Now that we have the revenues for a competitive firm and a competitive market, we're ready to maximize profit. Remember, profit equals total revenue minus total cost. We calculate total revenue by multiplying price times quantity. We can calculate total cost by multiplying the average total cost times the quantity. We see that in the term in this second equation that quantity is in both.
We can pull that quantity out and get an alternative calculation. for profit. So both total revenue minus total cost and price minus average total cost times quantity will give us the profitability or pi for a firm. The second equation will become useful when we interpret our competitive firm graphically. So how do we determine profit maximization?
Remember, economists think at the margin and profit maximization is no different. Profit maximization means that we're exhausting all the potential gains that we could have from profit. Well, recall that in a competitive market, marginal revenue reflects the price-taking price that all firms face. But marginal cost from our cost module shows us that while it may initially fall, it eventually is going to begin to rise again due to diminishing marginal product. So we use this difference to determine the quantity that we should produce.
If the marginal revenue is greater than the marginal cost, We need to continue quantity, continue producing. If our marginal cost exceeds marginal revenue, we've gone too far and we need to scale back. But just the right amount is where marginal revenue is equal to marginal cost. That is our profit maximizing quantity. That's the quantity we wanna find because at this point, we've exhausted all the gains from profit that we can have.
Let's take a look at the example. In Sam's flower barn, he's looking at a variety of quantities and total revenues that we've already calculated. We've now added in total cost, and we can calculate profit using our formula of total revenue minus total cost.
This is one way that you can find profitability. However, for the economist, we're looking at exhausting gains. And as you can see here, both a quantity of 4 and a quantity of 5 produce the same level of profit. So economists turn to marginal thinking, marginal revenue and marginal cost.
As we said, in a perfectly competitive market, the marginal revenue is always equal to the price, regardless of the quantity that we sell. We can calculate marginal cost by looking at the change in total cost over the change in quantity. That is, as we go from one to two units, our total cost increases from three to five, which represents a change. of 2 and so on for the remaining values.
We see here if we compare marginal revenue and marginal cost, remember, we want these values to be equal to maximize profit. There's only one place that they are and that's down here where both values are equal to 5. At this point, the quantity that's produced is also equal to 5. So here for this firm, marginal revenue and marginal cost are equal at five dollars for a quantity of five units. The last column represents what we reflect as marginal profit for the change in profit, the difference between marginal revenue and marginal cost.
Remember we're saying that the competitive firm wants to exhaust all the gains. As they increase their quantity, that is as they go down the table, they're gaining more profit, but They don't exhaust profit until they reach that quantity of 5. At the quantity of 5, marginal revenue is equal to marginal cost. And profit is the highest level of any of the values.
But notice what happens if they increase production by one more unit to 6. Now marginal cost is greater than marginal revenue. The firm is still making a positive profit. That doesn't mean that they're losing money overall.
It just means that they're losing money on that individual unit. Producing that sixth unit costs them $1 in profit. They make $1 less in profit by increasing production to six over remaining at a quantity of five, where profit is maximized at a value of $8. Let's look at this graphically.
If we take our cost curves that we've drawn before, our typical cost curves. The two that are the most important for profit maximization are our average total cost and our marginal cost. Those two are important because marginal cost of course helps us to determine our profit maximizing point, average total cost helps us to determine profit. So we need both of these curves in order to find profit maximization graphically.
We can also add our demand curve here for the individual firm. Remember, we said because everyone is a price taker, because there's so many substitutes in the market, the demand curve for the perfectly competitive firm is perfectly elastic. That is, it is... perfectly horizontal but this demand curve comes directly from that price taking market price and for a competitive firm that price also gives them their marginal revenue curve and their average revenue curve in other words in a competitive market for the firm the individual demand curve the marginal revenue curve and the average revenue curve are all the same When we look at a graphical profit maximization problem, we can follow a three-step process. The first step is we want to set marginal revenue equal to marginal cost to get our profit maximizing quantity.
Looking at our graph, we can see that we have our marginal revenue and our marginal cost. Where those two values intersect is here, and that gives us our profit maximizing Q. QM.
The next step is we want to ask the question, what price do we pay? Well, for any price in any mark in any competitive market, we're going to pay that price taking price. So we go to the individual firm's demand curve.
For this quantity, we of course always are going to pay the competitive going market price of P. Finally, what is our profit for this firm? Remember, Profit is total revenue minus total cost, but for this firm in this graph, we don't have total revenue and we don't have total cost directly.
So we can use our second formula, price minus average total cost times our quantity. That is the going market price minus the average total cost of the quantity we choose to produce multiplied by that quantity. Well, at profit maximization, we're going to produce that QN. We're going to charge a price of P.
The average total cost for this quantity can be determined by going up to the average total cost curve for that quantity. Then we can track it over to our left-hand axis to get the average total cost for the profit-maximizing quantity. Using our formula, price minus average total cost is represented by the height and our quantity.
is represented by the length of this rectangle. Therefore, the graphical interpretation of profit is going to be this area here. That area represents, of course, a positive profit because the price is greater than the average total cost for this firm. In Sam's case, he makes a profit of $8.
And that's the highest level of profit he can make under any quantity conditions given this going market price of $5 in the market. We can follow this three-step process in any competitive situation that we're given. And for any of our market structures, we're going to be able to follow this three-step process to always find profit maximization graphically for any of our firms.