Represents quantity demanded when price is zero (Qd = a – bP)
Represents how much quantity demanded changes for a unit change in price (Qd = a – bP, enter positive value for 'b')
Represents quantity supplied when price is zero (Qs = c + dP)
Represents how much quantity supplied changes for a unit change in price (Qs = c + dP, enter positive value for 'd')
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.style.display = "none";
resultDiv.innerHTML = "";
if (isNaN(demandIntercept) || isNaN(demandSlope) || isNaN(supplyIntercept) || isNaN(supplySlope)) {
resultDiv.style.display = "block";
resultDiv.className = "result error";
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (demandSlope <= 0) {
resultDiv.style.display = "block";
resultDiv.className = "result error";
resultDiv.innerHTML = "The demand slope coefficient (b) must be a positive value for a typical downward-sloping demand curve (Qd = a – bP).";
return;
}
if (supplySlope a – bP = c + dP
// a – c = dP + bP
// a – c = P(d + b)
// P = (a – c) / (b + d)
var equilibriumPrice = (demandIntercept – supplyIntercept) / (demandSlope + supplySlope);
// Calculate Equilibrium Quantity (Q) using either demand or supply function
// Q = a – bP
var equilibriumQuantity = demandIntercept – (demandSlope * equilibriumPrice);
// Or using supply: Q = c + dP
// var equilibriumQuantity = supplyIntercept + (supplySlope * equilibriumPrice);
resultDiv.style.display = "block";
resultDiv.className = "result"; // Reset to default result class
if (equilibriumPrice < 0 || equilibriumQuantity < 0) {
resultDiv.innerHTML = "Calculated Equilibrium:" +
"Equilibrium Price: " + equilibriumPrice.toFixed(2) + "" +
"Equilibrium Quantity: " + equilibriumQuantity.toFixed(2) + "" +
"Note: Negative price or quantity suggests that an economic equilibrium does not exist under normal market conditions with these functions, or that the functions intersect outside the economically relevant positive quadrant.";
} else {
resultDiv.innerHTML = "Calculated Equilibrium:" +
"Equilibrium Price: " + equilibriumPrice.toFixed(2) + "" +
"Equilibrium Quantity: " + equilibriumQuantity.toFixed(2) + "";
}
}
Understanding Equilibrium Price and Quantity
In economics, the concept of equilibrium price and equilibrium quantity is fundamental to understanding how markets function. It represents the point where the forces of supply and demand are balanced, leading to a stable market condition.
What is Equilibrium?
Market equilibrium occurs when the quantity of a good or service that consumers are willing and able to buy (quantity demanded) is exactly equal to the quantity that producers are willing and able to sell (quantity supplied) at a specific price. At this point, there is no surplus (excess supply) or shortage (excess demand) in the market.
The Demand Function
The demand function describes the relationship between the price of a good and the quantity consumers are willing to purchase. A common linear demand function is expressed as:
Qd = a - bP
Qd: Quantity Demanded
a: The demand intercept, representing the quantity demanded when the price (P) is zero. It reflects all non-price determinants of demand.
b: The absolute value of the slope of the demand curve. It indicates how much the quantity demanded changes for every one-unit change in price. Since demand curves typically slope downwards, 'b' is a positive value, making '-bP' a negative relationship.
P: Price of the good
For example, if Qd = 100 - 2P, it means that at a price of 0, 100 units are demanded, and for every $1 increase in price, the quantity demanded decreases by 2 units.
The Supply Function
The supply function illustrates the relationship between the price of a good and the quantity producers are willing to offer for sale. A common linear supply function is:
Qs = c + dP
Qs: Quantity Supplied
c: The supply intercept, representing the quantity supplied when the price (P) is zero. It reflects all non-price determinants of supply.
d: The slope of the supply curve. It indicates how much the quantity supplied changes for every one-unit change in price. Since supply curves typically slope upwards, 'd' is a positive value.
P: Price of the good
For example, if Qs = 10 + 3P, it means that at a price of 0, 10 units are supplied, and for every $1 increase in price, the quantity supplied increases by 3 units.
Calculating Equilibrium
To find the equilibrium price and quantity, we set the quantity demanded equal to the quantity supplied (Qd = Qs) and solve for P (equilibrium price). Once the equilibrium price is found, we substitute it back into either the demand or supply function to find the equilibrium quantity.
Given:
Qd = a - bP
Qs = c + dP
At equilibrium:
a - bP = c + dP
Rearranging to solve for P:
a - c = dP + bP
a - c = P(d + b)
Equilibrium Price (P) = (a – c) / (b + d)
Once P is known, substitute it into either equation to find Q:
Equilibrium Quantity (Q) = a – bP (or Q = c + dP)
How to Use the Calculator
Our Equilibrium Price & Quantity Calculator simplifies this process. You just need to input the coefficients from your demand and supply functions:
Demand Function Intercept (a): Enter the 'a' value from your demand equation (Qd = a – bP).
Demand Function Slope Coefficient (b): Enter the positive 'b' value from your demand equation.
Supply Function Intercept (c): Enter the 'c' value from your supply equation (Qs = c + dP).
Supply Function Slope Coefficient (d): Enter the positive 'd' value from your supply equation.
Click "Calculate Equilibrium," and the tool will instantly display the equilibrium price and the corresponding equilibrium quantity for your market.
Example Scenario
Let's consider a market for a new gadget with the following demand and supply functions:
Demand Function:Qd = 150 - 5P (Here, a = 150, b = 5)
Supply Function:Qs = 30 + 7P (Here, c = 30, d = 7)
Using the calculator:
Demand Function Intercept (a): 150
Demand Function Slope Coefficient (b): 5
Supply Function Intercept (c): 30
Supply Function Slope Coefficient (d): 7
The calculation would be:
P = (150 – 30) / (5 + 7) = 120 / 12 = 10
Q = 150 – (5 * 10) = 150 – 50 = 100
Or Q = 30 + (7 * 10) = 30 + 70 = 100
The equilibrium price is 10, and the equilibrium quantity is 100 units.