# Competitive market equilibrium

> IB Economics SL · IB Economics SL Unit 2: Microeconomics
> Source: https://www.owlsprep.com/study/ib-economics-sl-u2-competitive-market-equilibrium/

This sub-topic explains how supply and demand interact to set price and quantity in perfectly competitive markets. You will learn how markets adjust from disequilibrium and how shifts in curves change equilibrium outcomes.

**Prerequisites:** [Supply and demand curves and their determinants](https://www.owlsprep.com/study/ib-economics-sl-u2-supply-and-demand/)

## Learning objectives

- Define competitive market equilibrium and identify equilibrium price/quantity
- Explain how excess supply and excess demand drive price adjustment to equilibrium
- Analyze the effect of supply and demand shifts on equilibrium outcomes
- Calculate equilibrium price and quantity from linear supply and demand functions

## Definition and Mathematical Representation

**Competitive market equilibrium** — A stable market state where the quantity of a good demanded by consumers equals the quantity supplied by producers. There is no inherent pressure for price or quantity to change, so it is also called market clearing.

*Example:* At \$3 per coffee, 1000 coffees are demanded and 1000 supplied, so the market is in equilibrium.

For linear demand and supply functions, equilibrium is found by setting quantity demanded equal to quantity supplied, then solving for price, then substituting back to find quantity:

$$Q_d = a - bP \\ Q_s = c + dP \\ \text{Set } Q_d = Q_s: \\ a - bP = c + dP \\ a - c = P(b + d) \\ P^* = \frac{a - c}{b + d}$$

**Worked example:** Given $Q_d = 50 - 3P$ and $Q_s = 5 + 2P$, calculate equilibrium price and quantity.

1. Start with the equilibrium condition: quantity demanded equals quantity supplied:
2. $$50 - 3P = 5 + 2P$$
3. Rearrange to isolate $P$ by collecting like terms:
4. $$50 - 5 = 3P + 2P \implies 45 = 5P \implies P^* = 9$$
5. Substitute $P^* = 9$ into the demand function to find equilibrium quantity:
6. $$Q^* = 50 - 3(9) = 50 - 27 = 23$$
7. Verify the result by substituting into the supply function to confirm equality:
8. $$Q^* = 5 + 2(9) = 5 + 18 = 23 \quad (\text{matches, so correct})$$

## Disequilibrium and Price Adjustment

When the market price is not equal to the equilibrium price, the market is in disequilibrium, with either excess demand or excess supply. The price mechanism (often called the invisible hand) automatically adjusts price to restore equilibrium over time.

**Excess demand (shortage)** — Occurs when the current market price is below the equilibrium price, so quantity demanded is greater than quantity supplied.

**Excess supply (surplus)** — Occurs when the current market price is above the equilibrium price, so quantity supplied is greater than quantity demanded.

Adjustment works through incentive changes: excess demand leads to frustrated consumers who bid up prices, encouraging producers to increase output until equilibrium is reached. Excess supply leaves producers with unsold stock, who cut prices to clear inventory, reducing output until equilibrium is restored.

**Worked example:** In the coffee market, equilibrium price is \$3 and equilibrium quantity is 1000. If the current market price is \$4, with $Q_d = 500$ and $Q_s = 1200$, explain the adjustment back to equilibrium.

1. First, identify the type of disequilibrium: price is above equilibrium, so we have excess supply:
2. $$\text{Excess supply} = Q_s - Q_d = 1200 - 500 = 700$$
3. Producers cannot sell all their output at \$4, so they have a direct incentive to cut prices to clear unsold inventory.
4. As price falls, quantity demanded increases (movement down along the demand curve) and quantity supplied decreases (movement down along the supply curve).
5. This adjustment continues until price reaches \$3, where quantity demanded equals quantity supplied at 1000, and equilibrium is restored.

> **tip**
>
> Always clearly label the gap between Qd and Qs on your disequilibrium diagram to earn full marks in IB exams.

