Quantitative Analysis of Price Ceilings and Floors: Finding Areas - Online Tutor, Practice Problems & Exam Prep

Understanding consumer surplus, producer surplus, and deadweight loss is crucial when analyzing price floors and ceilings. A price floor, set above equilibrium, reduces consumer surplus to area A, while producer surplus becomes areas D and F, leading to deadweight loss in areas C and E. Conversely, a price ceiling below equilibrium increases consumer surplus to areas A, B, and D, but limits producer surplus to area F, also resulting in deadweight loss from unexploited trades. Key calculations involve identifying demand and supply axis prices, equilibrium prices, and the missing price for accurate area determination.

Graph Intuition

Alright, now we're going to put all of our algebra tools to work to calculate consumer surplus, producer surplus, and deadweight loss in situations where we have price ceilings and price floors. So it's going to get pretty in-depth here, but I think you're going to see that a lot of it has to do with stuff we've already been doing. Alright, so let's go ahead and first review what we're going to be looking for on the graph, right? When we're dealing with price floors and price ceilings, we're going to be dealing with these areas looking for consumer surplus and producer surplus.

Alright, so first let's talk about this price floor. Okay, a situation where we have a price floor, and we have our equilibrium. So let's label our graph price and quantity here, right? Our downward demand, upward supply. And where's our equilibrium? We got it right here in the middle, right, at a price of \( p^* \) and here's \( Q^* \) over here, right? So we're going to talk about an effective price floor. When is the price floor effective? Well, that's when it's above equilibrium, right? And just to remember, we've got our trick for the ceiling, right? The price ceiling below equilibrium, right? Because the ceiling, we make the house there and the ceiling would be below, so the price floor is going to be above. So we're going to pick this price right here as our price floor price. Okay, I'm going to put for our price floor and let's go ahead and discuss what we're going to be looking for in this problem, right?

So, first when we're at equilibrium, right, and we have a price floor, or excuse me, when we're at equilibrium what is our consumer surplus when we're at equilibrium? Well, we know that it's everything above the price but below the demand curve, right? So when we're at equilibrium, everything in the purple triangle above the \( p^* \) is going to be consumer surplus. So that's going to be A plus B plus C, right? When we're at equilibrium and how about that producer surplus? That was everything below the price and above the supply curve. Excuse me. Alright. So that's going to be that green area which we'll call D plus E plus F, right? That's everything that is under the price but above the supply curve and you should remember that when we are at equilibrium, we're being efficient and we have no deadweight loss, right? There's no deadweight loss when we're at equilibrium.

So let's go ahead to this situation where we have a price floor, right? When we have a price floor, what's our consumer surplus? So we've got this high price right up here and everything above that price is going to be consumer surplus, right, and below the demand curve. So consumer surplus is going to be just this little area right here, area of A. So that's our consumer surplus with the price floor is just A. And remember when we're doing this, we're going to be doing this with algebra and we're going to be calculating the area of A. We're going to want to know what that area is and to find out what that area is, we're going to need to have like we've used before our demand axis price. Remember these axis prices that we were solving for? So this one up here is our demand axis price, right? So we're going to need that demand axis price and we're going to need the price floor amount and we're also going to need this quantity here, right? This quantity, at the price floor, I'll call it \( Q_L \) for like a lower quantity, we're going to need that number as well to be able to calculate that area, alright? So I'm just priming you, right, for the kind of numbers we're going to be searching for and how we're going to look for them.

