[MUSIC] Let's go through a numerical example. I'm going to use the same numerical example that we used for price floors and price ceilings. Where the demand is equal to 70- Q, and the supply is equal to 10 + 2Q. We found the equilibrium quantity by setting the supply equals demand and we found an equilibrium quantity of 20. We plugged the 20 into the supply equation or the demand equation to find the equilibrium price of 50. And consumer surplus is this triangle which is 20 times 20 divided by 2 or 200, and producer surplus is 50- 10, which is 40 times 20 divided by 2, which is 400. So that total surplus is 600. Now that we have a tax in place, what we need to do is to realize that the price to the producer and the price to the consumers are not the same. Because, of course, the government is standing in between taking some of this money out, so that what the consumer is paying minus the tax is equal to what the producer is pocketing. So lets set the tax at $15 per unit. So again, my tax is going to be $15 per unit. And now I can set these two equations together, taking this third equation in to account. So, what do we have? We have 70- Q, right, the price to consumers, minus the tax is equal to the price that the producers are getting, which is 10 + 2Q. Let's solve this equation. Moving Q to this side we get 3Q. Moving the 10 to this side we get 70- 25. Which is equal to 45 and we get that Q is equal to 45- 3, which is 15. Graphically what we've done of course, is we've shifted up the supply curve By 15 units, and what we found is this new quantity here. And we've said that quantity is 15. We can plug the quantity of 15 back into the demand equation, and we get the price to the consumers. As being 70- 15 which is equal to 55. So this price here is 55 and we can see that the price to the consumers has increased by $5. We can take the quantity of 15 and plug it into the supply equation, and we get that the price that the producers are getting is 15 times 2, which is 30, plus 10, which is 40. In other words, this price here is equal to 40. And we can see that the price to them has dropped by $10. And just to double check, we can see that 10 + 5 is equal to 15. So we found the new equilibrium quantity, Q1. We found the new price to the consumers, the price that the consumers pay, which is 55, and we found the price that the producers get which is equal to 40. We are now ready to calculate consumer surplus, producer surplus, government revenues, and total surplus. Let's go ahead and do that.