переведи на русский чтоб звучало логично,постарайся избегать дословного перевода Hey everyone and welcome back to the channel. So today we're going to be looking at another homework question, namely we're going to be looking at the difference between a shortage and a surplus. With that said, let's get into things. So we have our demand equation on the left and our supply equation on the right, so we'll use our method to calculate Q and P star.
If you don't know how to do this, we've actually already made a video on this, so feel free to check that one out and we'll link it in the description. So we know at the equilibrium point of the supply and the demand curve, which is located right here, we know that quantity demanded is equal to quantity supplied. And so we have these two equations right here and we're going to let them equal one another. So then we have 600 minus 500p is equal to 300p.
I'm going to rearrange this equation. I'm going to put the 500 on the other side, which gives me 600 is equal to 800p. Therefore, P must be equal to 0. 75.
Now I know that this is P* and I can now label it on my supply and demand graph and this will be 0. 75. Now I know that the next step is to take this P* and to sub it into either the Qs or Qd equations and I know that they're both going to give me the exact same Q value and that will actually be my Q*. So I'm going to sub it into Qs as that's significantly easier and we'll do that right now.
So my p* value is right here and we'll sub in to qs for my q* value. So q* is simply equal to 300 times p and I know that p is 0. 75 therefore q* is equal to 225. And so now I have my labeled graph.
Don't forget of course to label your axes so q and p Now I've got my labeled equilibrium which is a price of 0. 75 and a quantity of 225. But now we're going to look at two scenarios, a shortage and a surplus, and we're going to take a look at what that means for the supply and demand graph. We'll start by looking at a surplus.
Let's say that for some reason instead of being 0. 75 the price was actually set approximately one dollar. so we'll have this line right here represent the new price and it'll be at 1. 00 or 1 dollar well now we don't have an equilibrium point but we actually have two different intersection points right here where the new price intersects the demand curve and over here as well where the new price intersects the supply curve and these are not at equilibrium so how do we calculate these two quantities Well, we actually have to sub in $1 into both the QD and QS equations separately.
So let's do that. So first let's sub it in to the QD equation. So QD is equal to 600 minus 500 times the price. Well, this new price is actually one.
So QD is going to be 600 minus 500, which is 100. So this value right here is equal to 100. Now let's do the same thing for QS. So Qs is simply equal to 300 times p, while p is just one.
So Qs is equal to 300. Now, what do we notice about this? Well, we notice that Qd is strictly less than Q*. That is in this scenario, we have a surplus and Qd is 100 and Q* is 225. So it's an obvious statement that 100 is less than 225.
Therefore, in this scenario, Qd is less than Q*. At the same time, we notice that 300 is greater than 225. Therefore Qs is greater than Q*. Now does this logically make any sense? Well it does.
Via the law of demand you would expect that if the price goes up demand for the good goes down. So we actually see a decrease in demand by this amount here 225 minus 100 so a decrease in demand by 125 units. At the same time an increase in the price due to the law of supply would assume that supply increases So we see that an increase in supply happens by this amount here, the difference between 300 and 225, which is 75. So there's two different effects happening and that does make sense via the law of demand and the law of supply.
So in this case, demand is really low. It's at 100 and supply is really high. It's at 300. So we have way more products being supplied in the market than there is a demand for and we would call this a surplus.
Meaning that there's more supply in the market than demand. And you might be wondering, well, how much actually gets traded in the market then? Well, at a price of $1, you will always trade at what we call the short side of the market. So if you're working your way from left to right, it will always be the first intersection point with the price, which actually happens to be at Q equals 100. which means that in this market at a price of $1, only 100 units will be traded in the market.
Even though there's an additional 200 units being made available, the difference between 300 and 100, even though there's an additional 200 units available, because there's no demand for them, they won't actually be sold at a price point of $1. So there's a surplus of 200 units in the market. And that's simply the difference between how much is supplied and how much is actually demanded. So 100 units will be traded in the market even though there's 300 units available, there's only demand for 100 units.
Now let's take a look at what happens when there's a shortage. Now let's say that the price is actually something lower. Let's say 50 cents or 0. 5.
Well, we're going to do the same thing that we did before. We're going to sub this new price, this one down here, into both the QD and the QS equations, and we'll see where these two intersections are made. So if we sub this into QD, then we get 600 minus 500 times 0. 5, which is 600 minus 250, which is equal to 350.
So where the demand curve intersects this price line is at 350 units over here. On the contrary, QS, let's sub it into this equation and see what happens. 300 times P, which is 0. 5.
And this is simply equal to 150, which is over here somewhere. So now the reverse is true. We're actually seeing a shortage in the market. And you can see this as QS is strictly less than QD.
150 is less than 350. And so therefore, even though there's a demand at a price of 50 cents, even though there's a demand of 350 units, there's only 150 units available in the market. So there's actually a shortage. Well, how do you know how much the shortage is? We just take the difference in demand and supply.
So we know that the demand is 350 units. So that's how many at 50 cents. That's how many units are demanded in the market. However, we know that only at that price point, producers don't want to sell at 50 cents because their profits would go down.
They want to wait till the price goes back up. So there's only 150 units available and the difference between QD and QS will tell you how big or small the shortage is. In this case, 350 minus 150 is a shortage of 200 units in the market. So which one of these points will actually be consumed at? Well, 150 units, because even though there's demand way up here, there's no supply and therefore you cannot actually trade more than 150 units.
So the new point of trade happening in this market would be a price point of 0. 5 and a quantity value of 150. Now what needs to happen is the price needs to increase until we get back to a point of equilibrium right here at a price of 0. 75.