Alright, so how about producer surplus when we have a price floor in that situation, right? So our producer surplus, if you remember from our previous discussion, is everything below the price, but it's not going to include C and E, right? Because those trades don't happen. This price floor is stopping those trades from happening, right? We are only going to trade up to quantity \( Q_L \) and we don't reach \( Q^* \), so those trades where C and E exist, those didn't happen so those are not going to be surplus, right? So we're going to see that BD and F, D plus F is our producer surplus. So there, the producers have effectively taken some of the surplus from the consumers, but at a cost to society of this deadweight loss, right? And that's what we see here in C and E. These trades didn't happen. Society would have been better off with them, but we get nothing out of this, right? We've lost these benefits. So that is our deadweight loss. C plus E, right? So notice producer surplus and deadweight loss. These are all things that we could calculate but to calculate, producer surplus, let's talk about that one first. For the producer surplus, we're definitely going to need this supply axis price down here, right? We're going to need this one, the very bottom of the graph. The supply axis price, right, where it's crossing here and this is the demand axis price here. The price floor right here, \( p^* \) right here, and there's one more number that we're going to need, right? It's this last price and I call it the missing price. There's no real term for it, but I call it the missing price because there's always going to be this one extra price that we need to solve for and that's going to be the last piece of the puzzle, right?

So what do you see in this situation, right? We're going to see that we have a demand access price, the price floor, the equilibrium price, the missing price, and the supply access price. There are 5 prices that we need to find out what they are if we need to solve for all of this. Remember when you see these problems in the exam, they're usually going to only ask you for a portion, right? They're going to say what was consumer surplus only? They're not going to say in one multiple choice what was consumer surplus, what was producer surplus, what was deadweight loss? That would be really intense, right? But you might get a few questions where you solve this in pieces, right? So we're going to need those 5 prices and we're going to need these 2 quantities, right? 2 quantities. So when we're solving for everything, we're going to need all of these numbers to successfully figure out what consumer surplus is, producer surplus, and deadweight loss, right?

So let's do the same thing with the price ceiling. Okay. So now with the price ceiling, right, we already set up an effective price ceiling, we made the house. It's going to be somewhere below equilibrium, right? So here's going to be our \( P^* \) equilibrium price and equilibrium quantity, right? And we're going to say a price ceiling. I'm going to put PC for the price ceiling right here as a price below equilibrium, right? So in this situation when we have a price below equilibrium, let's go ahead and find our consumer surplus, our producer surplus, and deadweight loss. Let's start with producer surplus because it's easier. That's going to be this green area right here, right? Everything below the price but above the supply curve. So that's the only producer surplus in this case and that's just F, right? F is the only producer surplus and to calculate that again we're going to need that supply. Let me do it in black. That supply axis price, right? Supply axis price just like we've used in previous videos, and that's that point right there where it touches the price axis.

Okay. So now let's do consumer surplus. Just like before, we're going to see that it's going to be this area A, B, and D, right? It's not going to include C and E because those trades didn't happen and we did not get that benefit. So here we go. We've got A, B, and D right above the price but below the demand curve, and that is going to be our consumer surplus. So let's write it in here, A plus B plus D and when we're calculating that area, we're going to need that demand axis price up here, right? Demand axis price and that's where it's touching the curve there, but we're also going to need to because when we calculate this, this is a pretty weird shape. So we would split it up into 2 shapes just like we would do with producer surplus on the other side. So let me do this in blue real quick We would split it up into this rectangle and we would solve the area of the rectangle and then add the area of the triangle up here, right? So we would treat it as 2 shapes. So to get that area of the rectangle, we would need that missing price in this case, but notice the missing price in this one is not where the missing price was in the other one, right? They're in a different spot. So that's why it's handy to have the graph and do it with the graph because you can see and you just start putting in the numbers as you solve it, you put them where you have them on the graph. So again, the last thing we're going to need here because to solve that, we also need this length right here, right? What is this quantity? And I'm going to call it \( Q_L \) again, right, the lower quantity because of inefficiency. And so that yeah.

