Now let's see how we can calculate the price the buyers pay and the price the sellers receive in the case of a tax when we're given equations and use algebra. All right, so, we're going to do the same thing. We've got a few steps we're going to follow but you're going to see that we're still just solving for equilibrium, right. We're gonna figure out some numbers. It's gonna be pretty similar to what we've been doing. So we've got a couple of steps here, but the end goal is to find out, what is the price the buyers pay and what is the amount the sellers receive when we've got a tax. It's gonna be easiest to do with an example, so let's go ahead and just jump right in. It says the original supply and demand curves are as follows: what is the new equilibrium pricing quantity if suppliers are taxed $1 per unit. Suppliers are taxed $1 per unit, right? So we're gonna look for the new equilibrium price and quantity and then we're gonna look for the amount the suppliers receive and the amount the consumers pay, right? So there's gonna be a shift to the supply curve because of the tax and then we are going to also see the new prices, right. So let's go ahead and just start following these step by step.
So we've got our 2 equations there. 1 for supply, 1 for demand and it tells us to replace p with p minus tax in the supply, right? Or p with p plus tax in the demand. Well, in this case, it's the suppliers that are taxed, right? So we're gonna use this first one. It's gonna be 1 or the other here depending on who's taxed, but regardless we will end up at the same answer, right? We've seen that with taxes that no matter who's taxed, we'll get the same answer. So even if we were to do the p plus tax, we'd end up at the same place here. Well, we'd have a different equilibrium, I guess. We would have a different equilibrium, but our prices would end up the same. So to get the correct equilibrium, we have to shift the correct graph and that is by replacing P with P minus tax in the supply, right? And this makes sense that we're gonna replace P with P minus tax because the suppliers are gonna receive less, right? By the amount of the tax. They're gonna have to pay a tax, so they're gonna the end money that they end up with is gonna be the P minus the tax, right? So let's go ahead and do that. We've got our supply equation, which was quantity supplied equals 2p minus 6, right? 2p minus 6, but we're gonna replace that p with p minus tax And in this case, the tax was $1. Right? That's the tax. So let's do it. Quantity supplied equals 2 and instead of p, I'm gonna put p minus tax. Right? And then I'll put in the $1 in a second minus 6. Right? So there's our whole our original equation, but instead of p I've substituted in p minus tax. So let's continue here. Quantity supply equals 2 and I'm still not gonna do it out. I'll go p minus and now we'll put the tax in. Right? It's $1 here from the problem minus 6. Okay. Now we have to, what's it called? Foil this out. Right? 2p. Oh man. It's been a ride been a while. So 2 times the p and then two times the $1. 2p minus 2 and then we still got this minus 6 out here. Right? So 2p minus 2 minus 6. We're gonna get a new quantity supplied equation 2p minus 8. Cool? Alright. So now that we've got our new supply equation, this is the supply equation with the tax. This is essentially a shifted supply equation and we've also got, our quantity demanded, right? They gave us the quantity demanded, equation so next all we got to do is find equilibrium at this price, right? Or excuse me, at this with this new curve. So this was step 1 right here that we just did. Let's go ahead and do step 2 over here. We're gonna solve for equilibrium. We've done this before. The only difference here is that we have a new curve, right? We created this curve right here by shifting with the tacks, right? So we're going to use that quantity supplied, not the original one. So we've got 2p minus 8, right? That's our supply and remember this quantity supplied equals quantity demanded at equilibrium. So if 2p minus 8 is gonna equal 10 minus p, right? That 10 minus p is our demand equation over here. So we've set quantity supplied equal to quantity demanded, which is what we want at equilibrium. So let's solve for p. We're gonna get all the p's on one side and all the numbers on the other and let's see what we get. So these cancel. These cancel. We're gonna get 3p. Oops. Let me do it in red. 3p equals 18. We're gonna get p equals 6, right? So our new equilibrium price with the tax is gonna be 6, but equilibrium is gonna be only for 1 party, right, because there's the part the buyer and the seller are gonna have different prices, right. So here is the new equilibrium price. We don't know whose price that is. It's gonna be either be the seller or the buyer's price. We'll get to that in a second. Let's go ahead and get our equilibrium quantity in this situation. I'm just going to use our quantity demanded because it's it's very easy. Right? 10 minus and we put in our equilibrium price of 6 to find our equilibrium quantity. So quantity demanded is gonna be 4, right, and that is our equilibrium quantity. Right? At equilibrium, quantity supplied equals quantity demanded. So that is going to be the equilibrium quantity here of 4. Okay. So we've got our equilibrium price and quantity. So that's step 2 and now in step 3, it's easy enough. It just tells us that in step 3, the equilibrium price is the amount paid by the non taxed party. Well, in this case the supplier was the tax party, right? So the non taxed party was the demand. So demand price, right, this is gonna be PB is gonna equal this 6, right? That is, that's how we do it. The non tax party gets that equilibrium. Okay, and then last, we need to solve for the remaining price. Well that's easy enough, right? If we know that this one's $6, well the suppliers are gonna receive $1 less, right? The supply price is gonna be $1 less because that is the amount of the tax. So the supply price let me scroll down a little more. The supply price which is ps is gonna be that 6 minus $1 tax. They're gonna get a price of 5. Right? So what is our new equilibrium? Our new equilibrium is $6, right, and a quantity of 4. That's the new equilibrium after we've shifted the supply curve for the tax. The suppliers are gonna receive $5 and the demanders are gonna pay $6. Right? And we can confirm we can confirm that that's gonna all work out, right, because we've got a dollar tax and there's a dollar in between the suppliers receive and the consumers pay. So that seems good to me. Alright, let's go ahead and do a practice problem where you guys can try these steps out and solve for the the the prices of the buyer and the seller. Alright. Let's do that in the next video.
