How to Calculate Equilibrium Price

Equilibrium Price and Quantity Calculator

Quantity demanded when price is zero (Qd = a – bP)

Absolute value of the change in quantity demanded per unit change in price

Quantity supplied when price is zero (Qs = c + dP)

Change in quantity supplied per unit change in price

Results:

Equilibrium Price (Pe): –

Equilibrium Quantity (Qe): –

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); if (isNaN(demandIntercept) || isNaN(demandSlope) || isNaN(supplyIntercept) || isNaN(supplySlope)) { document.getElementById('equilibriumPriceOutput').innerHTML = 'Equilibrium Price (Pe): Please enter valid numbers for all fields.'; document.getElementById('equilibriumQuantityOutput').innerHTML = 'Equilibrium Quantity (Qe): -'; return; } if (demandSlope <= 0 || supplySlope <= 0) { document.getElementById('equilibriumPriceOutput').innerHTML = 'Equilibrium Price (Pe): Demand and Supply slopes must be positive.'; document.getElementById('equilibriumQuantityOutput').innerHTML = 'Equilibrium Quantity (Qe): -'; return; } if ((demandIntercept – supplyIntercept) / (demandSlope + supplySlope) < 0) { document.getElementById('equilibriumPriceOutput').innerHTML = 'Equilibrium Price (Pe): Cannot be negative. Check your inputs.'; document.getElementById('equilibriumQuantityOutput').innerHTML = 'Equilibrium Quantity (Qe): -'; return; } var equilibriumPrice = (demandIntercept – supplyIntercept) / (demandSlope + supplySlope); var equilibriumQuantity = demandIntercept – (demandSlope * equilibriumPrice); // Or using supply function: var equilibriumQuantity = supplyIntercept + (supplySlope * equilibriumPrice); if (equilibriumQuantity < 0) { document.getElementById('equilibriumPriceOutput').innerHTML = 'Equilibrium Price (Pe): No positive equilibrium quantity exists with these inputs.'; document.getElementById('equilibriumQuantityOutput').innerHTML = 'Equilibrium Quantity (Qe): -'; return; } document.getElementById('equilibriumPriceOutput').innerHTML = 'Equilibrium Price (Pe): ' + equilibriumPrice.toFixed(2); document.getElementById('equilibriumQuantityOutput').innerHTML = 'Equilibrium Quantity (Qe): ' + 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 quantity of a good or service demanded by consumers perfectly matches the quantity supplied by producers. At this point, the market is said to be in balance, with no surplus (excess supply) or shortage (excess demand).

The Forces of Supply and Demand

To grasp equilibrium, we must first understand its two main components:

• Demand: This refers to the quantity of a good or service that consumers are willing and able to purchase at various prices during a specific period. The Law of Demand states that, all else being equal, as the price of a good increases, the quantity demanded decreases, and vice versa. A typical linear demand function is expressed as:
  Qd = a - bP
  where Qd is quantity demanded, P is price, a is the demand intercept (quantity demanded at zero price), and b is the absolute value of the slope of the demand curve (how much quantity demanded changes with price).
• Supply: This refers to the quantity of a good or service that producers are willing and able to offer for sale at various prices during a specific period. The Law of Supply states that, all else being equal, as the price of a good increases, the quantity supplied increases, and vice versa. A typical linear supply function is expressed as:
  Qs = c + dP
  where Qs is quantity supplied, P is price, c is the supply intercept (quantity supplied at zero price), and d is the slope of the supply curve (how much quantity supplied changes with price).

Calculating Equilibrium

Equilibrium occurs when the quantity demanded equals the quantity supplied (Qd = Qs). By setting the demand and supply equations equal to each other, we can solve for the equilibrium price (Pe) and then use that price to find the equilibrium quantity (Qe).

Given the linear functions:

Qd = a - bP

Qs = c + dP

To find the Equilibrium Price (Pe):

a - bP = c + dP

a - c = dP + bP

a - c = P(d + b)

Pe = (a - c) / (d + b)

Once you have Pe, you can substitute it back into either the demand or supply equation to find the Equilibrium Quantity (Qe):

Qe = a - b * Pe

or

Qe = c + d * Pe

Example Scenario

Let's consider a market for a new gadget with the following demand and supply functions:

• Demand Function: Qd = 100 - 2P (Here, a = 100, b = 2)
• Supply Function: Qs = 20 + 3P (Here, c = 20, d = 3)

Using the calculator above, you would input:

• Demand Intercept (a): 100
• Demand Slope (b): 2
• Supply Intercept (c): 20
• Supply Slope (d): 3

Let's calculate the equilibrium manually:

1. Find Equilibrium Price (Pe):

Pe = (a - c) / (d + b)

Pe = (100 - 20) / (3 + 2)

Pe = 80 / 5

Pe = 16

So, the equilibrium price for the gadget is $16.

2. Find Equilibrium Quantity (Qe):

Using the demand function:

Qe = 100 - 2 * 16

Qe = 100 - 32

Qe = 68

Using the supply function (to verify):

Qe = 20 + 3 * 16

Qe = 20 + 48

Qe = 68

Thus, the equilibrium quantity is 68 units. At a price of $16, consumers will demand 68 gadgets, and producers will supply 68 gadgets, leading to a balanced market.

Importance of Equilibrium

Understanding equilibrium is crucial for businesses, policymakers, and economists. It helps in:

• Pricing Strategies: Businesses can use this to set optimal prices for their products.
• Market Analysis: It provides insights into market efficiency and potential imbalances.
• Policy Making: Governments can analyze the impact of taxes, subsidies, or price controls on market equilibrium.

The calculator above simplifies this process, allowing you to quickly determine the equilibrium price and quantity for any given linear demand and supply functions.