Quantitative Analysis of Price Ceilings and Price 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 and creates deadweight loss from untraded goods. Conversely, a price ceiling below equilibrium increases consumer surplus but limits producer surplus, also resulting in deadweight loss. Key calculations involve identifying demand and supply axis prices, equilibrium price, and the missing price to determine these surpluses and losses effectively. Mastering these concepts enhances comprehension of market efficiency and the implications of government interventions.

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 get 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 do everything. We're going to solve for all the prices, all the quantities, but on the test, and 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 23000p. Alright. The last step is to isolate the p by dividing by 23000. Alright. And we are going to get an equilibrium price here, p equal to 150. So we figured out equilibrium price is \$150. 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 I draw the graph and remember there were those 5 prices and 2 quantities that are gonna be important, right? So let's go ahead and draw it. So this is kind of gonna be the standard drawing that we're going to have when we do these is gonna be something like this, right? We're going to have 5 prices, so we wanna mark five 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 access 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 the equilibrium price is \$150. 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 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 star, right? Because it's going to be the same for demand at supply at equilibrium it's gonna 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 star. 3,000,000 minus 1,500,000. That's gonna give us 1.5 million. Right? That's the answer. Whoop. Let me get it out of the way. 1.5 million, that is gonna be our Q star, 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 1.5 million, right, at q star. 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? \$1000 and 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 gonna 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 gonna solve for 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 0 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 used 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 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 axis 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 supplyз axis 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, 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, we're going to calculate that lower quantity and then we're gonna calculate the areas for consumer surplus, producer surplus, and deadweight loss. Alright, so the first step is we're gonna 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 gonna 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 gonna use the for ceilings, we're gonna 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 gonna be a1000 this case, right, and we're gonna solve for that other quantity and I'm gonna show you a trick in a second, regarding this idea. So let's use our supply equation and our price of $1,000. So $1,300 remember we're looking for what that quantity supplied is at this price ceiling price. Coin supplied equals $1,300 times $1,000, right? Minus 450,000. So the quantity supplied is gonna equal 1,300,000 minus 450,000 which equals 850,000. Right. That is going to be our lower quantity and it's gonna 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 gonna 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 floor ceiling quantity. Alright? And what does it tell us here? It says for floors, use the supply equation and for ceilings, which is what we have, we're going to use the demand equation and the floor ceiling quantity. Alright? So it's the quantity we just solved for, we're going to plug it into the other equation, alright? So that's kind of the flow. So if you had forgotten which was which in the first equation, once you figured it out now you know that you used the other equation for this one, right? So here we're gonna use the demand equation, and we are going to use the floor ceiling quantity. So the floor ceiling quantity was this 850,000 so this was step 4 right here. Right? And let's go ahead and do step 5 right under it. So we're gonna use that floor_ceiling quantity of 850,000, and we're going to set that equal that's going to be what our quantity demanded is. So let's see what the price is when that is the quantity demanded. 3,000,000 minus 1,000

