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

Understanding price ceilings and floors is crucial in economics. A price ceiling, effective when set below the equilibrium price, leads to excess demand or a shortage, while a price floor, effective above equilibrium, results in excess supply or a surplus. For example, with a price ceiling of $1,000 in a rental market where the equilibrium price is $1,500, quantity demanded rises to 2,000,000, but quantity supplied falls to 850,000, creating a shortage of 1,150,000 units. This illustrates the impact of government interventions on market equilibrium.

Quantitative Analysis of Price Ceilings and Price Floors: Finding Points

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. Alright, so we're going to find out quantity demanded and quantity supplied, 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 going to have a different quantity demanded and a different quantity supplied. Alright, so we've got our step-by-step kind of like we're used to when we do these types of things, and I want you to notice that step 1, which we've already done before, right? We're finding the equilibrium price and quantity by setting them equal to each other, right? And then, one more thing before we go down, it's always easier to do these with examples. Ceiling effective? Well, ceiling effective? Well, if you don't remember, 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 it 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 if they're the opposite, above equilibrium, right? So notice what we're going to 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 going to 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. Alright? 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 our quantity demanded and our quantity supplied here, or excuse me, let's start with our equilibrium, right. That's step 1. Let's find our equilibrium. So we've got quantity demanded and quantity supplied isolated, and 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: \( 3,000,000 - 1,000p = 1,300p - 450,000 \). Right? They're equal to each other. Let's go ahead and isolate \( p \) so we can solve for \( p \) now. So we're going to add 450,000 to both sides, add 1,000 \( p \) to both sides, right, to get the \( p \)'s 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, 2,300 \( p \). Right? \( 1,300p + 1,000p \). Now we just divide by 2,300 and we'll have what \( P \) is. So we do that math, and \( P \) is going to come out to be 1,500 in this case, right? $1,500 is the equilibrium rental price, and let's go ahead and find out what the equilibrium quantity is going to be. So, to find the equilibrium quantity, we just take our equilibrium price and plug it into either equation. I'm going to pick demand; it looks a little easier. I'm going to start here: 3,000,000 so, or excuse me, quantity demanded equals 3,000,000, and this quantity demanded really is just the equilibrium quantity, right, because it also equals quantity supplied and it's going to be the equilibrium quantity. \( 3,000,000 - 1,000 \times 1,500 \), right? That is our \( P \), 1,500. So let's go ahead and solve for \( Q^* \) and it's \( 3,000,000 - 1,500,000 \), which is going to be 1,500,000. So let me draw this one in red so you see that it stands out, this 1,500, and that's the price from right up here. Right. 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 $1,500 and a quantity down here of 1.5 million. Alright. So in this question, right, it said calculate quantity supplied and quantity demanded if the price ceiling is $1,000, right? So our price ceiling is $1,000, We found our equilibrium price and quantity. That was step 1, right? Step 2, confirm that it is an effective price floor or ceiling in the problem. So they've given us a price ceiling of $1,000. Is that going to be effective in this case? Well, price ceilings are effective when they're below equilibrium, right? And in this case, equilibrium is $1,500, the price ceiling is $1,000, right? $1,000 is less than the $1,500. It's going to be below equilibrium. Right? So we're going to be somewhere down here. $1,000, I'll do it in a different color. Right? This price of a thousand 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 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? At this price ceiling of $1,000, 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 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, plug the floor ceiling price, which is the $1,000 in our case. We're going to plug that into each equation, the equation for quantity demanded, and quantity Let's go ahead and plug our ceiling price into the quantity demanded and quantity supplied equation. So I'm going to start with demand right here, and we're going to have quantity demanded equals 3,000,000 minus 1,000, and instead of \( P \), right, we are going to put our price ceiling price which is $1,000. Let me do that in blue. Right, so let's go ahead and solve for quantity demanded. It's going to equal 3,000,000 minus 1,000,000. So it's going to be 2,000,000 in this case. Quantity demanded is equal to 2,000,000. So that's the first part of our answer, right? Quantity demanded equals 2,000,000 and that is this number right here, and we feel pretty good about that, right. The 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. Supply. Am I in the way? No, cool. So supply is going to be \( 1,300p - 450,000 \), so quantity supplied equals \( 1,300p - 450,000 \). Right? So, oh excuse me, not \( 1,300p \), we need to put in our price for \( P \), right? So \( P \) is going to be our price ceiling price of $1,000 minus 450,000, right? So that's our quantity supplied at a price of $1,000. Let's go ahead and solve for that. Quantity supplied is going to equal 1,300,000 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 quantity supplied is only 850,000, the quantity demanded is 2,000,000 apartments at this price of $1,000, 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 us, the shortage is going to be the difference between the quantity demanded and the quantity supplied. So let's go ahead and calculate that. The shortage is going to equal quantity demanded minus the quantity supplied, which equals 2,000,000 minus 850,000, which is going to equal 1,150,000. Right? That is the shortage, and we figured out quantity 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? 

