Short Run Equilibrium:
In a perfectly competitive market, a firm's short run equilibrium is determined by the interaction of demand and supply. In the short run, a firm is unable to change its fixed inputs, such as capital and plant size, but it can adjust its variable inputs, such as labor and raw materials.

Profit Maximization:
In the short run, a firm aims to maximize its profits. It does so by producing a level of output where marginal cost (MC) equals marginal revenue (MR). This is because in a perfectly competitive market, a firm is a price taker and faces a horizontal demand curve, which means that its marginal revenue is equal to the market price.

Price Determination:
The market price is determined by the intersection of the market demand and supply curves. Each firm in the market takes this price as given and adjusts its output accordingly. If the market price is above the average variable cost (AVC), the firm continues to produce in the short run. If the market price is below the AVC, the firm shuts down and incurs a loss equal to its fixed costs.

Short Run Equilibrium:
In the short run, a firm's equilibrium is determined by the point where the firm's marginal cost curve intersects the market price. At this equilibrium point, the firm is producing the level of output where it maximizes its profits. If the market price is below the average total cost (ATC), the firm incurs losses, but it continues to produce in the short run as long as the price is above the AVC.

Differences from Long Run Equilibrium:
In the long run, all inputs become variable, including fixed inputs. This means that a firm can adjust its plant size and capital to optimize its production process. In the long run, firms can enter or exit the market, causing changes in market supply and prices.

Entry and Exit:
If firms in the industry are making profits in the short run, new firms are attracted to the market, increasing the market supply. This causes the market price to decrease, reducing profits for existing firms. Conversely, if firms are incurring losses, some firms may exit the market, reducing the market supply. This causes the market price to increase, improving profits for the remaining firms.

Long Run Equilibrium:
In the long run, a firm's equilibrium is reached when it is producing at the minimum point on its average cost curve (AC). This implies that the firm is producing at the most efficient scale and is earning normal profits. Normal profits are the minimum level of profit required to keep the firm in the industry. At this equilibrium, all firms are earning zero economic profit, and there is no incentive for firms to enter or exit the market.

Conclusion:
In summary, in a perfectly competitive market, a firm's short run equilibrium is determined by the interaction of demand and supply. The firm aims to maximize its profits by producing at the point where marginal cost equals marginal revenue. In the long run, all inputs become variable, and firms can enter or exit the market. Long run equilibrium is reached when firms are producing at the minimum point on their average cost curve, earning normal profits.