How to Calculate the Equilibrium Quantity

The equilibrium quantity represents a market state where the quantity of a good or service supplied by producers precisely matches the quantity demanded by consumers. This balance between supply and demand leads to a stable market price and quantity.

Understanding Supply and Demand Equations

Determining the equilibrium quantity relies on mathematical expressions describing the relationship between price and the quantity supplied or demanded. A supply equation illustrates the quantity sellers are willing to offer at various price points. A demand equation shows the quantity buyers are willing to purchase at different prices.

These relationships are often represented by linear equations in the form Q = a + bP, where ‘Q’ is quantity and ‘P’ is price. In a demand equation, the coefficient ‘b’ is negative, indicating that as price increases, the quantity demanded decreases. For a supply equation, the coefficient ‘b’ is positive, reflecting that producers are willing to supply more as prices rise. The ‘a’ coefficient in both equations represents the quantity when the price is zero, serving as an intercept.

Calculating Equilibrium Quantity

The process of finding the equilibrium quantity begins by setting the quantity demanded equation equal to the quantity supplied equation. This reflects the market condition where consumers’ desired amount matches what producers are willing to sell. For instance, if the demand equation is Qd = 100 – 2P and the supply equation is Qs = 20 + 3P, you would set 100 – 2P equal to 20 + 3P.

The next step involves solving this combined equation for the equilibrium price (P). Continuing the example, solving 100 – 2P = 20 + 3P yields an equilibrium price of 16. This price is the point at which the market achieves balance between supply and demand.

To determine the equilibrium quantity, substitute the calculated equilibrium price back into either the original demand equation or the original supply equation. Using the demand equation (Qd = 100 – 2P) and the equilibrium price of 16, the quantity demanded would be 100 – 2(16), resulting in an equilibrium quantity of 68. Using the supply equation (Qs = 20 + 3P) with the price of 16, the quantity supplied would be 20 + 3(16), also resulting in an equilibrium quantity of 68. Both equations should yield the identical equilibrium quantity.

Verifying Your Calculation

After calculating the equilibrium price and quantity, it is prudent to verify the accuracy of your results. One effective method is to substitute the calculated equilibrium quantity back into both the demand and supply equations. When you perform this substitution, both equations should yield the same equilibrium price.

Alternatively, you can substitute the determined equilibrium price into both the demand and supply equations. This action should result in both equations producing the same equilibrium quantity. If the values derived from both equations do not match, it indicates a miscalculation, and the previous steps should be re-examined to identify any algebraic errors.