Alright, now let's calculate consumer and producer surplus when we're given equations and we have to use just a little bit of algebra. Let's do it. Alright, so when we're calculating consumer and producer surplus, at least in this video, we're only going to deal with equilibrium. We're going to be at equilibrium, calculating consumer, but I just want to point out that first step 1, this is something we've done in a previous video. This is finding the equilibrium price and quantity using a little bit of algebra and we've done that before. I suggest if you don't remember how to do that, to watch that video again, but we're going to do it in an example here just to reiterate. Alright? And in step 2, I want to note this term, axis price that I'm using. So, find the axis price when demand equals 0. I made up this term; that's not the real term. That's kind of how I think about it. So let me just show you what I mean over here before we get to the example. I'm going to draw a little example standard supply-demand curve graph over here. So let's say we've got our supply and demand right there, right, and we've got our equilibrium. So this is our price axis, our quantity axis, right? We've got our equilibrium price right here P star and our equilibrium quantity right here Q star, right, and notice that, to calculate our areas of our producer and consumer surplus, so if this is our consumer surplus right here, right, the area below the demand curve, above the market price, this triangle right here, to calculate that we're going to need this price way up here where the demand curve is crossing the axis, and that's what I call the axis price, the demand axis price right there. Right, and then down here we're also going to be solving when we do our producer surplus we're going to need this point where the supply curve is crossing the price axis over there, right? This point right here where the supply curve touches the axis, we need that number to be able to calculate our producer surplus, just to get the length of that segment. So that's going to be our supply axis price right there. Okay. So let's go ahead and jump into the example and we'll see all of this in action. Alright.
So the example says to calculate consumer and producer surplus using the given information and just so you know, these demand and supply curves represent the market for apartment rentals. That's kind of where I got this example from. Okay, so let's go ahead and, on the graph, I'm just going to draw our standard price quantity and just, you know, get those lines out there just to have the visual support, right? So it doesn't really matter what you draw it like. There's no scale here, but one thing you want to make sure is that you cross, the supply curve on the price axis here. Right. You don't want to draw it like this, because we want to cross it on the price axis because in all these examples we're going to have that type of supply crossing the price axis so we can calculate that axis price, right? So we're going to need 3 prices here. We're going to need the P star, we're going to need the demand axis price up here, and we're going to need the supply axis price down here, and we're going to need Q star, right, the quantity in equilibrium to be able to make our calculations of consumer and producer surplus. So let's go ahead and start with step 1 of the algebra, which you see up above. This is what we've done before and it's going to be finding the equilibrium price and quantity. Alright?
So if you remember, when we're at equilibrium, quantity demanded equals quantity supplied, right? Quantity demanded equals quantity supplied at equilibrium. So what we can do is set these equations equal to each other, right? Because quantity demanded equals quantity supplied, that means these equations are equal to each other at that point. So let's do it. We've got 3,000,000 minus 1000p equals 1300p minus 450,000. Alright. So what we want to do is we want to solve for p, which is our equilibrium price. So what I'm going to do is I'm going to try and get all the ps on one side, all the numbers on the other side. So I'm going to go ahead and add 450,000 to both sides. That'll get rid of the -450 on that side, and let's get all the ps on the same side. So I'm going to add 1000p on this side and add 1000p on that side. Alright. So these are going to cancel out right here and this is going to cancel out right here. So what are we left with? We've got 3000000 plus 450000 is 3450000 and that's going to equal on the other side 1300p + 1000p, which is 2300p. Right? So the last thing to isolate our price is to divide both sides by 2300. This is going to cancel right here, and when we do 3,450,000 divided by 2300, I'm going to just mental math real quick. Just kidding. But the answer is going to be 1500. P star is going to equal 1500. Alright, so we've gotten our P star, in this case, so I'm going to go ahead and put that onto our graph. 1500 right here. That is going to be our equilibrium price. Let's go ahead and find our equilibrium quantity. I'm going to scroll down a little bit. Alright, equilibrium quantity to do that, all we have to do is we take our equilibrium price and plug it into either equation. I'm going to go ahead and use the demand equation. It looks a little easier to me. So we're going to have quantity demanded which is also quantity supplied at equilibrium, right? Quantity demanded equals quantity supplied, so it's going to be that equilibrium quantity equals 3,000,000, right? I'm taking our quantity demanded equation from up above, this equation up here. 3,000,000 minus 1000, and now instead of p I'm going to put in our equilibrium price of 1500. So let's find out what the quantity is at this price. So quantity demanded, well I'm just going to use Q star really because this is our equilibrium quantity right? So 3,000,000 minus 1000 times 1500 is 1,500,000. So if we do that, Q Star is going to be 3,000,000 minus 1,500,000, which is 1,500,000. Alright, so we've got Q star now. That's going to be this number right here. 1,500,000 is our Q star. Alright, So let's go up here and let's see what the next step was. We just finished step 1, finding equilibrium price and equilibrium quantity. Now we need to find the axis price when quantity demanded equals 0 and the axis price when quantity supplied equals 0. Okay, so let's start with the axis...