So there you kind of see the parallel, right, with the price floor and last but not least, we've got the deadweight loss, right? This C plus E, the trades that didn't happen, the surplus that was lost, right? C plus E again is deadweight loss. So to calculate that, we would need the missing price and the pricing, right? We would need this length right here. C to E. So we would need the missing price and the price ceiling number there and we would need the difference between the quantities, right? This height right there is the difference between \( Q^* \) and \( Q_L \). So we would need all those numbers there. Pretty intense, right? So in the end, you're going to see that a lot of the steps we do is stuff that we've done before, right? Again, we're dealing with this demand axis price that we've solved for before, supply axis price we've solved for, \( p^* \) we've solved for, the price ceiling has been given to us, right. They're going to have to tell us that number in the question or else we're not going to know what the ceiling was or the price floor. So really the only new thing that's happening here is solving for that missing price, right, and potentially this lower quantity as well. So there's not so much new stuff here. We're going to see that there's a lot of parallels to what we've been doing, but then you know it just adds that little extra layer. So let's go ahead and move on to the next video where we can start and you'll see the kind of stuff that's already similar to what we've been doing. Alright, let's go ahead and do that in the next one.

The Steps We've Done Before

Alright, so let's go ahead and do this example and follow our step-by-step. In this video, we're going to do the steps that you should be used to already, things that we've done previously. Alright, so it's telling us to calculate consumer surplus, producer surplus, and deadweight loss if a price ceiling of 1000 is in effect. Alright, a price ceiling of 1000 is in effect. We're going to calculate consumer surplus, producer surplus, and deadweight loss. When you get this on a test, I wouldn't expect you to solve everything at once, so you might not have to solve for everything, right? This is going to take a while because we're going to solve all the prices, all the quantities, but on the test, we'll see when we do some practice problems, you can skip some steps because you don't need all the information when you're not looking for everything. Alright, so look at step 1. Find equilibrium price and quantity. Boom. We do this all the time, right? We're used to this. Let's go ahead and do that right now. So we're going to set these equal to each other right. We've got 3,000,000 minus 1000p equals 1300p minus 450,000. Right. So let's get all the p's on one side, all the numbers on the other side. So we're going to get this out of here. Put it over here. Alright. So what's going to cancel? This is gone. This is gone. What's left? 3,450,000 equals 2300p. Alright. Last step is to isolate the p by dividing by 2300. Alright. And we are going to get an equilibrium price here, p equal to 1500. So we figured out equilibrium price is 1500. Right? Now we've done this example before, so I don't know those numbers off the top of my head. So what I like to do is draw the graph and remember there were those 5 prices and 2 quantities that are going to be important, right? So let's go ahead and draw it. So this is kind of going to be the standard drawing that we're going to have when we do these is going to be something like this, right? We're going to have 5 prices, so we want to mark 5 different prices here where we're going to have this demand axis price, we're going to have this one here, right? One of these is going to be the missing price, one of these is going to be the price ceiling or the price floor. We've got our equilibrium price in the middle and then our supply axis price on the bottom, right? And then we're going to have these 2 quantities as well. We'll have the quantity when it's low and the quantity at equilibrium, right? All of these numbers are going to be important, when we solve this, right? So what have we solved so far? We just found that equilibrium price is $1500. So we've gotten that one. Let's go ahead and get our equilibrium quantity. Right? So all we're going to do is plug that into either equation right because at equilibrium the quantities are the same. So let's do that now. I'm going to pick the demand equation, looks easier. So we've got quantity demanded which is q* right? Because it's going to be the same for demand and supply at equilibrium it's going to be the same. So 3,000,000 minus 1000 times P at equilibrium which was 1500, right? So let's go ahead and solve for Q*. 