Output Optimization: Total Revenue / Total Cost

Video Transcription

Hi, welcome to economics. This is Kate. This tutorial is on output optimization looking at total revenue and total cost. As always, my key terms are in red and my examples are in green. In this tutorial, we'll be looking at profit maximization on a graph. And you'll see that it's actually the point where the distance between total revenue and total cost is the greatest, obviously with total revenue being higher than total cost. You will also understand why the slope of these two curves, total revenue and total cost, will be equal where profit's being maximized.

So we know that the point of owning a business is to make a profit, right? We also know that profit equals revenues minus costs. In many tutorials, we're focusing on one or the other. But in this tutorial, we'll be looking at both revenue and costs, because now we're trying to figure out what's maximizing profit.

So total revenue is all sales generated by a firm from the sale of a product or service. It's price times quantity. It's everything that a business is selling times the price of that good, whereas total cost is everything it costs to get their product to market. So it's all variable and fixed costs associated with production, which also includes opportunity cost, remember, in economics. OK, and then finally, we take our total revenue and we subtract our total cost, we're left with profit.

All right, so let's look at an example here. I just made up some numbers. I'm using an example of perfect competition because the price of the product each time is the same. They're a price taker. They're only charging $20 each time.

Notice that total revenue is just the price times quantity. So it goes up by $20 each time. And total cost is our fixed cost plus our variable costs. I left those off of here just to make this chart nice and neat and easy to read. But keep in mind that total cost would be those two different fixed and variable added together.

Then profit is just this column minus this column. Notice in the beginning, profit is negative, because they haven't produced anything yet. Yet they had a fixed cost that they had to pay. It only starts to rise as you begin to produce more and more and more.

OK, so one of the things I wanted to point out is that the goal when we're looking at profit maximization is not simply to minimize cost. Because minimizing costs would mean here. But that's not at all where our profit is the highest, because of what I just said.

And it's actually not to maximize total revenue. A lot of people think that, oh, we should just crank out as much as possible. Well, notice that at some point, profit actually begins to go back down. So the point is not to maximize total revenue necessarily.

Instead we're looking at where is profit the highest. And you can see that there's two places. But right in here, profit is the highest where the distance or the difference between total revenue and total cost is the greatest. Since profit is total revenue minus total cost, wherever these two are the greatest amount apart is where profit is going to be the highest.

So let's look at this on a graph. OK, so here's total revenue. And because I had the price be $20 each time, total revenue is just this line right here. And then total cost is this curve here. OK, and then this one would be profit in green.

Notice that profit was negative at first, right? It eventually reached its high point and then started to taper off again. Profit is the highest where there's the biggest gap between total revenue and total cost. That's why I put this gray line in here to show you that at peak of profit, that's where these two are the furthest amount apart. And that's how you can see it on this graph, OK?

Note also, that this is where the slope of total revenue and total cost are equal. OK, Let's talk about that for a second. So slope, see, right here where the difference is the greatest, where profit is the highest, the slope of total cost, if we put that line right there to show you right there, is exactly the same as the slope of total revenue.

Why is that? Let's think about it. First of all, here's the definition of slope for you. It's just rise over run. It's change in the value of the y-axis variable relative to a change in the x-axis variable. So we're looking at the rate of change of total revenue and the rate of change of total cost.

So if total revenue is steeper than total cost, that would be here. Notice how total revenue is rising faster. Total cost is not as steep. That would mean that revenues are increasing faster than costs, which is a good thing. But if we want to maximize profit, we need to produce more, because producing more means that we're going to add more to the revenue side than to the cost. So that means we could actually do better by producing more.

If instead total cost is steeper-- as it is here-- than total revenue, that's the opposite situation. It means that as we're producing more, we're adding more to cost, because they're increasing faster than revenues. And if that's the case, we definitely need to scale back and produce less. It's only where the slope are equal where profit is the highest, OK? So you will do the best by equating the slope of these two curves, because that's where profit will be the highest.

So in this tutorial we talked about how a firm will maximize profit where there's the greatest difference or, on a graph, as you can see it as distance between total revenue and total cost. And it turns out that that's also where the slope of total revenue and total costs are equal. Thanks so much for listening. Have a great day.