4.3:
The Mathematics of Equilibrium
The mathematics of market equilibrium can be understood by using the equations for quantity demanded and quantity supplied.
Consider a hypothetical example of a sugar market.
The quantity demanded and supplied can be represented using linear equations. Here, 'P' is the price of the product.
In an equilibrium state, quantity demanded equals quantity supplied. This means that the equations become equivalent.
Solving for P gives six hundred dollars.
This price, P, is the equilibrium price. Substituting the equilibrium price into either of these equations gives the equilibrium quantity. Here, the equilibrium quantity equals 12 million metric tons.
This represents the point at which the sugar market is in perfect balance, with quantity supplied meeting quantity demanded.
This mathematical model assumes that all other factors remain constant and focuses on the relationship between price and quantity. However, in reality, many other factors can affect supply and demand and, as a result, the market equilibrium.
4.3 The Mathematics of Equilibrium
Consider the market for compact cars as an example, where 'P' stands for the price of a compact car in thousands of dollars. We can model the quantity demanded (Qd) and quantity supplied (Qs) with the following linear equations:
Quantity Demanded for Compact Cars: Qd = 60−3P
Quantity Supplied for Compact Cars: Qs = 20+2P
At market equilibrium, Qd = Qs.
By setting these two equations equal to each other, we can solve for 'P', the equilibrium price: 60−3P = 20+2P
Solving this equation gives us the equilibrium price, which is P=8 thousand dollars.
Substituting this price back into either the demand or supply equation yields the equilibrium quantity. For instance, the market will balance at 36 million compact cars. This represents the point at which the supply of compact cars perfectly meets consumer demand.
It's important to recognize that this simplified model assumes other factors remain constant. In the real world, supply and demand are influenced by many factors, such as economic conditions, consumer preferences, and technological innovations, which can alter the relationship between the market price and the quantity demanded or the quantity supplied. This would shift one or both of these curves and thus affect market equilibrium.