3,000,000 minus 1,500,000. That's going to give us 1 and a half million. Right? That's the answer. Whoop. Let me get it out of the way. 1 and a half million, that is going to be our Q*, right? So we've now gotten this number down here. Let me scroll down just a little bit and we figured out that this is 1 and a half million, right, at Q*. So we've gotten 2 out of the seven numbers already and that's stuff that we're already used to. So let's look at step 2, confirm that the price floor or ceiling is effective. We've done this before too, right? Price ceiling is effective, so remember that whole house thing, right? My house method, so that helps us with price ceilings, right? We're going to have our demand and our supply and we get the house when we're below equilibrium, right? Equilibrium being right here and we're below. So the price ceiling is when we are below equilibrium is when it's effective. Price floor is the other one is when we're above, right? So we need to confirm is this an effective price ceiling? They told us the price ceiling is 1000, right? The quantity or excuse me, the price at equilibrium is 1500. So it's less, right, it's below equilibrium. It is going to be effective. And just like that, we're ready to put this one in right here, right. This one's going to be our price ceiling of 1000. We just put it into our graph. Yeah, I'm going to come in right here. So we just took the price ceiling and we put it in our graph where it would go, right? So now we know the missing price number is going to be this one. This is going to be the missing price number, the price ceiling is in there, but we're not going to solve for the missing price yet. That's the new thing. Right? We're going to do that in the next video. So in this video, we're going to do the rest that we're comfortable with, which was solving for the supply access price and the demand access price. This is stuff we've done before, right? So what we need to do is we're going to set quantity demanded equal to 0 and we're going to set quantity supplied equal to 0 and that will give us the demand access price and supply access price. So let's start here with demand. So right here, demand. So when is demand equal to or what is the price when demand is equal to 0? So quantity of demand is 0 equals, so I'm using our demand equation up here, right? 3,000,000 minus 1000p. So quantity demanded is 0 equals 3,000,000 minus 1000p. Right? So we're just going to add 1000 to both sides or not 1000, 1000p, right? So 1000p is going to equal whoops 1000p is going to equal, 3,000,000. So what is going to be p? We divide by 1000 on both sides. Oops. Oh, I'm out of space there. Oh, no. Oops. Sorry about that. Let's let's get back to where we were. Alright. So there we go. 3,000,000. We're going to divide both sides by 1000, right, and we are going to get a price. I'm going to go this way. P equals 3,000,000 divided by 1000, 3000 right. So that is going to be our demand access price because we use the demand equation. So P is 3000 when quantity demanded equals 0, and let's go ahead and do the supply one right here right behind me. Alright. So supply, What do we have? Quantity supplied. So we're going to use our supply equation. We're going to set quantity supplied equal to 0. Right? And let me put these zeros in in a different color so you can see that that's what I was doing there. Okay. So 0 is going to equal 1300p minus 450,000. Right? That's our supply equation and we set quantity supplied equal to 0, so let's add 450,000 to both sides. Right. And we are going to get, 450,000 equals I'm going to put this line right here. 450,000 equals 1300p. And when we divide this by 1300 on both sides, we're going to get a minimum price or excuse me, a supply access price of I'm going to go over here. P equals 346. Right? We're going to round this off to 346. Oops. Alright. No decimals there, we'll keep it easy. So that is our supply access price, right? And guys this is all stuff we've done before, right, we've done all these steps before, we've been able to solve all of these just using what we've done in previous videos. So now in the following video, we're going to go ahead and we're going to solve for the missing price, we're going to get that quantity and we're going to start calculating areas. Alright, let's go ahead and do that now.

