In economics, the equilibrium price is the market price at which supply and demand are balanced When the equilibrium price is reached, the quantity producers want to supply is equal to the quantity consumers want to buy Calculating the equilibrium price is a fundamental process in microeconomics that involves using supply and demand functions. Follow these 4 straightforward steps to find the equilibrium price in any market
Step 1: Determine the Supply Function
The first step is to identify the supply function for the good you are analyzing The supply function shows the quantity that producers are willing to supply at each market price
Supply functions generally take the form:
Qs = a + bP
Where:
Qs = Quantity supplied
P = Price
a = The intercept
b = The slope
For example, let’s say the supply function for textbooks is:
Qs = 5 + 3P
This means:
- At a price of $0, the quantity supplied would be 5 textbooks
- For every $1 increase in price, the quantity supplied will increase by 3 textbooks
So if the price rose to $10, the quantity supplied would be 5 + 3($10) = 35 textbooks.
Step 2: Determine the Demand Function
Next, you need the demand function for the good. The demand function shows the quantity that consumers are willing to buy at each price.
Demand functions generally take the form:
Qd = c – dP
Where:
Qd = Quantity demanded
P = Price
c = The intercept
d = The slope
For example, the demand function for textbooks might be:
Qd = 50 – 5P
This means:
- At a price of $0, the quantity demanded would be 50 textbooks
- For every $1 increase in price, quantity demanded will decrease by 5 textbooks
So if the price was $10, the quantity demanded would be 50 – 5($10) = 25 textbooks.
Step 3: Set the Two Quantities Equal
Now that you have the supply and demand functions, set them equal to each other. This represents the equilibrium point where quantity supplied equals quantity demanded.
Using the textbook example:
Qs = 5 + 3P
Qd = 50 – 5P
Set them equal:
5 + 3P = 50 – 5P
Step 4: Solve for Equilibrium Price
The final step is to solve the equation from Step 3 to find the equilibrium price. Add like terms and isolate the price variable:
5 + 3P = 50 – 5P
10P = 45
P = 45/10 = $4.50
Therefore, the equilibrium price for textbooks is $4.50. At this price, the quantity supplied and quantity demanded are both 30 textbooks.
- If the price was below $4.50, excess demand would exist since quantity demanded would exceed quantity supplied
- If the price rose above $4.50, excess supply would exist because quantity supplied would exceed quantity demanded
- Only when price = $4.50 will supply equal demand at the equilibrium quantity of 30 textbooks
This 4-step process can be used to calculate the equilibrium price for any product. The same principles apply whether you’re analyzing the market for bread, airline tickets, electronics, or anything else. Just determine the supply and demand functions, set them equal, and solve for price to find the equilibrium point.
Some key tips when calculating equilibrium price:
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Make sure to label the intercepts and slopes in the supply and demand functions based on whether the relationship is positive or negative. Quantity supplied has a positive relationship with price, while quantity demanded has a negative relationship.
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Remember that equilibrium price is determined by the market and consumer preferences. It is not simply the mid-point between the highest and lowest prices.
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If supply or demand changes, the equilibrium price will shift as well. Factors like production costs, income levels, and substitutes affect equilibrium price.
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Equilibrium price is a theoretical concept that assumes markets clear instantly. In reality, prices constantly fluctuate towards equilibrium.
Mastering these 4 steps to calculate equilibrium price provides a crucial foundation for further microeconomic analysis. Understanding equilibrium gives you a framework for examining the impacts of government policies, technological changes, and any other factor that can influence supply and demand. Whether you are studying economics formally or just want to make better sense of real-world markets, knowing how to find equilibrium price is an indispensable skill.
Finding Equilibrium with Algebra
We’ve just explained two ways of finding a market equilibrium: by looking at a table showing the quantity demanded and supplied at different prices, and by looking at a graph of demand and supply. We can also identify the equilibrium with a little algebra if we have equations for the supply and demand curves. Let’s practice solving a few equations that you will see later in the course. Right now, we are only going to focus on the math. Later, you’ll learn why these models work the way they do, but let’s start by focusing on solving the equations. Suppose that the demand for soda is given by the following equation:
where Qd is the amount of soda that consumers want to buy (i.e., quantity demanded), and P is the price of soda. Suppose the supply of soda is
where Qs is the amount of soda that producers will supply (i.e., quantity supplied). (Remember, these are simple equations for lines). Finally, recall that the soda market converges to the point where supply equals demand, or
We now have a system of three equations and three unknowns (Qd, Qs, and P), which we can solve with algebra. Since
we can set the demand and supply equations equal to each other:
Step 1: Isolate the variable by adding 2P to both sides of the equation and subtracting 2 from both sides.
Step 2: Simplify the equation by dividing both sides by 7.
The equilibrium price of soda, that is, the price where Qs = Qd, will be $2. Now we want to determine the quantity amount of soda. We can do this by plugging the equilibrium price into either the equation showing the demand for soda or the equation showing the supply of soda. Let’s use demand. Remember, the formula for quantity demanded is the following:
Taking the price of $2, and plugging it into the demand equation, we get
So, if the price is $2 each, consumers will purchase 12. How much will producers supply, or what is the quantity supplied? Taking the price of $2, and plugging it into the equation for quantity supplied, we get the following:
Now, if the price is $2 each, producers will supply 12 sodas. This means that we did our math correctly, since
and both Qd and Qs are equal to 12. That confirms that we’ve found the equilibrium quantity.
Watch this video for a closer look at market equilibrium:
Equilibrium occurs at the point where quantity supplied = quantity demanded.
Equilibrium: Where Supply and Demand Intersect
When two lines on a diagram cross, this intersection usually means something. On a graph, the point where the supply curve (S) and the demand curve (D) intersect is the equilibrium. The equilibrium price is the only price where the desires of consumers and the desires of producers agree—that is, where the amount of the product that consumers want to buy (quantity demanded) is equal to the amount producers want to sell (quantity supplied). This mutually desired amount is called the equilibrium quantity. At any other price, the quantity demanded does not equal the quantity supplied, so the market is not in equilibrium at that price. It should be clear, from the previous discussions of surpluses and shortages, that if a market is not in equilibrium, then market forces will push the market to the equilibrium.
If you have only the demand and supply schedules, and no graph, then you can find the equilibrium by looking for the price level on the tables where the quantity demanded and the quantity supplied are equal (see the numbers in bold in Table 1 in the previous page that indicates this point).