Q_D = 45 - 2P
Q_S = -15 + P

• A. 2
• B. 3
• C. 4
• D. 5
• E. 6

The supply and demand curves for a product are as follows. What is quantity supplied if a price ceiling of $4 is set? 

Q_D = 600 - 100P
Q_S = -150 + 150P

• A. 150
• B. 200
• C. 300
• D. 450
• E. 600

Here’s what students ask on this topic:

How do you calculate the equilibrium price and quantity in a market?

To calculate the equilibrium price and quantity, set the quantity demanded (Q_d) equal to the quantity supplied (Q_s). For example, if Q_d = 3,000,000 - 1,000P and Q_s = 1,300P - 450,000, set them equal: 3,000,000 - 1,000P = 1,300P - 450,000. Solve for P by isolating it on one side of the equation. Once P (price) is found, substitute it back into either the Q_d or Q_s equation to find the equilibrium quantity (Q). This process ensures you find the point where the market is in balance.

What is the impact of a price ceiling set below the equilibrium price?

A price ceiling set below the equilibrium price creates a shortage in the market. For instance, if the equilibrium price is $1,500 and a price ceiling is set at $1,000, the quantity demanded will increase while the quantity supplied will decrease. Using the given equations, if Q_d = 3,000,000 - 1,000P and Q_s = 1,300P - 450,000, at P = $1,000, Q_d = 2,000,000 and Q_s = 850,000. This results in a shortage of 1,150,000 units (2,000,000 - 850,000).

How do you determine if a price floor or ceiling is effective?

A price ceiling is effective if it is set below the equilibrium price, causing a shortage. Conversely, a price floor is effective if it is set above the equilibrium price, leading to a surplus. For example, if the equilibrium price is $1,500, a price ceiling of $1,000 is effective because it is below equilibrium, resulting in excess demand. Similarly, a price floor of $2,000 would be effective as it is above equilibrium, causing excess supply.

What are the steps to calculate quantity demanded and supplied with a price ceiling?

First, find the equilibrium price and quantity by setting Q_d equal to Q_s. Next, confirm the price ceiling is effective (below equilibrium). Then, substitute the ceiling price into the Q_d and Q_s equations. For example, with Q_d = 3,000,000 - 1,000P and Q_s = 1,300P - 450,000, and a ceiling price of $1,000, Q_d = 2,000,000 and Q_s = 850,000. This results in a shortage of 1,150,000 units (2,000,000 - 850,000).

How do you calculate the shortage caused by a price ceiling?

To calculate the shortage caused by a price ceiling, first determine the quantity demanded (Q_d) and quantity supplied (Q_s) at the ceiling price. For example, if Q_d = 3,000,000 - 1,000P and Q_s = 1,300P - 450,000, and the ceiling price is $1,000, then Q_d = 2,000,000 and Q_s = 850,000. The shortage is the difference between Q_d and Q_s: 2,000,000 - 850,000 = 1,150,000 units.