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 \( p - \text{tax} \) in the supply, right? Or \( p \) with \( p + \text{tax} \) in the demand. Well, in this case, it's the suppliers that are taxed, right? So we’re gonna use the 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 \( p + \text{tax} \), 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 \( P - \text{tax} \) in the supply, right? And this makes sense that we’re gonna replace \( P \) with \( P - \text{tax} \) 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 \( P - \text{tax} \), right?
So let's go ahead and do that. We’ve got our supply equation, which was Qs=2p-6, but we’re gonna replace that \( p \) with \( p - \text{tax} \) And in this case, the tax was $1. There's our original equation, but instead of \( p \) I've substituted in \( p - \text{tax} \).
So continuing here, Qs=2(p-1)-6=2p-2-6=2p-8.
Now that we’ve got our new supply equation, this is the supply equation with the tax. This is essentially a shifted supply equation. Next, all we got to do is find equilibrium at this price. We’re gonna solve for equilibrium. We've done this before. The only difference here is that we have a new curve. So we're going to use that quantity supplied, not the original one.
So we've got Qs=Qd=10-p=2p-8. Solving for \( p \), we get \( 3p = 18 \), hence \( p = 6 \). So our new equilibrium price with the tax is going to be 6.
The equilibrium quantity using our quantity demanded is then \( 10 - 6 = 4 \). That is going to be the equilibrium quantity here of 4.
In step 3, since the suppliers are the taxed party, the equilibrium price is the amount paid by the non-taxed party, which is the demand. So the demand price \( P_B = 6 \). If we know that this one's $6, well the suppliers are going to receive $1 less, \( P_S = 6 - 1 = 5 \).
So our new equilibrium is $6, and a quantity of 4. The suppliers are going to receive $5 and the demanders are going to pay $6. So that seems good.
Alright, let's go ahead and do a practice problem where you guys can try these steps out and solve for the prices of the buyer and the seller. Let's do that in the next video.
