How to Calculate Equilibrium Price and Quantity from Demand and Supply Equations?

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied. Given the equations:

• Demand: p = 200 – 1qd
• Supply: p = 100 + 1qs

At equilibrium, qd = qs. Let’s denote this common quantity as q.

Now we can set the two equations equal to each other:

200 - q = 100 + q

Next, we solve for q:

200 - 100 = q + q

100 = 2q

q = 50

The equilibrium quantity (q) is 50.

Now, to find the equilibrium price, we can substitute q back into either the demand or supply equation. We’ll use the demand equation:

p = 200 - 1qd

p = 200 - 50

p = 150

The equilibrium price (p) is 150.

In summary:

• Equilibrium Quantity: 50
• Equilibrium Price: 150