The algebraic approach to equilibrium. The algebraic approach to equilibrium analysis is to solve, simultaneously, the algebraic equations for demand and supply. In the example given above, the demand equation for good X was
and the supply equation for good X was
To solve simultaneously, one first rewrites either the demand or the supply equation as a function of price. In the example above, the supply curve may be rewritten as follows:
Substituting this expression into the demand equation, one can solve for the equilibrium price:
The equilibrium price of good X is found to be $2. Substituting the equilibrium price of 2 into the rewritten supply equation for good X, one has:
The equilibrium quantity is found to be 4 units of good X.
A graphical depiction of equilibrium. The graphical approach to equilibrium analysis is illustrated in Figure . The equilibrium price and quantity are determined by the intersection of the two curves. The equilibrium quantity is 4 units of good X, and the equilibrium price is $2 per unit of good X. This result is the same as the one obtained by simultaneously solving the algebraic equations for demand and supply.
A price of $2 and a quantity of 4 units of X are the equilibrium price and quantity only when the demand and supply for good X are exactly as depicted in Figure . If either the demand curve or the supply curve shifts, the equilibrium price and quantity change. Examples of shifts in the demand and supply curves and the resultant changes in equilibrium are illustrated in Figures (a) and (b). In Figure (a), a shift to left of the demand curve, from D A to D B, leads to a decrease in both the equilibrium price and quantity of good X, while a shift to the right of the demand curve, from D A to D C, leads to an increase in both the equilibrium price and quantity of good X, assuming supply is held constant‐the ceteris paribus assumption. In Figure (b), a shift to the left of the supply curve, from S A to S B, leads to an increase in the equilibrium price of good X but a decrease in the equilibrium quantity of good X, assuming demand is held constant. A shift to the right of the supply curve, from S A to S C, leads to a decrease in the equilibrium price of good X but an increase in the equilibrium quantity of good X, again assuming that demand is held constant.