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The above answer is mostly correct, but I would like to add a little to it to tell you WHY a firm in perfect competition can not influence the market --- WHY it must be a price taker.
The major reason for this is that the product it sells is identical to that of its competitors. Therefore, it can not, for example, raise its price above that of its competitors and claim that its product is superior. If it raises its prices above those of its competitors, it will simply be unable to sell any goods.
Take, for example, eggs which, in America at least, are graded by size and quality. One Grade A egg is essentially identical to another. Therefore, one egg supplier can not possibly claim its eggs are superior to those of other suppliers.
This is why a firm in perfect competition must be a price taker.
One small quibble with the above answer:
In perfect competition, firms may easily enter the market. Because of this, firms in this market structure, by definition, make zero economic profit in the long term. This is why they do not lower prices -- it's not because they have no incentive to do so -- it's because if they do they make negative profit.
In response to assessment of my answer at Post #2 as "mostly correct" by Ponphei in post #3 above, I would like to present my views on some of the issues mentioned in that post.
It is said that when 3 economists discuss an issue they are sure to have between them 4 different views. So Ponphei may be right, but I differ with him on some issues.
Undifferentiated products is one of the condition existing in a perfectly competitive market, but that is not the primary reason for the firm being a price taker. Besides the sameness of the identical products does not determine the quantity sold by a firm. In a perfectly competitive market there are many firms selling identical product, but the quantities they sell is not identical.
The firm is a price taker because of the limited scope of economies of scale available to it. If a firm was able to increase its production to a very high level without reaching the bottom of its marginal cos curve, it will be able to affect market price and quantity in spite of identical product, changing the market structure to monopoly, and therefore will become a price maker instead of a price taker.
On the assertion of Ponphei that firms in perfectly competitive market do not lower price because they are making zero economic profit, is it implied that if a firm is making more than zero economic profit, it will lower its price? If so, why don't monopolistic firms sell at a price so that will give them zero economic profit?
A perfectly competitive firm in the question, I believe refers to a firm operating in a perfectly competitive market. By definition a perfectly competitive market is one in which no single firm has to influence either the equilibrium price of the market or the the total quantity supplied in the market. Thus, a firm operating in a competitive market has no incentive to supply at a price lower than market equilibrium price, as it can sell all it wants to supply at equilibrium. At the same time, the firm cannot sell at price higher than the market price, because it will be able find no buyers at that price, and its sales volume will drop down to zero. Thus, a firm operating in perfectly competitive market has to accept whatever is the market equilibrium price, and therefore it is called a price taker.
In contrast, a monopoly firm is the only supplier in the market and therefore has full control over the market prices and total market supplies. Therefore, a firm operating in a monopoly market fixes its price in such a way that for the quantity demanded by customers at that market price the marginal revenue of the firm is equal to its marginal costs. In this way way it decides the market price as well as the total quantity if a commodity supplied in the market, and therefore it is called a price maker.
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