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today we're going to talk about how to equilibrium price and quantity using linear demand and linear supply equations for our example today we'll be using movie tickets for which the demand equals 80 minus 4p and the quantity supplied equals negative 20 plus 8 P the first thing we would like to do is actually plot our demand and supply equations for movie tickets to do this we must plot a couple of points for both demand and supply let's start with demand the first point we can plot on our demand curve is easy because we know that the cue intercept or the quantity that would be demanded at a price of 0 is 80,000 movie tickets so we can put a point right there on our quantity axis we need one more point to draw our linear demand curve so let's choose a price along our P axis and find out what the quantity would demand it would be at that price let's look at the quantity demanded at a price of 10 QD equals 80 minus 4 times 10 clearly we can see that at a price of 10 the quantity demanded equals 80 minus 40 or 40 so let's put a point at a price of 10 and at a quantity of 40 with two points along along a linear demand curve we can draw our demand graph there we have our demand graph our demand curve next we want to find the supply curve for movie tickets now we don't have a negative range on a quantity axis so the Q intercept of negative 20 isn't much help to us here what we can find very easily though is the P intercept or where the supply curve intercepts the vertical price axis to do this we simply set the quantity supplied as 0 and solve for P so 0 equals negative 20 plus 8 P 20 equals 8 P divide both sides by 8 and we see that P the price at which quantity supplied zero is 2.5 this tells us that our price our sorry our supply curve begins at 2.5 on the vertical axis which is approximately here now all we need to do is find one more point in our supply curve and we can show the supply curve so let's choose a price again of 10 or I'm sorry a quantity of 10 so if so let's find out what the quantity supplied would be at a price of 10 to do this we simply plug 10 into our supply equation so quantity supplied at a price of 10 equals negative 20 plus 8 times 10 which is 80 therefore the quantity supplied at a price of 10 equals 60 so now we can put one more point on our graph and we'll have our supply curve at a price of 10 the quantity supplied is equal to 60 now we've drawn both our supply and our demand curves but the next question is what is the exact equilibrium price and the equilibrium quantity of movie tickets judging from this graph we can see that the equilibrium price is somewhere around between 8 and 9 dollars and the equilibrium quantity is somewhere between 40 and 50 movie tickets however these are hardly accurate estimates so to find the actual equilibrium price and quantity all we have to do is set the quantity demanded equal to the quantity supplied since we know that the equilibrium price is the price at which quantity demanded and quantity supplied are equal so this shouldn't be hard let's just set our two equations equal to each other 80 minus 4p equals negative 20 plus 8p now when we solve for P we will know the equilibrium price for movie tickets to solve for P simply add 4p to both sides so we have 12 P and then add 20 to both sides equals 100 divide both sides by 12 so the equilibrium price equals 100 divided by 12 which is 8 point 3 3 now we know a more accurate calculation of the actual equilibrium price which we can now label on our graph as 8 dollars and 33 cents per movie ticket the next step of course is to find the equilibrium quantity to do this all we have to do is plug our equilibrium price into either the demand equation or the supply equation so let's start with demand and see what we get QD equals 80 minus 4 times 8.33 simplify and we see the QD equals 80 minus 33 point 3 2 the quantity demanded at equilibrium we'll call that QE equals 46 point six eight thousand movie tickets now to confirm this let's go ahead and solve for the quantity supplied at a price of eight point three three Q s equals negative 20 plus eight times eight point three three simplify and we see the quantity supplied equals negative 20 plus sixty six point six four so we see that the quantity at equilibrium is forty six point six four of course the reason we didn't get the exact result is because we rounded our numbers at one point so we should see that approximately forty six point six four thousand movie tickets would be demanded at the equilibrium price of 8.30 three cents so we've just shown how you can calculate equilibrium price and quantity using linear demand and supply equations