[MUSIC] I'd like us to use a numerical example to look at the effects of a price ceiling. We found using the supply equation and the demand equation that we have an equilibrium price of 50 and an equilibrium quantity of 20 units. Suppose the government decides that the price of 50 is too high, and instead sets a price ceiling at $40 a unit. Graphically, we know that the amount that's exchanged in the market is going to be the minimum of the quantity supplied and quantity demanded. Let's go ahead and find what is the quantity demanded at this price of 40 and what is the quantity supplied at this price of 40. Let's start with the quantity demanded. What we do here is we plug the price of 40 into our demand equation. And we get 40 is equal to 70 minus quantity demanded or quantity demanded is equal to 70 minus 40 which is 30 units. So at this lower price, quantity demanded is, of course, greater than the quantity demanded at a higher price, and precisely in this case, the quantity demanded is 30 units. Similarly, we can go ahead and find the quantity supplied at this price ceiling of $40. We'll do that by plugging 40 into the supply equation. We set 40 is equal to 10 plus 2 times quantity supplied, and we get that 2Qs is equal to 30, or Qs is equal to 15. Not surprisingly, quantity supplied at this binding price is less than the quantity supplied at a price of 50, because supply is upward sloping. And at a lower price, sellers will be willing to sell only a smaller quantity. So we can see the quantity supplied, I'm sorry, quantity demanded exceeds quantity supplied, and again, we have a shortage or excess demand. And in this particular case, we have excess demand of exactly 15 units. 30 minus 15 is 15. What about the total surplus that's generated in the economy? At equilibrium, the total surplus was this whole triangle here. But now we have the government intervene, and the amount that's exchanged in the market is the minimum of quantity supplied and quantity demanded. The amount that exchange in the market is going to be limited to 15 units. And so what we're losing is this triangle here. This triangle here is our deadweight loss. Let's go ahead and calculate deadweight loss. Again, an area of a triangle is height times base divided by two. It's easy to see what the base is, we were producing 20 units, now we're producing 15 units, so the base here is equal to 5. What about the height? The height is the difference between this price of 40 and whatever number this is. So we have to go ahead and calculate this number. The way we do that is by using our equation of the demand curve. We take this quantity of 15, and we plug it into our demand curve. So we get the marginal benefit at a quantity of 15 units is whatever the demand curve tells us. 70 minus the quantity of 15, and we get that the marginal benefit is $55. So this number here is $55. Now we can calculate the height. The height is 55, I'm sorry 55 minus 40, which is equal to 15, and we have everything that we need to calculate deadweight loss. Again, a deadweight loss is the height. So that's 15 times the base, which is five divided by two, and that in dollars is equal to our deadweight loss. What is the meaning of the deadweight loss? We calculated total surplus at the equilibrium, and we found that it's equal to $600. We can compare that to the total surplus at the price ceiling of $40, and what we will find is that it's equal to the original $600 minus our deadweight loss. Okay, so that's the meaning of the deadweight loss. It's the shrinking of the total sub less by the amount of the deadweight loss, due to the fact that the government stepped in and set a price ceiling.