The New Steps

Alright, let's keep it moving here. So here you're going to see the new steps, right? Here we are going to calculate that missing price, calculate that lower quantity, and then we're going to calculate the areas for consumer surplus, producer surplus, and deadweight loss. Alright, so the first step is we're going to find that quantity, right? So if you go down here, on the graph I've already brought over the information from the previous video, right? If you want to pause and just update this graph so you have it all here. I'll be here when you get back, don't worry. So let's go ahead and do step 4, okay? So we're going to find the floor-ceiling quantity by plugging the floor-ceiling price into the correct equation, right? So in this case, we have a ceiling, right? We have a price ceiling, so we're going to use the ceiling, we're going to use the supply equation and the floor-ceiling price, right. The price the floor-ceiling price, right, I say both because it could be either, is going to be $1000 in this case, right, and we're going to solve for that other quantity and I'm going to show you a trick in a second, regarding this idea. So let's use our supply equation and our price of $1000. So $1300 remember we're looking for what that quantity supplied is at this price ceiling price.

Coin supplied equals   1300 × 1000 − 450000

So the quantity supplied is going to equal 1,300,000 minus 450,000 which equals 850,000. Right. That is going to be our lower quantity and it's going to be this number right here, right? So just to reiterate, these are the numbers we're looking for in this video, right? That missing price and this quantity down here, right? This quantity which we just solved for is 850,000.

Now I want to give you a real quick tip because it might be hard to remember, oh, if it's a ceiling use supply equation, if it's a floor use the demand, right? You might forget and on the test, what I would do is I would just try 1, right? If you try to use the demand equation in this situation, you're going to end up with a quantity, a quantity that's bigger than equilibrium, right? You would end up with some quantity out here, right? Some bigger number and you would know that's wrong, right? Because we're looking for a lower quantity. We want the quantity to be less than equilibrium. So worst-case scenario, you can try it in either equation, you go ahead and try the demand equation and if you get a number bigger than your equilibrium quantity, you know you got to use the other equation, okay? So in this case, we've got our steps, it told us to use supply and we've got this lower quantity, alright?

So the last thing to find is our missing price before we calculate areas.

Alright? So let's find the missing price at...

The supply and demand curves for a product are as follows. What is producer surplus if a price floor of $21 is set? 

Q_D = 45 – 2P 

Q_S = -15 + P

• A. 6.25
• B. 10.5
• C. 12.5
• D. 13.5
• E. 18

The supply and demand curves for a product are as follows. What is deadweight loss if a price ceiling of $2 is set? 

Q_D = 600 – 100P 

Q_S = -150 + 150P

• A. 150
• B. 187.5
• C. 212.5
• D. 300
• E. 375

Here’s what students ask on this topic:

What is the difference between consumer surplus and producer surplus in the context of price ceilings and floors?

Consumer surplus is the area above the price and below the demand curve, representing the benefit consumers receive from purchasing goods at a price lower than their maximum willingness to pay. Producer surplus is the area below the price and above the supply curve, representing the benefit producers receive from selling goods at a price higher than their minimum acceptable price. In the context of price ceilings (set below equilibrium), consumer surplus increases to areas A, B, and D, while producer surplus is limited to area F. For price floors (set above equilibrium), consumer surplus is reduced to area A, and producer surplus becomes areas D and F.

How do you calculate deadweight loss in the presence of a price ceiling or floor?

Deadweight loss represents the loss of economic efficiency when the equilibrium outcome is not achieved. To calculate deadweight loss in the presence of a price ceiling or floor, identify the areas of unexploited trades. For a price floor, deadweight loss is the sum of areas C and E, representing the trades that do not occur due to the higher price. For a price ceiling, deadweight loss is also the sum of areas C and E, representing the trades that do not occur due to the lower price. These areas can be calculated using the formula for the area of a triangle: $\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$.

What are the key prices needed to calculate consumer and producer surplus with price ceilings and floors?

To calculate consumer and producer surplus with price ceilings and floors, you need the following key prices: the demand axis price (where the demand curve intersects the price axis), the supply axis price (where the supply curve intersects the price axis), the equilibrium price (P*), the price ceiling or floor, and the missing price (an additional price needed for calculations). These prices help determine the areas representing consumer and producer surplus and deadweight loss on the graph.

How does a price floor above equilibrium affect consumer and producer surplus?

A price floor set above the equilibrium price reduces consumer surplus to area A, as consumers pay a higher price and purchase a lower quantity. Producer surplus becomes areas D and F, as producers receive a higher price but sell a lower quantity. The trades that do not occur due to the price floor result in deadweight loss, represented by areas C and E. This loss indicates the inefficiency introduced by the price floor, as some mutually beneficial trades are prevented.

What is the impact of a price ceiling below equilibrium on market efficiency?

A price ceiling set below the equilibrium price increases consumer surplus to areas A, B, and D, as consumers pay a lower price and purchase a higher quantity. However, producer surplus is limited to area F, as producers receive a lower price and sell a lower quantity. The trades that do not occur due to the price ceiling result in deadweight loss, represented by areas C and E. This loss indicates the inefficiency introduced by the price ceiling, as some mutually beneficial trades are prevented.