Equilibrium Price and Quantity

Demand and supply curves are graphical representations of the relationships between price and quantity. Sometimes it is useful to characterize these relationships as straight lines, rather than the curved lines as in Figure 5-3 from the text. Once we know the equations for these relationships, it is a straightforward exercise in algebra to determine the equilibrium price and quantity.

The general equation for a linear (straight-line)
demand curve is *P* = *a* -*bQ _{D}*. (You will note this
conforms with the economics convention of placing the price on the vertical
axis and the quantity demanded on the horizontal axis, rather than our usual
interpretation of quantity as a function of price. This convention can be traced
to

The general equation for a linear supply curve is *P*
= *c* + *dQ _{S}*, where

To find the equilibrium price, we simply add the condition
that quantity demanded equals quantity supplied in equilibrium: *Q _{D}*
=

As long as the greatest price consumers willingly pay (*a*)
exceeds the lowest price at which producers will offer some output (*c*),
the equilibrium price will be positive:
> 0.

If we insert this value for the equilibrium quantity into
either the demand or supply equation, we can determine that the equilibrium
price is *P _{E}* = .
Since

Consider the following numerical example:

*P* = 20 - 0.6*Q _{D}*

*P* = 8 + 0.4 *Q _{S}*

*Q _{D}* =

In this market, *a* = 20, *b* = 0.6, *c*
= 8, and *d* = 0.4. Inserting these values into our general solutions yields
an equilibrium quantity of *Q _{E}* =
= 12, and an equilibrium price of