Enter the coefficients for your demand and supply functions to find the equilibrium price and quantity.
Understanding Market Equilibrium
Market equilibrium is a fundamental concept in microeconomics that describes the state where the quantity of a good or service that consumers are willing and able to buy (quantity demanded) is equal to the quantity that producers are willing and able to sell (quantity supplied). At this point, the market "clears," meaning there is no excess supply or demand. The price at which this occurs is known as the equilibrium price, and the corresponding quantity is the equilibrium quantity.
The Math Behind Equilibrium
We typically represent demand and supply using linear functions. A general linear demand function can be written as:
Qd = a – bP
Where:
Qd is the quantity demanded
a is the demand intercept (the quantity demanded when the price is zero)
b is the slope of the demand curve (representing how much quantity demanded changes with a change in price; it's typically positive, so we use -bP in the equation for a downward-sloping curve)
P is the price
A general linear supply function can be written as:
Qs = c + dP
Where:
Qs is the quantity supplied
c is the supply intercept (the quantity supplied when the price is zero, though often this is zero or near zero in practical examples)
d is the slope of the supply curve (representing how much quantity supplied changes with a change in price; it's typically positive for an upward-sloping curve)
P is the price
At market equilibrium, the quantity demanded equals the quantity supplied (Qd = Qs). To find the equilibrium price (Pe) and equilibrium quantity (Qe), we set the two equations equal to each other:
a – bPe = c + dPe
Now, we solve for Pe:
Rearrange the equation to group price terms: a - c = dPe + bPe
Factor out Pe: a - c = Pe(d + b)
Isolate Pe: Pe = (a - c) / (b + d)
Once the equilibrium price (Pe) is found, we can substitute it back into either the demand or supply equation to find the equilibrium quantity (Qe). Using the demand equation:
Qe = a – bPe
Or using the supply equation:
Qe = c + dPe
Both should yield the same result for Qe.
Calculator Inputs Explained
Demand Intercept (a): The maximum quantity consumers would demand if the price were zero.
Demand Slope (b): How sensitive the quantity demanded is to a change in price. A higher 'b' means demand changes more significantly with price.
Supply Intercept (c): The minimum quantity producers would supply if the price were zero. Often this is a small positive number or zero.
Supply Slope (d): How sensitive the quantity supplied is to a change in price. A higher 'd' means supply changes more significantly with price.
Use Cases
This calculator is useful for:
Students learning microeconomics to understand the mechanics of supply and demand.
Economists and analysts modeling market behavior.
Businesses predicting market outcomes based on price changes.
Policymakers assessing the potential impact of taxes, subsidies, or price controls.
By inputting the parameters of your specific market's demand and supply curves, you can quickly determine the equilibrium price and quantity, gaining valuable insights into market dynamics.
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 results
// Validate inputs
if (isNaN(demandIntercept) || isNaN(demandSlope) || isNaN(supplyIntercept) || isNaN(supplySlope)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
// Basic validation for slopes to ensure meaningful results (demand slope positive, supply slope negative for standard forms used in calculation logic)
// However, the formula handles positive slopes correctly for both as per standard linear equation formulation.
// The key is that 'b' in Qd = a – bP is the POSITIVE coefficient, and 'd' in Qs = c + dP is the POSITIVE coefficient.
// The formula Pe = (a – c) / (b + d) is derived from a – bP = c + dP, which implies P(b+d) = a-c.
// This requires the interpretation of 'b' and 'd' as positive values in the context of the formula's derivation.
var denominator = demandSlope + supplySlope;
if (denominator === 0) {
resultDiv.innerHTML = "Error: Demand and supply slopes are equal and opposite, leading to parallel lines or infinite solutions.";
return;
}
// Check if slopes are negative for demand and positive for supply, as is typical
if (demandSlope <= 0 || supplySlope <= 0) {
// This check is more about typical economic representation. The formula itself
// Pe = (a – c) / (b + d) works if 'b' and 'd' are the MAGNITUDES of the slopes.
// For example, if demand is Qd = 100 + 2P, then a=100, b=-2. If supply is Qs = 10 – 3P, then c=10, d=3.
// The formula used in the JavaScript assumes Qd = a – bP and Qs = c + dP where b and d are *positive* values representing the absolute change.
// Let's adjust the inputs to reflect this common convention or clarify the labels.
// Assuming the inputs are for standard forms: Qd = a – bP and Qs = c + dP where b and d are positive coefficients.
// If user enters negative for demand slope or positive for supply slope, the formula should still work assuming they mean the magnitude.
// The labels already guide towards a and b for demand, c and d for supply.
// Let's proceed with the calculation and add a note if results seem unusual.
}
var equilibriumPrice = (demandIntercept – supplyIntercept) / denominator;
var equilibriumQuantity;
// Calculate equilibrium quantity using the demand equation
equilibriumQuantity = demandIntercept – demandSlope * equilibriumPrice;
// Check for non-sensical economic results (negative price or quantity)
if (equilibriumPrice < 0 || equilibriumQuantity < 0) {
resultDiv.innerHTML = "Calculated equilibrium price or quantity is negative. This may indicate an unrealistic scenario or that equilibrium does not occur within positive price/quantity ranges.";
// Still display the calculated values if they are numerically valid
resultDiv.innerHTML += "Calculated Equilibrium Price (Pe): " + equilibriumPrice.toFixed(2) + "";
resultDiv.innerHTML += "Calculated Equilibrium Quantity (Qe): " + equilibriumQuantity.toFixed(2) + "";
} else {
resultDiv.innerHTML = "Market Equilibrium Found:" +
"Equilibrium Price (Pe): " + equilibriumPrice.toFixed(2) + "" +
"Equilibrium Quantity (Qe): " + equilibriumQuantity.toFixed(2) + "";
}
}