Determine the price where quantity supplied equals quantity demanded.
Understanding Equilibrium Price
The equilibrium price is a fundamental concept in economics that represents the price of a good or service where the quantity demanded by consumers equals the quantity supplied by producers. At this price, the market is considered to be in balance, with no surplus or shortage of the product. It's the point where the intentions of buyers and sellers align.
The Math Behind Equilibrium
To find the equilibrium price and quantity, we typically use simple linear supply and demand equations.
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 (quantity demanded when price is zero)
b is the slope of the demand curve (how quantity demanded changes with price; typically positive, but represented as a negative coefficient in the equation)
c is the supply intercept (quantity supplied when price is zero)
d is the slope of the supply curve (how quantity supplied changes with price; typically positive)
At equilibrium, the quantity demanded equals the quantity supplied (Qd = Qs). To find the equilibrium price (Pe), we set the two equations equal to each other:
a – bP = c + dP
Now, we solve for P:
a – c = dP + bP a – c = P(d + b) Pe = (a – c) / (b + d)
Once the equilibrium price (Pe) is found, you can substitute it back into either the demand or supply equation to find the equilibrium quantity (Qe). For example, using the demand equation:
Qe = a – bPe
How to Use This Calculator
This calculator simplifies the process. You need to input the coefficients of your linear demand and supply curves:
Demand Curve Intercept (a): The quantity demanded when the price is zero.
Demand Curve Slope (b): The absolute value of how quantity demanded changes per unit change in price.
Supply Curve Intercept (c): The quantity supplied when the price is zero.
Supply Curve Slope (d): How quantity supplied changes per unit change in price.
After entering these values, click "Calculate Equilibrium" to find the price at which the market will naturally settle.
Example Calculation
Let's consider a hypothetical market for artisan bread:
Demand Equation: Qd = 150 – 5P
Supply Equation: Qs = 30 + 3P
In this case:
Demand Intercept (a) = 150
Demand Slope (b) = 5
Supply Intercept (c) = 30
Supply Slope (d) = 3
Using the formula Pe = (a – c) / (b + d):
Pe = (150 – 30) / (5 + 3) Pe = 120 / 8 Pe = 15
The equilibrium price is 15. To find the equilibrium quantity, substitute P=15 into either equation:
Qd = 150 – 5(15) = 150 – 75 = 75 Qs = 30 + 3(15) = 30 + 45 = 75
So, the equilibrium quantity is 75 units. At a price of 15, 75 units will be demanded and 75 units will be supplied.
Importance of Equilibrium Price
The equilibrium price is crucial for understanding market dynamics. It helps businesses set prices, governments analyze the impact of policies (like taxes or subsidies), and economists predict market outcomes. Deviations from equilibrium lead to either shortages (price too low) or surpluses (price too high), prompting market forces to push the price back towards equilibrium.
function calculateEquilibrium() {
var demandIntercept = parseFloat(document.getElementById("demandIntercept").value);
var demandSlope = parseFloat(document.getElementById("demandSlope").value);
var supplyIntercept = parseFloat(document.getElementById("supplyIntercept").value);
var supplySlope = parseFloat(document.getElementById("supplySlope").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = "; // Clear previous result
if (isNaN(demandIntercept) || isNaN(demandSlope) || isNaN(supplyIntercept) || isNaN(supplySlope)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
// Ensure slopes are positive in the denominator calculation
// Demand slope 'b' is typically positive in the Q = a – bP form where P is price
// Supply slope 'd' is typically positive in the Q = c + dP form where P is price
// The formula derived P_e = (a – c) / (b + d) assumes b and d are the positive coefficients
// Check for valid economic conditions (e.g., slopes usually positive for supply, demand slope leading to positive quantity)
if (demandSlope <= 0) {
resultDiv.innerHTML = "Demand slope (b) should generally be positive in the equation Q = a – bP when interpreted as the coefficient.";
return;
}
if (supplySlope <= 0) {
resultDiv.innerHTML = "Supply slope (d) should generally be positive in the equation Q = c + dP.";
return;
}
if (demandIntercept 0) {
resultDiv.innerHTML = "Economic conditions suggest no equilibrium point (demand at zero price is less than supply).";
return;
}
var denominator = demandSlope + supplySlope;
if (denominator === 0) {
resultDiv.innerHTML = "Error: Denominator is zero. Cannot calculate equilibrium price.";
return;
}
var equilibriumPrice = (demandIntercept – supplyIntercept) / denominator;
// Calculate equilibrium quantity using the demand equation Q = a – bP
var equilibriumQuantity = demandIntercept – (demandSlope * equilibriumPrice);
// Check if calculated quantity is negative (economically nonsensical for this model)
if (equilibriumPrice < 0 || equilibriumQuantity < 0) {
resultDiv.innerHTML = "Calculated price or quantity is negative, indicating no realistic market equilibrium under these parameters.";
} else {
resultDiv.innerHTML = "Equilibrium Price: " + equilibriumPrice.toFixed(2) + " | Equilibrium Quantity: " + equilibriumQuantity.toFixed(2);
}
}