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Determining Amounts and Acting as Price Takers
If the three different suppositions of the perfect competition are carried out, a situation in which the individual companies do not have any control over the prices they can charge comes about. As a matter a fact, when there is perfect competition, economists call the companies price takers, because they have to accept the price as given and adjust according to it.
There are only two things that even the strongest company can control and that is how much of their product to produce and how much to charge for it. Given the fact that companies do not have any control over their prices under the perfect competition, the decision is limited to only one: the only thing the price taker companies can control is how much to produce.
The companies choose to produce the amount that will maximize the benefits. This is very convenient from the mathematical point of view because it turns out that the amount of a good that a company decides to produce controls the two things that determine the benefits, which are the total income and the total costs.
In order to be able to understand this completely, it is essential to know that the benefits of a company are simply defined as their total income minus their total costs. For example:
Benefits = TI – TC
TI would represent the total income and TC would represent total costs.
In the case of a competitive company, their TI (total income) is simply the amount, q, of their product that decides to sell multiplied by the market price, p, that they can obtain for each unit. For example:
TI = p x q
To give you an example, if you can sell pears at a price of $2 each and you sell 30 pears, your total income would be of $60.
Take note that given that the price at which you can sell (p) is out of your hands if you are a price taker, the only way you would control your total income is by deciding how many pears to sell. So a company can determine their total income by deciding how big or how small to make q.
In the following we will show you how the total costs (TC) of a company are determined by the size of q. the interesting thing is that while each additional unit of q that is sold gives an income of p dollars, the cost of each unit of q that has been fabricated depends on how many units of q have already been produced. The costs tend to increase as the companies produce more and more, so this means that each successive unit costs more than the previous one. This fact ends up limiting the number of units that a company may be willing to produce.
Let us suppose that you are able to sell as many pears as you want at the price of $2 each. Producing the first pear will cost you 20 cents and the next 40 cents and so forth. In this case, you would be willing to produce a total amount of twenty. But why? Because in each one of the first nineteen pears you would obtain a benefit, but in the twentieth pear you would neither be neither losing nor gaining. However, if you were to produce more, you would lose.
Therefore, as you can see both Total Income and Total Costs in the benefits equation are determined by the q choice of the company. The only thing left to find out would be exactly how big to make q in order to maximize the benefits. It turns out that there is a very easy and simply way to do this which completely resolves the question.