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The Graphical Approach

By now, we are familiar with graphs of supply curves and demand curves.
To find market equilibrium, we combine the two curves onto one graph. The
point of intersection of supply and demand marks the point of equilibrium.
Unless interfered with, the market will settle at this price and quantity. Why
is this? At this point of intersection, buyers and sellers agree on
both price and quantity. For instance, in the graph below, we see that at the
equilibrium price p*, buyers want to buy exactly the same amount that sellers
want to sell.

If the price were higher, however, we can see that sellers would want to sell
more than buyers would want to buy. Likewise, if the price were lower, quantity
demanded would be greater than quantity supplied. The following graph shows the
discrepancy in supply and demand if the price is higher than the equilibrium
price:
Note that the quantity that sellers are willing to sell is much higher than the
quantity that buyers are willing to buy.

We can also see what happens when one of the curves shifts up or down in
response to outside factors. For example, if we were to look at the market for
Beanie Babies before and after they became a popular fad, we would see a shift
outwards from the initial demand curve over time. The reason for this is that
as people began to like Beanie Babies, their preferences changed, and they began
to want Beanie Babies enough that they would pay much more for each Beanie Baby
than they would have previously. We can see this new preference for Beanie
Babies in the outward shift of the demand curve: for every price, buyers will
buy more Beanie Babies than they would have before the fad.

Note that this combines two effects we studied earlier: there is a shift in the
demand curve, which causes a movement up the supply curve. These two effects
combine to reach the new market equilibrium, which has both a higher price and a
higher quantity than the previous market equilibrium.

It is only through a shift in either the supply or the demand curve that the
market equilibrium will change. Why is this? If neither curve shifts, and we
move along one of the curves, the market will naturally shift back to
equilibrium. For example, if we look at a market in equilibrium, and a store
tries to move up its supply curve by selling goods at a higher price, the result
will be that no one will buy the goods, since they are less expensive at the
store's competitors. The store will have to either go out of business, or move
its prices back down to equilibrium.

What happens if both curves shift? Will we end up at the same equilibrium
point? In this model, it is not possible to reach the same equilibrium: either
the price or the quantity can be the same as the previous equilibrium, but not
both, unless the curves shift back to their original positions. To illustrate
why this is true, consider the graph below. The initial equilibrium, between
supply curve 1 and demand curve 1, has price p* and quantity q*. If supply
shifts to supply curve 2, both equilibrium price and quantity change. It is now
possible to change back to our original price by shifting the demand curve to
position 2 or it is possible to revert to our original quantity by
shifting the demand curve to position 3. Note that we cannot reach the original
equilibrium point unless we move the curves back to their original points.

For a real world example, consider the market for oil. The initial supply and
demand curves would be at position 1 (p1). When the suppliers decide to
collaborate and supply less oil for every price, this causes a backwards shift
in the supply curve, to supply curve 2. This cuts the quantity supplied from
quantity 1 (q1) to quantity 2 (q2) and raises the price paid for oil along
demand curve 1. We can either shift the demand curve in to curve 2, maintaining
previous price levels, but decreasing consumption even more, or we can shift our
demand curve out to curve 3, maintaining previous levels of consumption but
raising prices. Since there is a tradeoff between having steady prices or
steady consumption, the consumers have to make a decision about which is more
important to them. In the short run, they will probably decide to pay the
higher prices to keep consumption steady (that is, they will shift out to curve
3), but if the prices stay high for a long time, they will start finding ways to
economize, (thereby shifting in to curve 2).

The Algebraic Approach

We have worked with supply and demand equations separately, but they can also be
combined to find market equilibrium. We have already established that at
equilibrium, there is one price, and one quantity, on which both the buyers and
the sellers agree. Graphically, we see that as a single intersection of two
curves. Mathematically, we will see it as the result of setting the two
equations equal in order to find equilibrium price and quantity.

If we are looking at the market for cans of paint, for instance, and we know
that the supply equation is as follows:

QS = -5 + 2P

And the demand equation is:

QD = 10 - P

Then to find the equilibrium point, we set the two equations equal. Notice that
quantity is on the left-hand side of both equations. Because quantity supplied
is equal to quantity demanded at equilibrium, we can set the right-hand sides of
the two equations equal.

QS = QD
-5 + 2P = 10 - P
3P = 15
P = 5

At equilibrium, paint will cost $5 a can. To find out the equilibrium quantity,
we can just plug the equilibrium price into either equation and solve for Q.

Q* = QS
QS = -5 + 2(5)
QS = Q* = 5 cans

Shifts up and down supply and demand curves are represented by plugging
different prices into the supply and demand equations: different prices yield
different quantities. For example, changing the price to $6 a can would
decrease quantity demanded from 5 cans to 4 cans, as we can see when we plug the
two prices into the demand function:

P = 5
QD = 10 - 5 = 5 cans

P = 6
QD = 10 - 6 = 4 cans

The equivalent of shifting supply and demand curves is changing the actual
supply and demand equations. Let's say that everyone in a small town just
recently painted their houses, and therefore no longer need any paint. This
means that they will be less willing to buy paint, even if the price doesn't go
up. Their new demand function might be:

QD = 7 - P

We can see that for any price, they will demand fewer cans of paint. At the old
equilibrium price of $5, they will only buy:

QD = 7 - 5 = 2 cans of paint

This new equation, representing a shift in demand, also causes a shift in market
equilibrium, which we can find by setting the new demand equation equal
to supply: