# 3.6. Market Equilibrium

#cfa #cfa-level-1 #economics #microeconomics #reading-13-demand-and-supply-analysis-introduction #study-session-4

An important concept in the market model is market equilibrium, defined as the condition in which the quantity willingly offered for sale by sellers at a given price is just equal to the quantity willingly demanded by buyers at that same price. When that condition is met, we say that the market has discovered its equilibrium price. An alternative and equivalent condition of equilibrium occurs at that quantity at which the highest price a buyer is willing to pay is just equal to the lowest price a seller is willing to accept for that same quantity.

As we have discovered in the earlier sections, the demand curve shows (for given values of income, other prices, etc.) an infinite number of combinations of prices and quantities that satisfy the demand function. Similarly, the supply curve shows (for given values of input prices, etc.) an infinite number of combinations of prices and quantities that satisfy the supply function. Equilibrium occurs at the unique combination of price and quantity that simultaneously satisfies both the market demand function and the market supply function. Graphically, it is the intersection of the demand and supply curves as shown in Exhibit 7.

Exhibit 7. Market Equilibrium Price and Quantity as the Intersection of Demand and Supply

In Exhibit 7, the shaded arrows indicate, respectively, that buyers will be willing to pay any price at or below the demand curve (indicated by ↓), and sellers are willing to accept any price at or above the supply curve (indicated by ↑). Notice that for quantities less than Q∗x , the highest price buyers are willing to pay exceeds the lowest price sellers are willing to accept, as indicated by the shaded arrows. But for all quantities above Q∗x , the lowest price willingly accepted by sellers is greater than the highest price willingly offered by buyers. Clearly, trades will not be made beyond Q∗x.

Algebraically, we can find equilibrium price by setting the demand function equal to the supply function and solving for price. Recall that in our hypothetical example of a local gasoline market, the demand function was given by Qdx=f(Px,I,Py) , and the supply function was given by Qsx=f(Px,W) . Those expressions are called behavioral equations because they model the behavior of, respectively, buyers and sellers. Variables other than own price and quantity are determined outside of the demand and supply model of this particular market. Because of that, they are called exogenous variables. Price and quantity, however, are determined within the model for this particular market and are called endogenous variables. In our simple example, there are three exogenous variables (I, Py, and W) and three endogenous variables: Px, Qdx , and Qsx . Hence, we have a system of two equations and three unknowns. We need another equation to solve this system. That equation is called the equilibrium condition, and it is simply Qdx=Qsx .

Continuing with our hypothetical examples, we could assume that income equals $50 (thousand, per year), the price of automobiles equals$20 (thousand, per automobile), and the hourly wage equals \$15. In this case, our equilibrium condition can be represented by setting Equation 14 equal to Equation 17:

Equation (19)

11,200 – 400Px = −5,000 + 5,000Px

and solving for equilibrium, Px = 3.

Equivalently, we could have equated the inverse demand function to the inverse supply function (Equations 15 and 18, respectively)

Equation (20)

28 – 0.0025Qx = 1 + 0.0002Qx

and solved for equilibrium, Qx = 10,000. That is to say, for the given values of I and W, the unique combination of price and quantity of gasoline that results in equilibrium is (3, 10,000).

Note that our system of equations requires explicit values for the exogenous variables to find a unique equilibrium combination of price and quantity. Conceptually, the values of the exogenous variables are being determined in other markets, such as the markets for labor, automobiles, and so on, whereas the price and quantity of gasoline are being determined in the gasoline market. When we concentrate on one market, taking values of exogenous variables as given, we are engaging in what is called partial equilibrium analysis. In many cases, we can gain sufficient insight into a market of interest without addressing feedback effects to and from all the other markets that are tangentially involved with this one. At other times, however, we need explicitly to take account of all the feedback mechanisms that are going on in all markets simultaneously. When we do that, we are engaging in what is called general equilibrium analysis.For example, in our hypothetical model of the local gasoline market, we recognize that the price of automobiles, a complementary product, has an impact on the demand for gasoline. If the price of automobiles were to rise, people would tend to buy fewer automobiles and probably buy less gasoline. Additionally, though, the price of gasoline probably has an impact on the demand for automobiles that, in turn, can feed back to the gasoline market. Because we are positing a very local gasoline market, it is probably safe to ignore all the feedback effects, but if we are modeling the national markets for gasoline and automobiles, a general equilibrium model might be warranted.

EXAMPLE 6

# Finding Equilibrium by Equating Demand and Supply

In the local market for e-books, the aggregate demand is given by the equation

Qdeb=2,000−400Peb+0.5I+150Phb

and the aggregate supply is given by the equation

Qseb=−516+300Peb−60W

where Qeb is quantity of e-books, Peb is the price of an e-book, I is household income, W is wage rate paid to e-book laborers, and Phb is the price of a hardbound book. Assume I is €2,300, W is €10, and Phb is €21.40. Determine the equilibrium price and quantity of e-books in this local market.

## Solution:

Market equilibrium occurs when quantity demanded is equal to quantity supplied, so set Qdeb=Qseb after inserting the given values for the exogenous variables:

2,000 − 400Peb + 0.5(2,300) + 150(21.4) = –516 + 300Peb – 60(10)

6,360 – 400Peb = −1,116 + 300Peb,

which implies that Peb = €10.68, and Qeb = 2,088.