Barry Haworth

University of Louisville

Department of Economics

Economics 201

### Some Quick Algebra Help: How to Find P* and Q*

**Need some quick help with calculating equilibrium price
and quantity algebraically?** In a microeconomics class,
calculating equilibrium price and quantity in a Demand and
Supply model is one of those constants - kind of like
death and taxes - you know you'll end up doing it.
How is it done? Using the numerical values from section
A of the handout "Who Pays the Tax", let's take a closer
look.

**Step 1:** What are the Demand and Supply equations?

- Demand: P = 3 - 0.5Qd

- Supply: P = 1 + 0.5Qs

**Step 2:** At equilibrium, Qd = Qs, and so let's
substitute Q into the Demand and Supply equations
(since Qd and Qs will be the same anyway).

- Demand: P = 3 - 0.5Q

- Supply: P = 1 + 0.5Q

**Step 3:** Equilibrium occurs where Demand crosses
Supply. Therefore, let's set the Demand and Supply
equations equal to one another and solve for equilibrium Q.

- 3 - 0.5Q = 1 + 0.5Q

- 3 - 1 = 0.5Q + 0.5Q

- 2 = Q
- Q* = 2

**Step 4:** Find the equilibrium price P* by plugging
the equilibrium quantity Q* into either the Demand or
Supply equation (it doesn't matter which one if we're
calculating equilibrium). Let's do both anyway, just to
double check ourselves.

- Plugging Q = 2 into the Demand equation:
- P* = 3 - 0.5(2) = $2

- Plugging Q = 2 into the Supply equation:
- P* = 1 + 0.5(2) = $2

**The equilibrium price and quantity?**

- P* = $2
- Q* = 2

Return to the handout
"Who Pays the Tax?"