. Right. So we're gonna I'm gonna get the the p's on the left hand side of the equation and the the money on the other side are just the numbers. So let me do that better. I'm gonna do plus 1,000p out here and minus 850,000 on both sides. Right? To get the eight hundred the numbers on one side and the p on the other side. So this is gone. This is gone. What's left? We've got 1,000p equals 2,150,000. Let's go ahead and divide by a 1,000 on both sides and what's that left with? We're going to get a p of 2,150. Right, so there we go, 2,150. Hopefully that wasn't in the way the whole time there, but there you go. So let's go ahead and use 21.50 that is our missing price right here. So now we have all the numbers we need. We're ready to start calculating and start with consumer surplus, right? Actually, let's go ahead and start with consumer surplus, right? Actually let's start with producer surplus because it's gonna be the easiest one. So we've got a price of a 1,000 and producer surplus we've been using green, right. At a price of a 1,000, producer surplus is everything that's below the price of a 1,000. Right? So we'll start with this one because it's just a triangle. Right? We've got a triangle in this case, and we just need to find the area of the triangle and we've got our producer surplus. So let's go ahead. I'm gonna write producer surplus here and let's do the calculation. Right? So what is our base and what is our height? Base there and height there. Right? That is gonna be the base and height of the triangle. So we're gonna go half times base and the base here, right, it's gonna be the 1,000 minus the 346. Right? That's the length of that segment and we're going to multiply that by the height and the height is always just going to be the quantity that we use there, so the height here is going to be 850,000. We didn't go all the way to equilibrium, We can only go to the $850,000. So let's go ahead and calculate what the producer surplus would be. I'm getting out my handy dandy calculator. 1,000 minus 346 is 654 times half times 850,000. Wow, so we get a producer surplus of 277,950,000. Alright, that is our producer surplus. We're dealing with big numbers here. Right? That's a big quantity. We're gonna get a big number. So our producer surplus, I'm gonna write it in this box, 277950,000 right? There we go. Almost doesn't fit. So let's go ahead and do consumer surplus now, right. So our consumer surplus, when we have the price floor, we're gonna have everything above the price but below the demand curve. Right? Well, let me get rid of this basin height because we're gonna have a different one now, but we're only gonna go up to this low quantity, right, because the trades beyond that didn't happen because of the price floor. So it's going to be this area right here that I've shaded it in purple. Right? So how do we calculate that area? Well, it's a little tricky, but we're going to break it up into 2 pieces. So I'm gonna highlight here in I'll use green to mark off the areas we're gonna calculate. So here is a rectangle that we're gonna calculate and then we're also gonna calculate this triangle, right? So when we calculate the 2 of them, we just add the areas together and we'll have the total area. Let's start with the rectangle. So consumer surplus oops consumer surplus. Alright? So let's start with the rectangle. So rectangle is just base times height, right? The base times the height without the half part. So what is the base? Well we're going to have this right here right from 2,150 to 1,000 and our height is going to be this distance right here up to the quantity of 850,000. Right, so let's go ahead and do that. So our base is gonna be 2,150 minus 1,000, right? That's the length of that segment times our height, which is just 850,000 Right? That's the quantity exchanged. That's the length of that segment. So let's do this math. 2,150 - 1,000 is 1,150. Right? Times the 850,000. That's gonna give us a consumer surplus of 977 , 500 , 000 . Quite a big number there as well. Alright, so there we go, we've oh, excuse me, that's not our consumer surplus, of course, right, that's only part of our consumer surplus. We also need to find the area of the triangle and this is a huge mistake students make all the time and it almost caught me right there, so you gotta be really careful just like I was right here, okay? So let's go ahead and find the area of the triangle. So I'm gonna write here rectangle, right? Let's go ahead and do the triangle, and it might even be better actually now that I think about it to label this before you start doing the math, right? Then you can't forget if you're just written rectangle and then started math, you'd be like okay time for the triangle, right? So it's usually good to do those headings first and I will make sure to do that in the future. So let's go ahead and calculate the area of the triangle. So we've got half times 3,000 minus 2,150. That's going to be this sorry. This is the base right here now. Whoops. The base is going to be this length right between the 3,000 and the 2,150 and we've got that same height, right? The height of the quantity. So half times 3,000 minus 2,150, that's the length of that segment times our height of 8,500 , 000 , right ? So this is the other part of the producer consumer surplus. Let me get out of the way. So let's go ahead and calculate that. 3,000 minus 2,150. Alright. Times 0.5 times 8 150,000 and we're gonna get that the triangle has an area of 361,251,000. Right. So now all we gotta do is add both of these together, right, and that's going to be our total consumer surplus. So if we add that plus 9,775,500 , 000 , we get our total consumer surplus of $ 1 , 000 , 001 , 750 , 338 right ? Huge number here. So that is our total consumer surplus. Let's go ahead and write that in the box. 1,000,000,000 338,750,000. Alright. So that's our consumer surplus. Let's go ahead and finish up with the deadweight loss, right? So this one's a little tricky, but let's go ahead and highlight the area on the graph here. It's gonna be this blue area. Right ? The trades that weren't made, we lost this surplus. So how do we calculate that triangle? Well, let me erase that. So we're gonna need this right here. Right? That is going to be our our base and this is going to be our height, right? From there to there. So we can need the difference between the quantities for the height now and the difference between those prices for our base. So let's go ahead and do that. I'm gonna do it right here at the bottom. We're kind of running out of space. So I'll do it right here. Deadweightloss. Alright. So it's a triangle right? So we're gonna use our triangle equation half times base times height. So half times our base. Our base is going to be this length right? The length of the prices. So it's going to be the 2,150 minus the 1,000 right? That's the those two prices there right? That length is the difference between those and the height is the difference between the quantities, right? This right here, the length of the of that that size. So what's the difference between those? 1,500,000 minus $850,000. Right? So once we do all this math, we will have our deadweight loss. Let's go ahead and do this. So it's easier to do, everything inside the parentheses first. I like to do my subtractions first. You can't mess up your order of operations. So we've got the 1 and a half 1000000 minus the 850,000 is 650,000 right? So I'm gonna do half times and 2,150 minus a1000 is 11.50 and 1 and a half 1000000 minus 850,000 is 6 $150,000. Right? So let's just multiply it out and we're gonna get $373,750,000 All right. That's our deadweight loss and wow that was a quite a hefty problem right? But remember on the exam, they're not going to generally ask you to solve for everything in one question. You'll probably get multiple points right? You'll get points for the consumer surplus, points for producer, points for deadwei

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 impact of a price ceiling on consumer surplus, producer surplus, and deadweight loss?

A price ceiling set below the equilibrium price increases consumer surplus because consumers can purchase goods at a lower price. However, it reduces producer surplus as producers receive less revenue. The price ceiling also creates deadweight loss, which represents the lost economic efficiency due to trades that do not occur. To calculate these areas, you need to identify the demand axis price, supply axis price, equilibrium price, and the price ceiling. The deadweight loss is the area of the triangle formed by the difference between the equilibrium quantity and the quantity supplied at the price ceiling.

How do you calculate consumer surplus and producer surplus with a price floor?

To calculate consumer surplus and producer surplus with a price floor, you first need to identify the equilibrium price (P_e) and quantity (Q_e). A price floor set above the equilibrium price reduces consumer surplus to the area above the price floor and below the demand curve. Producer surplus is the area below the price floor and above the supply curve, excluding the areas of trades that do not occur. The deadweight loss is the area of the triangle formed by the difference between the equilibrium quantity and the quantity demanded at the price floor. Key prices include the demand axis price, supply axis price, equilibrium price, and the price floor.

What are the key prices needed to calculate surpluses and deadweight loss in price ceiling and price floor scenarios?

To calculate consumer surplus, producer surplus, and deadweight loss in price ceiling and price floor scenarios, 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_e), the price ceiling or price floor, and the missing price (a price needed to complete the calculations, often found through algebraic methods). These prices help determine the areas on the graph that represent surpluses and deadweight loss.

How does a price floor above equilibrium affect market efficiency?

A price floor set above the equilibrium price disrupts market efficiency by creating a surplus of goods, as the quantity supplied exceeds the quantity demanded. This results in a reduction of consumer surplus to a smaller area above the price floor and below the demand curve. Producer surplus may increase initially but is limited to the area below the price floor and above the supply curve, excluding untraded goods. The deadweight loss, represented by the area of the triangle formed by the difference between the equilibrium quantity and the quantity demanded at the price floor, indicates the loss of economic efficiency due to untraded goods.

What is deadweight loss and how is it calculated in the context of price ceilings and floors?

Deadweight loss is the loss of economic efficiency that occurs when the equilibrium outcome is not achieved. In the context of price ceilings and floors, it represents the value of trades that do not happen due to the price intervention. To calculate deadweight loss, identify the equilibrium price (P_e) and quantity (Q_e), the price ceiling or floor, and the quantities traded at these prices. The deadweight loss is the area of the triangle formed by the difference between the equilibrium quantity and the quantity traded at the price ceiling or floor, using the relevant prices and quantities.