Let's find quantity supplied and quantity demanded when there are price limitations using equations. Algebra time!
Quantitative Analysis of Price Ceilings and Price Floors: Finding Points
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So let's discuss how we find the quantity demanded and the quantity supplied when we have a price floor or a price ceiling, and we're using algebra and equations to figure it out. All right, so we're gonna find out quantity demanded and quantity supply, right? We have a price floor or a price ceiling that's affecting the market and it's causing us not to be at equilibrium. So we're gonna have a different quantity demanded and a different quantity supply. Alright, So we've got our step by steps kind of like we're used to when we do these types of things and I want you to notice that step one something we've already done before, right? We're finding the equilibrium price and quantity by setting them equal to each other. Right? And then um one more thing before we go down. It's always easier to do these with examples, I just want to confirm here that a price ceiling must be above or below equilibrium to be effective. Do you guys remember when is a price ceiling effective? Well, if you don't remem you always go straight to the graph and you make your ceiling here, right. Like I like to make I make the ceiling and I know that the ceiling right here is when it's effective? So where is that is that above or below equilibrium equilibrium is right here and that price right here is above, right? That's the equilibrium price and our one right there is below equilibrium. Right? So we know ceilings are effective when they're below equilibrium and price floors are effective. They're the opposite above equilibrium. Right? So, notice what we're gonna be dealing with. When we do this calculation is right here, right? When we have this price ceiling or when we have a price floor, we're gonna have this difference in quantity demanded and quantity supplied here. Right? This is the quantity supplied and quantity demanded. We want to figure out what those numbers are. All right? So let's go ahead and do our step by step with this example. So this is the example of a rental market and let's go ahead and calculate um our quantity demanded and our quantity supplied here. Excuse me, let's start with our equilibrium. Right? That's step one. Let's find our our equilibrium. So we've got quantity demanded and quantity supplied isolated. And are when we're at equilibrium, we know that quantity demanded equals quantity supplied, right? That's when we're at equilibrium. So let's go ahead and set these equal to each other. Three million minus 1000 P. Equals 1300 p minus 450,000. Right? They're equal to each other. Let's go ahead and isolate P. So we can uh so we can solve for P. Now, So we're gonna add 450,000 to both sides, add 1000 to both sides. I got 1000 P. Right to get the ps on one side and the numbers on the other. So that cancels. And that cancels what's left? We've got 3,450,000 over here equals uh 2300 PPI right? 1300 P plus 1000 P. Now we just divide by 2300 and we'll have what P. Is. So we do that math and P. Is gonna come out to be uh 1500. 1500 in this case. Right? $1500 is the equilibrium rental price. And let's go ahead and find out what the equilibrium quantity is gonna be. So to find the equilibrium quantity, we just take our equilibrium price and plug it into either equation. I'm gonna pick demand. It looks a little easier. I'm gonna start here three million. So the quantity demanded equals three million. And this quantity demanded really is just the equilibrium quantity, right? Because it also equals quantity supplied and it's gonna be the equilibrium quantity three million minus 1000. And instead of p I'm gonna put our um equilibrium price of 1500 right? That is RP 1500. So let's go ahead and solve for Q. Star and it's three million minus 1.5 million, which is gonna be 1.5 million. So let me draw this one in red. So you see that it stands out this 1500 and that's the price from right up here. Right? Um so there we go. We've got our equilibrium price and our equilibrium quantity, let's put this on the graph. Just to kinda have the visual along with this. So price and quantity demand curve, supply curve. Right? And we just found out that this point the equilibrium has a price of 1500 and a quantity down here of 1.5 million. Right? So in this question, right, it's a calculate quantity supplied and quantity demanded if the price ceiling is 1000. Right? So our price ceiling is 1000. We found our equilibrium price and quantity that was step one, right. Step to confirm that it is an effective price floor or ceiling in the problem. So they've given us a price ceiling of 1000. Is is that gonna be effective in this case we'll price ceilings are effective when they're below equilibrium. Right? And in this case equilibrium is 1500 the price ceiling is 1000 1000 is less than the 1500 it's gonna be below equilibrium. Right? So we're gonna be somewhere down here. 1000 I'll do it in a different color. Right. This price of 1000 is going to be an effective price ceiling. So we can go on right if it was an ineffective price ceiling or price floor that we were given. We know that when it's ineffective, we'll just trade at equilibrium. So we would have been done at this case, we would have known quantity demanded and quantity supplied would have been 1.5 million if it was ineffective. Right? So since it's effective, let's go ahead and find out what what the quantity supplied and quantity demanded are so notice at this price ceiling which makes our house right? We've got our house right here with our ceiling right there, right? Um at this Price ceiling of 1000, what is our quantity supplied and quantity demanded? Right. So right here, quantity supplied right here, quantity demanded. Right, and these are the numbers that we're looking to to find out what these numbers are. Right, those are the answers we're looking for. So let's go ahead and see what our next step is. It says if it's effective, which it is plugged the floor ceiling price, which is the $1000 in our case, we're gonna plug that into each equation. The equation for quality demanded and the equation for quantity supplied. And we're gonna get what the supply and demand would be in those cases. So here we go. Step three down here. Right. Step two was to check if it was effective. Let's go ahead and plug our ceiling price into the quantity demanded And quantity supplied equation. So I'm gonna start with demand right here and we're gonna have quantity demanded equals three million minus 1000. And instead of p right, we are going to put our price, ceiling price, which is 1000. Let me do that in blue. Alright, so let's go ahead and solve for quantity demanded. It's gonna equal three million minus one million. So it's gonna be two million in this case, quantity demanded is equal to two million. So that's the first part of Answy, right, quantity demanded equals two million. And that is this number right here and we feel pretty good about that. Right equilibrium was 1.5 million. And we got a number bigger than that. So that feels pretty good. So let's go ahead and do the quantity supplied. So we'll do that right here. Uh supply in the way. No. Cool. So supply is going to be um what was our supply curve? 1300 p minus 4,450,000. So quantity supplied equals 1300 P minus 450,000. Right, so excuse me not 1300 P. We need to put in our price for P. Right, So P is going to be our price ceiling price of 1000 minus 450,000. Right, So that's our quantity supplied at a price of 1000. Let's go ahead and solve for that quantity supplied, it's gonna equal 1.3 million minus 450,000. And that's going to be 850,000. Right. That is going to be our answer there. So that is what our quantity supplied equals 850,000. So what do we have in this case we have a shortage. Right. The quality supply. It is only 850,000. The quantity demanded is two million apartments at this price of 1000. Right? So we've got a shortage in this amount between these two numbers and we can calculate that shortage too right, if they ask this, the shortage is gonna be the difference between the quantity demanded and the quantity supply. So let's go ahead and calculate that the shortage is gonna equal quantity demanded minus the quantity supplied, which equals two million minus 850,000, Which is gonna equal uh 1,150,000. Right, that is the shortage. And we figured out quality demanded quantity supplied. Alright, pretty cool. Let's go ahead and practice this a little bit.
The supply and demand curves for a product are as follows. What is quantity demanded if a price floor of $21 is set?
QD = 45 - 2P QS = -15 + P
The supply and demand curves for a product are as follows. What is quantity supplied if a price ceiling of $4 is set?