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No, a perfectly competitive firm cannot price discriminate because it lacks market power.

To better understand this question, let's first define each concept.

What is a perfect competition?

Perfect Competition is a market where they are many buyers and sellers who have perfect knowledge of the prevailing market condition and the price being charged.

In general, a perfect competitive market has the following characteristics: buyers and sellers have perfect information of the prevailing market conditions, there is no market power among firms, the demand curve for individual firms is perfectly elastic, and the goods supplied are homogeneous

What is price discrimination?

Selling a good at a different price to different customers for reasons unrelated to the cost of production is known as price discrimination.

For a firm to price discriminate, three conditions must be met:

First, the firm must have market power. That is, the firm must be a price maker.

Secondly, the firm must distinguish its market into segments based on the elasticity of the demand of customers.

Thirdly, the firm must be able to prevent the resale of its goods.

Why can't a perfectly competitive firm practice price discrimination?

The perfectly competitive firm cannot practice price discrimination because it fails to meet the three conditions for price discrimination.

First, it is a price taker and lacks the market power to charge more than marginal cost.

Secondly, perfectly competitive firms cannot price discriminate because it is not able to distinguish their customers based on elasticity.

Remember that a perfectly competitive firm faced a perfectly elastic demand so it must sell at the market prevailing price. 

If a perfect competitor decides to raise price above marginal cost or decides to sell at different prices to customers, it may lose most, if not all, of its customers to competitors.

Therefore, a perfectly competitive firm cannot practice price discrimination because it lacks market power and has a perfectly elastic demand

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