The long run equilibrium price of a perfectly competitive firm is always equal to the long-run average cost (LAC) of production. This is because in perfect competition, there are no barriers to entry or exit, and firms can freely enter or exit the market in the long run.

In a perfectly competitive market, there are many firms producing identical products. Each firm is a price taker, meaning it has no control over the market price and can only adjust its output level to maximize profits.

To understand why the long run equilibrium price is equal to the LAC, we can look at the behavior of firms in the market:

1. Perfectly elastic demand: In perfect competition, the demand for an individual firm's product is perfectly elastic. This means that the firm can sell as much output as it wants at the market price without affecting the price itself. Therefore, the firm's marginal revenue (MR) is equal to the market price.

2. Profit maximization: In the long run, firms aim to maximize their profits. They do so by producing at the level of output where marginal cost (MC) equals marginal revenue (MR). This is because if MC is less than MR, the firm can increase its profits by producing more, and if MC is greater than MR, the firm can increase its profits by producing less.

3. Minimum efficient scale: In the long run, firms also aim to operate at their minimum efficient scale (MES), where they achieve the lowest average cost of production. This occurs at the point where the firm's average total cost (ATC) is at its lowest.

4. Long-run equilibrium: In the long run, firms will enter or exit the market depending on their profitability. If firms are making positive economic profits, new firms will enter the market, increasing supply and reducing the price. If firms are making losses, some firms will exit the market, reducing supply and increasing the price. This process continues until firms in the market are making zero economic profits.

Therefore, in the long run equilibrium, the price is equal to the minimum average cost of production (LAC). This is because firms cannot sustain positive economic profits in the long run. If the price were above the LAC, firms would be making economic profits, attracting new firms to enter the market and increasing supply, which would eventually push the price down to the LAC. Conversely, if the price were below the LAC, firms would be making losses, causing some firms to exit the market and reducing supply, which would eventually push the price up to the LAC.

In summary, the long run equilibrium price of a perfectly competitive firm is always equal to the long-run average cost (LAC) of production because firms aim to operate at their minimum efficient scale and cannot sustain positive economic profits in the long run.