Economist claims that the equilibrium position of each firm in a perfectly competitive

industry the equilibrium can be at the point where D=P=MR=AR. At that point, you can
notice that the equilibrium market price, average revenue per unit is exactly equal to the
average cost per unit.
This means that AR*Q is exactly equal to AC*Q which means that TR is the same as TC.
Since cost and revenue are the same, this means that there is no profit. so why would any
producer stay in business if there is no profit to be gained from doing so?
NB: Your explanations should be supposed with a graph for more detail.

In a perfectly competitive industry, the equilibrium position of each firm occurs where demand (D), price (P), marginal revenue (MR), and average revenue (AR) are all equal. This equilibrium is typically represented by the intersection of the demand curve and the marginal cost curve.

When the equilibrium condition is met, the market price (P) is equal to both the demand (D) and the marginal revenue (MR) that the firm receives for each unit sold. It is also equal to the average revenue (AR) since AR is calculated by dividing total revenue (TR) by the quantity (Q) of units sold.

Since price (P) equals average revenue (AR), we can say that P * Q (price multiplied by quantity) is equal to AR * Q. Similarly, average cost (AC) multiplied by quantity (Q) is denoted as AC * Q, which represents the total cost (TC) incurred.

The important point here is that when AR * Q is equal to AC * Q, it means that total revenue (TR) is the same as total cost (TC). In other words, the revenue covers all the costs incurred in the production process.

When a firm has zero profit, it means that its total revenue just covers all its costs without any surplus remaining. In this case, the firm is said to be earning a "normal profit" or "breaking even." It doesn't make any additional profit but is able to cover its costs.

Even though there is no extra profit to be gained from being in a perfectly competitive market, producers may still stay in business for several reasons:

1. Economic Efficiency: Being in a perfectly competitive market allows firms to produce at the lowest possible cost. This efficiency can be achieved through cost-saving techniques, innovation, or economies of scale. By staying in business, firms can maintain their efficiency levels and potentially attract customers by offering competitive prices.

2. Non-Monetary Benefits: Some individuals or companies may have non-monetary objectives for being in business, such as personal satisfaction, fulfilling a passion, gaining market presence, or contributing to the community.

3. Long-Term Profit Potential: Even though there is no profit in the short run, firms may anticipate making profits in the long run. They may invest in research and development, marketing, or other strategies to differentiate themselves from competitors and capture more market share, which could lead to profitability in the future.

While the absence of immediate profit may discourage some producers, perfectly competitive markets offer opportunities for firms to thrive by maximizing efficiency, pursuing non-monetary goals, and investing in long-term success.