# Equilibrium analysis

**Chapter 3** – Equilibrium analysis (algebra review)

What is equilibrium? In a specified model, a lack of tendency to change.

This is static equilibrium – study of statics.

Is equilibrium desirable? Depends.

Partial equilibrium – only part of model considered, ie ceteris paribus.

**Solving a linear model**

Graph:

Economics | “Right” way |

No excess demand or supply implies that , so

This is the intersection of sets
and

**A non-linear example**

The demand function is a quadratic function

Only non-negative P’s and Q’s are considered so the demand curve is a segment of
a parabola.

Graph:

Excess demand = 0, so

The above is a quadratic equation that can be written as

aP^{2} + bP + c = 0

To solve for P:

The quadratic formula! A good formula to memorize.

Try this one:

Answer: P = 1, Q = 3

**Higher degree polynomials
**

Factoring by trial and error

Find a factor, then use quadratic formula or find another factor: