Market Equilibrium Price & Quantity Calculator
Enter the coefficients for your linear demand and supply equations to find the equilibrium price and quantity. This calculator assumes the following standard forms:
Demand Equation: Qd = a – bP
Supply Equation: Qs = c + dP
Understanding Market Equilibrium
Market equilibrium is a foundational concept in economics, representing a state where the quantity of a good or service demanded by consumers precisely matches the quantity supplied by producers. At this point, the market is said to "clear," meaning there is no surplus (excess supply) or shortage (excess demand), and the market price tends to remain stable, assuming all other factors influencing supply and demand are constant.
The Demand Curve
The demand curve illustrates the inverse relationship between the price of a product and the quantity consumers are willing and able to purchase. As the price of a good increases, the quantity demanded typically decreases, and vice-versa. This is known as the Law of Demand. A common linear representation of a demand equation is:
Qd = a – bP
- Qd: Quantity Demanded
- P: Price of the good
- a: The demand intercept, representing the quantity demanded when the price is zero. It signifies the maximum potential demand.
- b: The demand slope coefficient, which is typically a positive number. It indicates how responsive the quantity demanded is to a change in price. A larger 'b' means demand is more elastic (more sensitive to price changes).
The Supply Curve
The supply curve depicts the direct relationship between the price of a product and the quantity producers are willing and able to sell. As the price of a good increases, producers are generally incentivized to supply more of it, leading to an upward-sloping supply curve. This is known as the Law of Supply. A common linear representation of a supply equation is:
Qs = c + dP
- Qs: Quantity Supplied
- P: Price of the good
- c: The supply intercept, representing the quantity supplied when the price is zero. This can sometimes be a negative value in theoretical models, implying that producers will only supply a positive quantity once the price reaches a certain level.
- d: The supply slope coefficient, which is typically a positive number. It indicates how responsive the quantity supplied is to a change in price. A larger 'd' means supply is more elastic (more sensitive to price changes).
Calculating Equilibrium Price and Quantity
Equilibrium occurs where the quantity demanded equals the quantity supplied (Qd = Qs). To find the equilibrium price (P) and quantity (Q), we set the two equations equal to each other:
a – bP = c + dP
To solve for the equilibrium price (P), we rearrange the equation:
a – c = dP + bP
a – c = P(d + b)
Therefore, the Equilibrium Price (P) is:
P = (a – c) / (d + b)
Once the equilibrium price (P) is determined, you can substitute this value back into either the demand equation or the supply equation to find the Equilibrium Quantity (Q):
Using the demand equation: Q = a – bP
Using the supply equation: Q = c + dP
Both calculations should yield the same equilibrium quantity.
Example Calculation
Let's consider a market with the following demand and supply equations:
- Demand: Qd = 100 – 2P
- Supply: Qs = 20 + 3P
From these equations, we identify the coefficients:
- a = 100
- b = 2
- c = 20
- d = 3
Step 1: Calculate Equilibrium Price (P)
P = (a – c) / (d + b)
P = (100 – 20) / (3 + 2)
P = 80 / 5
P = 16
Step 2: Calculate Equilibrium Quantity (Q)
Using the demand equation:
Q = 100 – 2 * 16
Q = 100 – 32
Q = 68
Alternatively, using the supply equation:
Q = 20 + 3 * 16
Q = 20 + 48
Q = 68
In this example, the market equilibrium occurs at a price of 16 and a quantity of 68 units.