## Comparative Statics: Effects of Shifts

When supply or demand curves shift due to changes in non-price determinants (e.g. consumer income, input costs), the original equilibrium is disrupted. A new equilibrium forms, and we compare the original and new outcomes in an analysis called comparative statics.

- An increase in demand (right shift) raises equilibrium price and quantity
- A decrease in demand (left shift) lowers equilibrium price and quantity
- An increase in supply (right shift) lowers equilibrium price and raises equilibrium quantity
- A decrease in supply (left shift) raises equilibrium price and lowers equilibrium quantity

**Worked example:** Original demand for electric bikes is $Q_d = 100 - 2P$, supply is $Q_s = 20 + 2P$. Changing consumer preferences increase demand to $Q_d = 120 - 2P$. Calculate the new equilibrium and describe the adjustment.

1. Original equilibrium (pre-shift) is: $100 - 2P = 20 + 2P \implies P^* = 20$, $Q^* = 60$.
2. Set new Qd equal to unchanged Qs to find the new equilibrium:
3. $$120 - 2P = 20 + 2P \implies 100 = 4P \implies P^*_{new} = 25$$
4. Calculate new equilibrium quantity:
5. $$Q^*_{new} = 120 - 2(25) = 70$$
6. At the original price of 20, new quantity demanded is 80, which is greater than quantity supplied of 60, creating temporary excess demand. This bids up price, leading to an upward movement along the supply curve until the new equilibrium at $P=25, Q=70$ is reached.

## Common pitfalls

- **Wrong:** Confusing movement along a curve with a shift of the curve when analyzing equilibrium changes
  - Why it fails: Shifts of the entire curve come from changes in non-price determinants, while movements along the curve are only caused by price changes after the shift
  - Correct: First identify which curve shifts and its direction, find the new intersection, then describe movement along the unchanged curve during adjustment
- **Wrong:** Assuming excess demand always means the demand curve has shifted
  - Why it fails: Excess demand can occur with no shift in either curve, simply when price is set below the original equilibrium price
  - Correct: Always distinguish between temporary disequilibrium at the original curves and permanent shifts that create a new equilibrium
- **Wrong:** Calculating equilibrium by setting prices equal instead of quantities
  - Why it fails: The equilibrium condition requires quantity demanded to equal quantity supplied, not equality of demand-side and supply-side prices
  - Correct: Always rearrange functions to set $Q_d = Q_s$ when solving for equilibrium price and quantity
- **Wrong:** Claiming a definite change in price/quantity when both supply and demand shift
  - Why it fails: When both curves shift, one effect pushes price up and the other pushes it down, so the outcome depends on the size of the shifts
  - Correct: Always note that when both curves shift, one outcome (price or quantity) will be ambiguous unless shift magnitudes are given

## Cheatsheet

| Change in market | Effect on equilibrium price | Effect on equilibrium quantity |
| --- | --- | --- |
| Increase in demand (right shift) | Increase | Increase |
| Decrease in demand (left shift) | Decrease | Decrease |
| Increase in supply (right shift) | Decrease | Increase |
| Decrease in supply (left shift) | Increase | Decrease |
| Both demand and supply increase | Ambiguous | Increase |
| Both demand and supply decrease | Ambiguous | Decrease |
| Demand increases, supply decreases | Increase | Ambiguous |
| Demand decreases, supply increases | Decrease | Ambiguous |

## What's next

Understanding competitive market equilibrium is the core foundation for all further microeconomic analysis in IB Economics SL, including market failures, government intervention, and alternative market structures like monopoly. This simple price mechanism framework lets you predict outcomes of changes in consumer preferences, input costs, and other market shocks, and evaluate the welfare effects of government policies like price controls, taxes, and subsidies. Mastery of this topic is required for almost all microeconomics questions on both Paper 1 and Paper 2 of the IB exam.

- [Elasticity](https://www.owlsprep.com/study/ib-economics-sl-u2-elasticity/)
- [Government intervention in markets](https://www.owlsprep.com/study/ib-economics-sl-u2-government-intervention-in-markets/)
- [Types of market failure](https://www.owlsprep.com/study/ib-economics-sl-u2-types-of-market-failure/)

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