Calculate the market equilibrium quantity where supply and demand intersect.
Understanding Equilibrium Quantity
In economics, the equilibrium quantity represents the amount of a good or service that is produced and consumed at the market equilibrium price. At this point, the quantity supplied by producers exactly matches the quantity demanded by consumers. This balance signifies a stable market condition where there is no inherent pressure for the price or quantity to change, assuming all other factors remain constant.
The equilibrium is found at the intersection of the demand curve and the supply curve. These curves are typically represented by equations.
The Math Behind Equilibrium
The standard linear equations for demand and supply are:
Demand Equation:Qd = a - bP
Supply Equation:Qs = c + dP
Where:
Qd is the quantity demanded
Qs is the quantity supplied
P is the price
a is the demand intercept (the quantity demanded when price is zero)
b is the slope of the demand curve (typically negative, indicating that as price increases, quantity demanded decreases)
c is the supply intercept (the quantity supplied when price is zero)
d is the slope of the supply curve (typically positive, indicating that as price increases, quantity supplied increases)
At equilibrium, the quantity demanded equals the quantity supplied (Qd = Qs), and the price is the equilibrium price (Pe). To find the equilibrium quantity (Qe), we first set the two equations equal to each other and solve for the equilibrium price Pe:
a - bPe = c + dPe a - c = dPe + bPe a - c = Pe(d + b) Pe = (a - c) / (b + d)
Once we have the equilibrium price Pe, we can substitute it back into either the demand or the supply equation to find the equilibrium quantity Qe. Using the supply equation for simplicity:
Qe = c + d * Pe Qe = c + d * [(a - c) / (b + d)]
This calculator directly computes Qe using the provided intercept and slope values.
Example:
Suppose we have the following demand and supply functions:
Demand: Qd = 100 - 2P (Here, a = 100, b = 2)
Supply: Qs = 10 + 3P (Here, c = 10, d = 3)
Using the calculator inputs:
Demand Intercept (a): 100
Demand Slope (b): 2
Supply Intercept (c): 10
Supply Slope (d): 3
The calculator will determine the equilibrium quantity.