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Output Optimization: Marginal Revenue / Marginal Cost

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Source: Image of Total Revenue shaded graph created by Kate Eskra, Image of Total Cost shaded graph created by Kate Eskra, Image of Profit shaded graph created by Kate Eskra

Hi. Welcome to Economics. This is Kate. This tutorial is on Output Optimization, where we're looking at marginal revenue and marginal cost. In this tutorial, we'll be looking at how marginal revenue is the slope of total revenue, and marginal cost is the slope of total cost. And you'll understand why firms will maximize profit where we equate marginal revenue and marginal costs.

So we know that the point of owning a business is to make a profit. And we know that profit equals revenues minus costs. In many tutorials, we're focusing on one or the other. But in this tutorial, we're focusing on both, because now we're looking at putting it all together to see where we can maximize profit.

So marginal revenue is just the additional revenue we gain when we sell one more unit. It represents the change in total revenue. In these examples that I made up, I made them a price taker. This is a perfect competitor. There's only one price. And that price, it turns out, is $20. If we do marginal revenue for a perfect competitor, see how nice and easy it is? It's always going to be price, because the additional revenue, every time you sell one more, is the only price that you can charge. And in this example that is 20. So marginal revenue and price are the same for our perfect competitor.

So that means that this is what their demand curve looks like. This is a perfectly elastic demand curve, which shows that there's only one price, and in our example it was $20. It's marginal revenue, it's their demand curve, it's also price. So every time they sell one more, again, they gain the price of the product in additional revenue.

It also is the slope of total revenue. Remember, slope is just rise over run. It's the change in y as a proportion to the change in the x-axis. So because that's what it is, it represents the change in total revenue. OK? So the slope of it is constant. The change in total revenue is the same every time. It's an additional $20. So that's why marginal revenue and demand in price is a horizontal line in a perfect competitor situation.

Marginal cost is the additional cost of producing one more unit. And it is the change in total cost. So here, this one isn't as easy, sorry. This is not constant every time. We have marginal cost falling at first, but then rising. OK. So we're really just looking at the change in total cost each time.

If we would graph those numbers, we would come up with something that looks like this, the blue line. So this is the marginal cost curve. It also, just like marginal revenue was the slope of total revenue, this is the slope of total cost, because it measures the change in total cost. OK. So I want to point out that a lot of people are sometimes under the impression that maximizing profit is all about either minimizing cost or maximizing revenue. And that's not the case. And you can see that pretty easily here.

If we were minimizing costs, that would mean we would be producing nothing and profit is negative, because you always have a fixed cost that you have to pay, regardless of production levels. So that's certainly not what we want to do.

Maximizing revenue is not what we want to do either. A lot of people think, oh, just keep producing, keep producing, you'll make more profit. And you can see here, at some point profit begins to taper. So how is it that we arrive here where profit is maxed out?

Well, it's where, first of all, there's the greatest difference between total revenue and total cost. But it's also where marginal revenue and marginal cost are equal. So that's what we're going to spend a little bit of time talking about.

Why would we ever want marginal revenue and marginal cost to be equal? Why is that going to give us the highest profit? Well, let's think about it. If marginal revenue is greater than marginal cost, as I indicated, is all the way down this pink arrow here, marginal revenue is greater than marginal cost, each of these production levels, that means that producing one more is going to add more to the revenue side of things than to the cost side of things. OK?

So, for example, let's say, we are selling six t-shirts. And marginal revenue is 20, marginal cost is 12. That means that that sixth t-shirt added $8 to profit, because 8 more went to revenue than to cost, and that's exactly what happened. It went from 40 up to 48. OK. So you want to continue producing as long as marginal revenue is above marginal cost.

But at the opposite side of it, if we jump over here, where marginal cost has jumped up above marginal revenue, now you're adding more to cost than to revenue. If this firm were to produce the ninth t-shirt, they would add three more dollars to cost then they did to revenue. And so profit fell by 3. It went from 53 down to 50. So we would want to scale back. OK.

So if we go up to the point where the two are equal, that's where we will maximize profit. These two are not always going to be equal. The point is, you would never go past the point. You would want to stop before marginal cost jumped up above marginal revenue. I just tried to make it clear for you here, by giving you an example where the two are actually equal.

So if we look at this on a graph, this is at the marginal cost. Marginal revenue is in green. And now I've added an average total cost curve here. OK. So the price was $20. The first step, when you're looking at a graph like this, is to always look up to the point-- so like I said, we'll always go for MR equals MC. That is a big deal. So just always make your eyes go to this point right here.

So we found where marginal revenue equals marginal cost. Now we know that the quantity they're producing, whether they're maximizing profit or minimizing loss, would be 8. OK. Now we read everything along here. Is that a profit or loss? Well, now we know what we're generating in revenue, we're taking in $20 times 8, what's that costing us? Since price is per unit, we need cost per unit. And I'm showing you it's somewhere around $13 per unit.

OK, so looking at this graphically, this green area represents total revenue on the graph, because here is our price. Here's our quantity that we're selling. Price times quantity, that rectangle, that green rectangle, is total revenue, or $160. And if you need to flip back and forth between this and my chart, you can verify all of these numbers.

Our total cost, then, would be this rectangle right here, in red, because our price per unit was exactly $13.38, and I got that by taking total cost divided by quantity. And we know, again, we're producing eight of them. So the average total cost times the quantity would give us the total cost of $107, which looking on that chart you can go back and look and see that's was. But that's represented by that red rectangle there.

So then if we take that green rectangle, which was total revenue, and subtract out of the red rectangle, which I just showed you, we're left over with this. What would that be? You're right. That's profit. OK. And there's two ways to look at profit, total revenue minus total cost, or graphically, here, it's really the difference between the price per unit minus the cost per unit, or average total cost times the quantity.

And so $20 is what we're selling each one for. Our average total cost per unit was $13.38. If we do that math and multiply times 8, we get our profit of $53, which you can see on that chart. Or like I said, we could do total revenue minus total cost, 160 minus 107, and we'll get the same thing.

The idea here is we want to maximize the size of this green rectangle, because that represents profit. And you'll notice, every single time we equate marginal revenue with marginal cost, this is the biggest this rectangle can get. OK. If we move to the left or to the right, it will get smaller. So if we set marginal revenue equal to marginal cost and go from there, we will always have the largest profit.

So in this tutorial we talked about how a firm will maximize profit, where there's the greatest difference between total revenue and total costs. But what we're looking marginally-- at marginal revenue and marginal cost-- we'll be maximizing profit by equating the two of them. Marginal revenue, remember, is just the slope of total revenue, because it shows the change in total revenue. And marginal cost of the same thing. It shows the change in total cost. So it's the slope of total cost. Thank you so much for listening. Have a great day.