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