Alright, so now let's see how we can find equilibrium using the equations for the supply and demand curves. Alright, so I've got the steps listed here. The first thing we're going to want to do is make sure that for our demand equation and for our supply equation, the same variable is isolated. That means we want only the price on one side of the equation or only the quantity on one side of the equation, right. We want to isolate the same variable for both. After we do that, and that's if needed right, you could be given 2 equations where you're already isolated the same variables like you see here. Right here in both of these equations, the one for demand and supply, price is isolated in both situations, so we are good to go with step 1 in that situation, right?
So step 2 would be to take both of the curves and set them equal to each other, alright? We'll see how to do this in a second, but the idea is remember when we're at equilibrium, there is going to be the same quantity supplied as the quantity demanded. So quantity supplied and quantity demanded are going to be the same amount, that equilibrium quantity and the price is going to be the same too, right? The demand and then we're going to use a little bit of algebra to solve for the remaining variable, and then we're going to use a little bit of algebra to solve for the remaining variable and then once we get that answer, we'll use it in one of our original equations to get the second variable. So let's see it all in action.
So here I have the demand and supply curves that we were using earlier in this segment. On the left I have the price isolated, on the left or excuse me on the right I have the quantity isolated, and we're gonna do it both ways just so you see we get the same answer and that it doesn't matter which variable is isolated as long as it's the same one for both. Okay, so step isolated as long as it's the same one for both, okay? So step 1 is done already in the sense that we have price isolated here and and quantity isolated here. So we're gonna do 2 examples on the left, we'll do the example where price is isolated, on the right where quantity is isolated. Let's start with price. Scroll down a little more. So step 2 was to set the equations equal to each other, okay? So how do we do that? Remember price is going to be the same in both, okay? So if p is equal to 802QD and p is also equal to 200+QS, that means that 802QD is equal to 200+QS, alright? And one more thing is gonna be that we don't need to write QD or QS anymore, we can just use Q because the quantity demanded and quantity supplied are the same at equilibrium. 200+q. So you see what I did there? I took this side of the equation and this side of the equation and set them equal to each other. 802 Q D = 200 + Q S and again we just use q because quantity supplied and quantity demanded is the same at equilibrium. So let's go ahead to step 3. In step 3, we're gonna take the equation we just made and we're gonna solve for q.ນnright? The variable that's in there. So I'm gonna rewrite it here. 800 − 2 q = 200 + q So the first thing we want to do is get all the q's on one side of the equation, and I like dealing with positive numbers so I'm going to move them to the right. So I'm gonna take these 2 queues and I'm gonna add 2 there, and I'm gonna add 2 here. So this is gonna cancel out and we're gonna have 800 equals 200 plus 1 q + 2 q s 3 . Alright? So now let's go ahead and move the 200 to the other side. So we're gonna subtract 200 from each side there. We're gonna get 600 equals and this cancels out 3q and now we want just 1q right? We've got 3q so we gotta divide by 3 on both sides. So we're gonna divide by 3, I'll do it in blue, divide by 3, divide by 3, and what do we get? 600 divided by 3 is 200 and 3 divided 3 is 1, so 200 equals Q. We found our equilibrium quantity of 200. All right, so that's the step 3 and now step 4 is pretty easy. We're just going to take our equilibrium quantity that we just solved for and we're going to plug it into one of our original equations. So I'm gonna go up here and you can pick either one, you can pick the demand equation or the supply equation. I like to look at them and pick the easier one, the one that has less math involved and in this case it looks like the supply equation is a lot easier. It's just 200+q. So I'm gonna pick that P equals 200+q. So we've got P equals 200+q, and we know what q is right? We just solved for the equilibrium quantity so let's plug it in. P.equalsayeright)?["["p""]]200:eq("Error):(eq("Enterital")("P"))200("Error")200or:eq(ge(search)),,"REALt)))here)(("n ("e")")/te",â200(95Yo(")("RESULT("q")) Twinsry.ht(200("gmath")) Value,"Purpose':'question like",tm popular,200(**since])relayle than 200 "prettyal)(mpl('.wri 12003 equals P. We've got our equilibrium so P * is our equilibrium price is 400 and Q * our equilibrium quantity is 200. We just solved that using algebra. Pretty cool. Now let's go ahead and use the other side of the equations just so you see we get the same answers here. Right? Alright.
So let's go ahead and set these equal to each other right. Quantity is isolated by itself. We're gonna set this equal to this. 400 − 1 2 p = p − 200 . Alright? So now what we want to do is solve for P, and that's going to be step 3. I'm going to rewrite the equation 400 − 1 2 p = p − 200 . So I want to get all the p's on one side of the equation So that's going to take adding half a p here and adding half a p over here, and let me go back to red. So this is going to cancel and we're going to be left with 400 equals p+half p, so p is the same as 2p over 2 right? 2p over 2. So 2p over 2 plus 1p over 2 is going to give us three two p, right? 1 and a half p's. We had 1 p, we added another half p, we've got 3 over 2 p. Minus 200. Alright. And now let's go ahead and get the 200 on the other side. So we're gonna add 200 to both sides and we'll have 600 equals 3 over 2p, and this will cancel out. So how do we get the p by itself now, right? We've got 600 equals 3 over 2p. Well if you remember from algebra, the trick here is we're going to multiply by the reciprocal. So if we multiply 3 over 2p times twothree, This 2 thirds is gonna cancel. I'm just gonna get out of the way so I'm not dodging. The 2 thirds is gonna cancel with the 3 over 2, and we need to multiply the other side of the equation also by 2 thirds. Okay. So the 3 over 2 oh actually I'm going to write all those in blue times 2 thirds, and this side also times 2 thirds. Okay so let's go ahead and cancel stuff out. The 2's cancel, the 3's cancel, and we're left with just p on that side of the equation, and then we'll do 2 3 × 600 is gonna be 400. Alright? So there we go. We've gotten a price of 400, which we can confirm in step 4 the other time, we got a price of 400. So it looks like we're getting the same answer. And let's go ahead and do the last step where we solve for quantity using this price that we have. So again, I'm gonna pick the easier formula and to me it looks like the supply formula again is easier in this situation, so I'm gonna go ahead and plug actually I'm going to use the demand one just to prove that we could use either one. So I'm going to use quantity demanded equals 400 minus half P and I'm going to plug in our P there. So Q equals 400 minus half p, and p was 400. So we're going to get q equals 400 minus half of 400 is 200. So q equals 200 and that confirms what we just got on the other side, right? We got a p star here, a 400, and a q star of 200. So either way, either variable was isolated and we've got the same answer there. Cool? So let's go ahead and try some practice with this stuff.