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 (Q_d) and quantity supplied (Q_s) with the following linear equations:

Quantity Demanded for Compact Cars: Q_d = 60−3P

Quantity Supplied for Compact Cars: Q_s = 20+2P

At market equilibrium, Q_d = Q_s.

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.

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.

• Equilibrium in Mathematics - The concept of balance in numerical models and equations.
• Market Equilibrium Quantity - The level of quantity demanded equals quantity supplied.
• Equilibrium Microeconomics - The state in economic theory when supply and demand is perfectly balanced.
• Equilibrium Price - In economics, the price at which the quantity demanded equals the supplied quantity.
• Equilibrium Quantity - The number of goods or services demanded equals the number offered.

• Define Equilibrium in Mathematics – Understand the point of balance in mathematical context (e.g., equilibrium in mathematics).
• Contrast Quantity Demanded vs Quantity Supplied – Recognize key characteristics each exhibit in market context (e.g., market equilibrium quantity).
• Explore Market Equilibrium – Understand how supply and demand balance (e.g., equilibrium microeconomics).
• Explain Equilibrium Price – In the context of supply and demand, explain how it aligns to market equilibrium.
• Apply Equilibrium Quantity – Understand its relevance in market balance and behaviour.

• What exactly is 'Equilibrium in mathematics', and how does it apply to economic models?
• How does 'Quantity demanded' contrast with 'Quantity supplied' in a market scenario?
• Why is 'Equilibrium Price' important in maintaining market balance and how is it determined?

• Students - Learn how the concept of equilibrium helps understand market behaviour.
• Educators - Benefit from a theoretical framework that simplifies the teaching about market equilibrium.
• Researchers - Gaining insight of equilibrium for their economic research methodologies.
• Economic Enthusiasts - Helps stimulate curiosity about market dynamics.