Learn to Accurately Calculate an Equilibrium Equation in Economics

Yin Yang Balance Harmony
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Economists use the term equilibrium to describe the balance between supply and demand in the marketplace. Under ideal market conditions, price tends to settle within a stable range when output satisfies customer demand for that good or service. Equilibrium is vulnerable to both internal and external influences. The appearance of a new product that disrupts the marketplace, such as the iPhone, is one example of an internal influence. The collapse of the real estate market as part of the Great Recession is an example of an external influence.

Oftentimes, economists must churn through massive amounts of data in order to solve equilibrium equations. This step-by-step guide will walk you through the basics of solving such problems.

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Using Algebra

The equilibrium price and quantity in a market is located at the intersection of the market supply curve and the market demand curve.

While it is helpful to see this graphically, it's also important to be able to solve mathematically for the equilibrium price P* and the equilibrium quantity Q* when given specific supply and demand curves.

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Relating Supply and Demand

The supply curve slopes upwards (since the coefficient on P in the supply curve is greater than zero) and the demand curve slopes downwards (since the coefficient on P in the demand curve is greater than zero).

In addition, we know that​ in a basic market the price that the consumer pays for a good is the same as the price that the producer gets to keep for the good. Therefore, the P in the supply curve has to be the same as the P in the demand curve.

The equilibrium in a market occurs where the quantity supplied in that market is equal to the quantity demanded in that market. Therefore, we can find the equilibrium by setting supply and demand equal to one another and then solving for P.

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Solving for P* and Q*

Once the supply and demand curves are substituted into the equilibrium condition, it's relatively straightforward to solve for P. This P is referred to as the market price P*, since it is the price where quantity supplied is equal to quantity demanded.

To find the market quantity Q*, simply plug the equilibrium price back into either the supply or demand equation. Note that it doesn't matter which one you use since the whole point is that they have to give you the same quantity.

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Comparison to the Graphical Solution

Since the P* and Q* represent the condition where quantity supplied and quantity demanded are the same at a given price, it is, in fact, the case that P* and Q* graphically represent the intersection of the supply and demand curves.

It is often helpful to compare the equilibrium that you found algebraically to the graphical solution in order to double check that no calculation errors were made.

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Additional Resources

 Sources:

Graham, Robert J. "How to Determine Price: Find Equilibrium Between Supply and Demand." Dummies.com, 

Investopedia staff. "What is 'Economic Equilibrium'?" Investopedia.com.

Wolla, Scott. "Equilibrium: The Economic Lowdown Video Series." The Federal Reserve Bank of St. Louis.