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 market, firms are price takers, meaning they have no control over the market price. The equilibrium position occurs where the demand (D) curve intersects with the marginal revenue (MR) curve, and both are equal to the market price (P). Additionally, the average revenue (AR) curve is also equal to the market price.

Let's examine the situation graphically:

1. Draw the demand curve (D) sloping downwards, indicating that as the price decreases, the quantity demanded increases.
2. The demand curve is also the average revenue (AR) curve and the market price (P) curve, as in perfect competition, each firm sells its output at the prevailing market price.
3. Draw the marginal revenue (MR) curve below the demand curve. It is shaped similarly to the demand curve but has twice the slope. This is because in a competitive market, each additional unit sold contributes to both total revenue and marginal revenue.
4. Plot the average cost (AC) curve, representing the typical cost per unit of production as the quantity produced increases. The AC curve initially decreases due to economies of scale, but eventually starts increasing due to diseconomies of scale.

Now let's address your question:

At the equilibrium point, where D=P=MR=AR, you will notice that the equilibrium market price (P) intersects with both the demand curve (D) and the marginal revenue curve (MR). This implies that the price received for each unit sold is exactly equal to the marginal revenue generated from selling that additional unit.

Additionally, at this equilibrium point, the average revenue per unit (AR) is equal to the average cost per unit (AC). This means that for each unit produced and sold, the revenue received is equal to the cost incurred in producing it.

If you calculate the total revenue (TR) by multiplying the equilibrium market price (P) by the quantity sold (Q), and compare it to the total cost (TC) obtained by multiplying the average cost per unit (AC) by the quantity produced (Q), you will find that TR = TC.

However, it is important to note that while there may be no economic profit (TR - TC), firms may still continue to operate in the market. The reason lies in the concept of accounting profit versus economic profit. Accounting profit considers only explicit costs, such as wages, rent, and materials, while economic profit also considers implicit costs, such as the opportunity cost of the resources employed.

In competitive markets, where barriers to entry are low, firms are assumed to earn zero economic profit in the long run. This means that they are covering all their costs, including opportunity costs, but are not generating any additional profit above what they could earn in alternative industries. However, they can still earn a positive accounting profit, which covers their explicit costs and provides a return on their investment.

Therefore, even though producers may not be making economic profit in a perfectly competitive market, they still have an incentive to stay in business as long as they are covering their costs and earning a positive accounting profit.