**Introduction**

In a perfectly competitive market, the price of a commodity is determined by the interaction of market forces, specifically the supply and demand for the product. In this equilibrium, the price of the commodity will be equal to both the marginal cost and the average cost of production. This relationship is important in understanding how prices are determined in a perfectly competitive market.

**Perfectly Competitive Market**

A perfectly competitive market is characterized by several key features:

1. Large number of buyers and sellers: There are numerous buyers and sellers in the market, none of whom have the ability to influence the market price.

2. Homogeneous product: The products sold in the market are identical or very similar, making it impossible for consumers to differentiate between them.

3. Perfect information: Buyers and sellers have complete information about the market, including prices and product quality.

4. Free entry and exit: Firms can easily enter or exit the market without any barriers.

5. Price takers: Both buyers and sellers in a perfectly competitive market are price takers, meaning they have no control over the market price.

**Marginal Cost and Average Cost**

To understand why the price in a perfectly competitive equilibrium is equal to both marginal cost and average cost of production, we need to define these terms:

1. Marginal Cost (MC): Marginal cost refers to the additional cost incurred from producing one additional unit of output. It can be calculated by taking the change in total cost divided by the change in quantity produced.

2. Average Cost (AC): Average cost refers to the total cost per unit of output produced. It can be calculated by dividing the total cost by the quantity produced.

**Equilibrium Price**

In a perfectly competitive market, firms aim to maximize their profits. They will continue to produce and sell goods as long as the price they receive exceeds their marginal cost. If the price is below the marginal cost, firms would be incurring losses and would eventually exit the market.

At the same time, in the long run, firms in a perfectly competitive market will also aim to cover their average costs. If the price is below the average cost, firms would not be able to cover their costs and would exit the market.

Therefore, in a perfectly competitive equilibrium, the price of the commodity will be equal to both the marginal cost and the average cost of production. This ensures that firms are able to cover their costs and earn a normal profit. If the price were higher than the marginal cost, firms would have an incentive to increase production and earn extra profits. If the price were lower than the average cost, firms would not be able to cover their costs and would exit the market.

**Conclusion**

In a perfectly competitive equilibrium, the price of a commodity is equal to both the marginal cost and the average cost of production. This ensures that firms are able to cover their costs and earn a normal profit. The relationship between price and costs is fundamental in understanding how prices are determined in a perfectly competitive market.

The average revenue (AR)of a firm is defined as total revenue per unit of output. if a firm's output is q and the market price is p, then TR equals p×q. Hence
AR=TR/q=p×q/q=p
The marginal revenue (MR)of a firm is defined as the increase in total revenue for a unit of increase in the firms output. When the firm increases its output by one unit, this extra unit is sold at the market price. Hence MR is precisely the market price
therefore in perfect competition p=AR=MR