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).

The Algebraic Approach

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:

Q = 25 - 2P

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,