Economist claims that the equilibrium position of each firm in a perfect 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 asTC.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? your explanation should be supposed with a graph for more detail.

In a perfectly competitive industry, the equilibrium position of each firm is determined by the intersection of the demand (D) curve, the marginal revenue (MR) curve, and the average revenue (AR) curve. At this equilibrium point, the price (P) is equal to the marginal revenue, which is also equal to the average revenue. This is because each firm in a perfectly competitive market is a price-taker, meaning they have no control over the market price and must accept the prevailing price determined by market forces.

To understand why producers would stay in business despite there being no profit, let's visualize this on a graph:

Graph Explanation:
- On the graph, the vertical axis represents price and quantity, while the horizontal axis represents quantity.
- The demand (D) curve slopes downward, indicating that as the price increases, the quantity demanded decreases.
- The marginal revenue (MR) curve is also downward sloping and lies below the demand curve.
- The average revenue (AR) curve is a horizontal line, as it is equal to price at all levels of quantity.
- The average cost (AC) curve shows the average cost per unit produced.

Now, let's analyze what happens at the equilibrium point:

1. Equilibrium Quantity (Q):
At the equilibrium point, the quantity (Q) is determined where the demand curve intersects with the marginal revenue curve. This is the profit-maximizing level of output for firms in a perfectly competitive industry.

2. Equilibrium Price (P):
At the equilibrium quantity (Q), the price (P) is determined where the demand curve intersects with the average revenue curve. This means that each unit sold by the firm fetches a price equal to the average revenue, which is also equal to the marginal revenue.

3. Average Revenue (AR) and Average Cost (AC):
At the equilibrium point, the average revenue per unit (AR) is exactly equal to the average cost per unit (AC). This means that the total revenue (TR), which is AR*Q (the area under the demand curve), is exactly equal to the total cost (TC), which is AC*Q (the area under the average cost curve). Therefore, TR = TC.

4. Zero Profit:
When total revenue (TR) and total cost (TC) are equal, it implies that there is no profit, but also no loss. This situation is known as a normal profit situation. In a perfectly competitive market, firms aim to cover their costs and earn a normal profit. They continue to produce because they can cover their costs of production and remain in business.

In summary, even though there is no economic profit in a perfectly competitive industry, firms can still earn a normal profit by covering their costs. As long as firms can cover their costs and exit barriers are low, they have incentives to stay in business, especially considering that other options may not provide better returns.