Definition of market equilibrium

The Allocation of Resources – Price Determination

Objective: Definition of Market Equilibrium

Imagine a bustling market stall where a vendor sells fresh lemonade. The price of lemonade is not fixed; it changes based on how many people want it (demand) and how many glasses the vendor can make (supply). When the price and quantity settle so that the number of glasses people want to buy equals the number the vendor is ready to sell, the market is in equilibrium – no one wants to change the price. 🍋

Key Terms

• Demand – the quantity of a good that buyers are willing and able to purchase at each price.
• Supply – the quantity of a good that sellers are willing and able to offer at each price.
• Market Equilibrium – the point where demand equals supply.
• Equilibrium Price (P^*) – the price at which quantity demanded equals quantity supplied.
• Equilibrium Quantity (Q^*) – the quantity sold at the equilibrium price.

Mathematical Representation

In a simple market, we can write the demand and supply functions as:

$D(P) = a - bP$
$S(P) = c + dP$

Market equilibrium occurs where $D(P) = S(P)$. Solving for $P$ gives the equilibrium price $P^*$, and substituting back gives $Q^*$. In symbols:

$$P^* = \frac{a - c}{b + d}$$
$$Q^* = D(P^*) = S(P^*)$$

Illustrative Example

Suppose the demand for a popular video game is $D(P) = 120 - 2P$ and the supply is $S(P) = 20 + 3P$ (prices in £). Find the equilibrium price and quantity.

1. Set $D(P) = S(P)$: $120 - 2P = 20 + 3P$.
2. Combine terms: $100 = 5P$.
3. Divide: $P^* = 20$ £.
4. Substitute back: $Q^* = 120 - 2(20) = 80$ units.

So, at £20 each, 80 copies of the game will be sold – the market is balanced. 🎮

Visualising Supply & Demand

The row where the two numbers match (price £20) shows the market equilibrium. Notice how at lower prices demand exceeds supply (a shortage), and at higher prices supply exceeds demand (a surplus). 📈📉

Take‑Away Questions

• What happens to the equilibrium price if the supply curve shifts to the right?
• How would a sudden increase in demand for a product affect the market price?
• Can you think of a real‑world example where a market is not in equilibrium?

Reflect on these questions and discuss with classmates. Understanding market equilibrium is the first step to mastering how resources are allocated in the economy. 🚀