A purely competitive (price taker) market exists when the following conditions occur:
• Low entry and exit barriers - there are no restraints on firms entering or exiting the market
• Homogeneity of products - buyers can purchase the good from any seller and receive the same good
• Perfect knowledge about product quality, price, and cost
• No single buyer or seller is large enough to influence the market price
Sellers must take the existing market price; if they set a price above the market price, no one will buy their product because potential buyers simply will go to other suppliers. Setting a price below the market price does not make any sense because the firm can sell as much as it wants to at the market price; selling below the market price will just reduce profits.

Because sellers must take the current market price a purely competitive market is also called a "price takers" market.

The firm can sell as much as it can produce at the existing market price, so demand is not a constraint for the firm. Revenue will be simply the market price multiplied by quantity produced.

Maximizing Profit in Perfect Competition
A price taker can sell as much as it can produce at the existing market price.

So total revenue (TR) will be simply P × Q, where P = price and Q = quantity sold.

Marginal revenue
(MR), the increase in total revenue for production of one additional unit, will always be equal to the market price for a price taker.

If the market price of a good is \$15, and a firm produces 10 units of a good per day, then its total revenue for the day will be \$15 × 10 = \$150. The marginal revenue associated with producing an eleventh unit per day would be the market price, \$15; total revenue per day would increase from \$150 to \$165 (11 × \$15).

Marginal costs will vary, depending upon the quantity produced. We would expect the firm to increase input up to the point where marginal cost is equal to the market price. In the short run, a firm will produce as long as its average variable costs do not exceed the market price. If the market price is less than the firm's total average cost, but greater than its average variable cost, then the firm will still operate in the short run. Its losses will be lowered by producing, since nothing can be done about fixed costs in the short run. Over the long run, the firm will need to cover all of it costs if it is to keep on producing.

If the market price at least covers the firm's variable costs, it may make sense to keep on operating. Any price in excess of the average variable cost will at least help to cover the fixed cost. Unless the firm decides to completely leave the business, it will come out ahead by continuing to operate.

If the market price is below the firm's average variable cost, it will not make sense for the firm to operate as it will lose even more money. If the firm believes that business conditions will improve, it will temporarily shut down. Seasonal businesses such as ski resorts or restaurants located by vacation areas will shut down temporarily at certain times. Manufacturers temporarily might shut down a factory and plan to reopen the factory when business conditions improve.

When Does a Firm Maximize Profit in Perfect Competition?
Profit (π) is equal to total revenue minus total cost. We can express this mathematically by stating:
π = TR - TC

In terms of calculus, we can state that profit will be maximized when the first derivative of the profit function is equal to zero:

= dTR  -dTC= 0
dQ dQ dQ

We also can rearrange the terms to state that profit maximization occurs when:

Formula 3.4

dTR = dTC
dQ      dQ

The term on the left represents the change in revenue from producing one more unit, which is called marginal revenue. The term on the right represents the change in total costs resulting from producing one more unit, which is marginal cost.

The firm's profit will be maximized at the level of output whereby the marginal (additional) revenue received from the last unit produced is just equal to the marginal (additional) cost incurred by producing that last unit. Maximum profit for the firm occurs at the output level where MR = MC.

For a firm operating in a competitive environment, the marginal revenue received is always equal to the market price. Therefore a firm operating under perfect competition will always produce at the level of output where the marginal cost of the last unit produced is just equal to the market price.

The following equation will hold:

Formula 3.5

MR = MC = P

 Exam Tip! You do not need to know calculus for the CFA level I exam. Just make sure you understand the relationship above.
Effects on Equilibrium in the Short and Long Run

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