Economists graphically represent the relationship between product price and quantity demanded with a demand curve. Typically, demand curves are downwards sloping, because as price increases, buyers are less likely to be willing or able to purchase whatever is being sold. Each individual buyer can have their own demand curve, showing how many products they are willing to purchase at any given price, as shown below. This graph shows what Jim's demand curve for graham crackers might be:

To find out how many boxes of graham crackers Jim will buy for a given price, extend a perpendicular line from the price on the y-axis to his demand curve. At the point of intersection, extend a line from the demand curve to the x-axis (perpendicular to the x-axis). Where it intersects the x-axis (quantity) is how many boxes of graham crackers Jim will buy. For instance, in the graph above, Jim will buy 3 boxes when the price is $2 a box.

Typically, economists don't look at individual demand curves, which can vary from person to person. Instead, they look at aggregate demand, the combined quantities demanded of all potential buyers. To do this, add the quantities which buyers are willing to buy at different prices. For instance, if Jim and Marvin are the only two buyers in the market for graham crackers, we would add how many they are willing to buy at price p=1 and record that as aggregate demand for p=1. Then we would add how many they are willing to buy at price p=2 and record that as aggregate demand for p=2, and so on. This results in the following graph of aggregate demand for graham crackers:

This method is called horizontal addition because you look at a price level, and add the separate quantities demanded across that price level, giving you total quantity demanded for that price.

There are many factors that can affect demand quantity, including income, prices, and preferences. Let's look at one good to see how this works. How much are you willing to pay for a cold soda? If you recently got a raise at your job, you might not mind buying a pricier soda, even if you don't need it. Your friend who has less money, however, might pick a generic brand, or they might stick with tap water. Below are possible demand curves for you (with your big raise) and your friend (without your big raise). Note that you are willing to buy more soda than your friend is:

What if soda cost a dollar yesterday and costs two dollars today? That might make you think twice about getting the same soda you drank yesterday. Likewise, if it cost two dollars yesterday and a dollar today, you might be more willing to buy the soda than usual. We can see this on the graph on a single demand curve. When the price is a dollar, the quantity demanded is higher than when the price is two dollars. What this means in the real world is that if two companies charge different prices for the same good, the company that charges a lower price will get more customers. (Exceptions to this general rule may occur when there is a real or perceived difference in quality of the goods being sold).

We have been looking at how changes in price can affect buyers' decisions: when price increases, demand decreases, and vice versa. However we have been assuming that when the price changes, all else is staying the same; this restriction allows us to use the same demand curve, with changes in demand being represented by movements up and down the same curve. This model of a buyer moving up and down one demand curve is correct if the only thing that is changing is the price of the good. If preferences or income change, however, the demand curve can actually shift.

For example, let's say that Conan's initial demand curve for concert tickets looks like curve 1. If Conan gets a new job, with a permanently higher income, however, his demand curve will shift outwards, to curve 2. Why is this? Conan realizes that he has more money, and that, as long as he doesn't lose his new job, he will always have more money. That means that he can buy more of what he likes, and he will have a higher demand curve for all normal goods.

Note that for any price level, Conan's demand is now higher than it was before the demand shift. This can also occur with a change in buyer preferences. If Conan suddenly decides that he wants to collect jazz CDs, and he now likes jazz CDs much more than he did before, his demand curve will shift outwards, reflecting his new appreciation of jazz, and his willingness to pay more for the same CDs, since they have become more valuable in his eyes. Shifts in demand curves are caused by changes in income (which make the goods seem more or less expensive) or changes in preferences (which make the goods seem more or less valuable).

It is also possible to model demand using equations, known as demand equations or demand functions. While these equations can be very complex, for now we will use simple algebraic equations. We have been showing demand as straight, downward-sloping lines, which can easily be translated into mathematical equations, and vice versa. Just as the graphs provide a visual guide to consumer behavior, demand functions provide a numerical guide to consumer behavior. For example, if Sean's demand curve for T-shirts looks like this: The corresponding equation that describes Sean's demand for T-shirts is simply the equation for the line on the graph, or: If we want to see how much Sean will buy if the price is 10, we plug 10 in for P and solve for Q. In this case, [25 - 2(10)] = 5 T-shirts. When we want to find aggregate demand using the algebraic approach instead of the graphical approach, we just add the demand equations together. So, if we're adding Sean's demand for T-shirts to Noah's demand for T-shirts, it looks like this: If price for T-shirts is still equal to 10, we find out that together, Sean and Noah will buy

[65 - 5(10)] = 15 T-shirts.

One caveat in this method is that you can only add the equations together when both will result in positive demand. For example, if the price of a T-shirt is $13, Sean would supposedly want to buy [25 - 2(13)] = -1 T-shirts. Obviously that is impossible, and Sean will buy 0 T-shirts. But because Sean's demand equation would yield the answer –1, adding the demand equations together would result in a wrong answer. When using this method, always check to make sure that there will be no negative demand for the given price before adding equations together. To find how many T-shirts Sean and Noah would buy in this case, you would only look at Noah's demand,