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

Alright, let's try this practice. The supply and demand curves for a product are as follows. What is producer surplus if a price floor of $21 is set? So notice they only ask us for producer surplus, not everything in this case, and they tell us that there's a price floor of $21 right? So the first thing I like to do is I like to set up my graph, right, when we're dealing with producer surplus, we're dealing with with price floors, and we've got equations, we're doing algebra here to calculate this area right when we have producer surplus, we know it's going to be an area. We're going to need those those 5 prices and those two quantities. Remember where we had those 5 prices? Demand access price, supply access price, all of this stuff. That's where this is all gonna come into play here. Right? So we're gonna have those 5 different prices and 2 different quantities, right? Here's the price. Here's a price. Here's a price. Here's a price. Here's a price. Here's a quantity and here's a quantity. Right? Those 5 prices in those two quantities. So the first thing we want to do is we want to find our equilibrium price, so that we can see if this price floor is even effective. So to do that we're going to set our equations equal to each other, right, and solve for price and that will be our equilibrium price. 45 minuteus 2p equals negative 15+p, right? And we can do that because the quantities are going to be the same at the equilibrium. So we're going to add 2p to both sides, Add 15 to both sides. Get the p's by themselves. Right. This cancels. This cancels. We're gonna have 60 equals 3p. Right? P+2p, divide by 3 to get the p's by themselves, and we're gonna have P equal 20, right? Our equilibrium price is 20. So there we go. We found our first number here, 20. That's our equilibrium price. Let's go ahead and find our equilibrium quantity. Okay, so equilibrium quantity is going to be you can use either equation. I'm going to use the supply. It looks pretty easy. Quantity equals negative 15 plus p and we're gonna put in our equilibrium price, which was 20 and we're gonna get a quantity of 5 at equilibrium, right? So now we're ready to see if this price floor is effective or not, right? So how do we know if this price floor is effective? When are price floors effective? Above or below equilibrium? Well, if you don't remember, we've got the trick where we build our little house and the ceiling is the effective price ceiling, right? So the effective price ceiling here is a number that's below equilibrium, right? So if we were to flip it, a price floor is going to be effective above equilibrium, okay? So is our price floor above equilibrium? The price floor is 21, equilibrium was 20. Yes, we have an effective price floor. So I'm going to go ahead and put it in right here. This is going to be our price floor number right there, and now I want to shade in the region that I want to solve for, right. It's gonna help me gauge what numbers I need to solve for. So what is producer surplus? So the producer surplus is going to be this area right here, right? It's going to be below that price floor price, but above the supply curve, and we're not going to go all the way to the end because these trades weren't made, right? That was the deadweight loss to the right there. So this is the area of the producer surplus. What numbers are we gonna need to solve this? Well first, this is how I'm gonna attempt to solve it is I'm gonna make these areas right here. So first, I'm going to look for the area of this rectangle and I'm going to add it to the area of this triangle down here, right? I'm gonna find both of those areas, sum them together, and that's going to be our producer surplus. So what numbers do we need? We're gonna need this missing price here, right? This one here, we're gonna need the supply axis price and we're gonna need this quantity supplied. So the only number we didn't end up needing really was the demand axis price in this case. So unfortunately, we're gonna have to solve for all of these, but let's go ahead and do it. Let's start with the supply axis price. This is pretty easy to do. So to find that all we need to do is set quantity equal to 0 in the supply curve. So we'll do that right here. 0 is gonna equal negative 15+p. So at what price is quantity supplied 0? We just add 15 to both sides, right? And we're going to get 15 equals p. That is going to be our supply axis price. Easy enough. Right? $15 right there. So now we just need the missing price and the missing quantity. So how do we solve for those? First, let's solve for the missing quantity, right? And to do that, what we need to do is we're gonna use our price floor amount and we're gonna put it into the correct equation. Now a lot of the times I forget even which equation I'm supposed to put it into. So the trick is is you pick 1 and if it's incorrect, you're gonna get a number a quantity bigger than equilibrium, right? We're looking for this quantity that's lower than equilibrium. 1 of the equations is gonna give us something bigger, one is going to give us something smaller. So I'm going to start with the supply one just because it's an easier equation and hope that it's correct. So now we're looking for the low quantity I'm going to call it right? That's what I've been calling it so far. It's not an official term, but that's gonna be the quantity that's actually exchanged, right? This lower quantity at the price floor. So let's start with the supply curve, right? Let's find out if I can use the quantity supplied equals negative 15 plus and I'm gonna put in our, price floor price of 21. Right? So let's see if we can figure that out. Quantity supplied equals negative 15 +21 is 6, right? We got 6 and equilibrium was 5 right? So in this case we got a wrong answer right? This number was too big to be our quantity, so what we need to do is go to our other equation, our quantity demanded equation and try the same thing. 45 minuteus 2 times 21. Right? Our price floor price. And what do we get now? Quantity of demand equals 45 minuteus 42 which equals 3. Right? So here we go. This looks better. Now we got a number that's less than 5 and that is what our quantity is gonna gonna be at this lower trade. So we got the 3 there. The only thing left to find is the missing price and the good thing about missing price is now that we've already had the struggle of which was the correct curve to use for the quantity, for the low quantity, for the missing price you use the other curve, right? We're going to use this low quantity and the other curve. So we use the quantity demanded curve to find the low quantity, right? So to find the missing price, we're going to use the quantity supplied curve, right? So we just use the other curve from the previous step. So let's go ahead and do that. Quantity supplied Oh, but our quantity supplied we're going to set equal to this 3. Right? So 3 equals negative 15+p. So let's go ahead and solve for p. We just have to add 15 to both sides. We're going to get 18 equals p. So there you have it. We've solved for all of our missing, variables of price and quantity. Now we just have to calculate the area. So I don't make a mistake, I'm going to label this first rectangle plus triangle, right? So let's start with the rectangle here and let's find its area. So we've got, this base right here, 21 to 18, right, and then this is the height, the length there, which is 3. So the rectangle is going to have a base 21 minus 18, right, times the height which is this quantity of 3. So we're going to get 21 minus 18 is 3 times 3. The area of the rectangle is 9. Let's do the triangle now. So the triangle is going to have this base right here and this height. Right? The height is still going to be the 3. So let's go ahead and do it. So area of a triangle is half times the base which was 18 minuteus 15 times the height which is the 3. Right? So let's go ahead and solve it. Times 3. 18-fifteen is 3. We're gonna get 4.5 here. So 9+9+4.5, right, is going to give us our final answer. Let me get out of the way just so you see that. 9+4.5 is our final answer of 13 0.5. So there we go. We found out what the producer surplus is and it's going to be d13.5. Alright. A lot of steps there, but we got through it and we got the right answer. Let's go on to the next video.

The supply and demand curves for a product are as follows. What i...

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2. Introductory Economic Models1h 10m

3. The Market Forces of Supply and Demand2h 26m

4. Elasticity2h 16m

5. Consumer and Producer Surplus; Price Ceilings and Floors3h 45m

6. Introduction to Taxes and Subsidies1h 46m

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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

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The supply and demand curves for a product are as follows. What is producer surplus if a price floor of $21 is set? QD = 45 - 2PQS = -15 + P

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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