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Market Equilibrium
Consumer & Producer Surplus

Understand how supply and demand determine equilibrium price and quantity, and how surplus measures the welfare gains for buyers and sellers.

AP Microeconomics

What Is a Market?

A market is any arrangement that brings buyers and sellers together. The interaction of demand (buyers' willingness to pay) and supply (sellers' willingness to sell) determines the price and quantity of goods exchanged.

Demand
The quantity buyers are willing and able to purchase at each price. Slopes downward.
Supply
The quantity sellers are willing and able to produce at each price. Slopes upward.

The Supply and Demand Model

Quantity (Q) Price (P) D S E
\(Q^*\)
\(P^*\)

Market Equilibrium Defined

Market equilibrium is the price-quantity pair \( (P^*, Q^*) \) where quantity demanded equals quantity supplied. There is no tendency for the price to change.

1
Surplus (excess supply): If \( P > P^* \), sellers supply more than buyers demand, pushing price down.
2
Shortage (excess demand): If \( P < P^* \), buyers demand more than sellers supply, pushing price up.
3
At equilibrium: \( Q_d = Q_s \). No pressure exists to change the price.

What Is Consumer Surplus?

Consumer surplus (CS) is the difference between what consumers are willing to pay and what they actually pay. It represents the net benefit to buyers from market transactions.

Quantity (Q) Price (P) D S
\(P^*\)
\(Q^*\)
 CS

What Is Producer Surplus?

Producer surplus (PS) is the difference between the price sellers receive and the minimum price they would accept. It represents the net benefit to sellers.

Quantity (Q) Price (P) D S
\(P^*\)
\(Q^*\)
 PS

Total Surplus and Efficiency

Quantity (Q) Price (P) D S E CS PS

Consumer vs Producer Surplus

Consumer Surplus Producer Surplus
Definition Willingness to pay minus price paid Price received minus cost of production
Graph Location Below demand, above \(P^*\) Above supply, below \(P^*\)
Who Benefits? Buyers Sellers
If Price Rises Decreases Increases
If Price Falls Increases Decreases

How to Calculate Surplus

1
Find equilibrium: Set \( Q_d = Q_s \) and solve for \( P^* \) and \( Q^* \).
2
Identify intercepts: Find the vertical intercept of the demand curve (\( P_{\max} \)) and the supply curve (\( P_{\min} \)).
3
Compute CS: \( CS = \frac{1}{2} \times Q^* \times (P_{\max} - P^*) \)
4
Compute PS: \( PS = \frac{1}{2} \times Q^* \times (P^* - P_{\min}) \)
5
Total surplus: \( TS = CS + PS \). Verify this equals \( \frac{1}{2} \times Q^* \times (P_{\max} - P_{\min}) \).

Example 1: Finding Equilibrium

Suppose demand is \( Q_d = 100 - 2P \) and supply is \( Q_s = 3P - 25 \). Find the equilibrium price and quantity.

1
Set equal: \( 100 - 2P = 3P - 25 \)
2
Solve for P: \( 125 = 5P \), so \( P^* = 25 \)
3
Find \(Q^*\): \( Q^* = 100 - 2(25) = 50 \)

Example 2: Computing CS and PS

Using the same equations: \( Q_d = 100 - 2P \), \( Q_s = 3P - 25 \), with \( P^* = 25 \) and \( Q^* = 50 \).

Q P D S 25 50 50 8.33 CS PS
CS
\( \frac{1}{2} \times 50 \times (50 - 25) = 625 \)
PS
\( \frac{1}{2} \times 50 \times (25 - 8.\overline{3}) \approx 416.67 \)
Total Surplus
\( 625 + 416.67 \approx 1041.67 \)

Example 3: Effect of a Price Ceiling

A government sets a price ceiling at \( P_c = 15 \), below \( P^* = 25 \). Using our equations:

Q P D S
\(P_c=15\)
 DWL
\(Q_s=20\)
\(Q_d=70\)

Understanding Deadweight Loss

Deadweight loss (DWL) is the reduction in total surplus when the market does not operate at equilibrium. It arises whenever the quantity traded differs from \( Q^* \).

Price Ceiling
Sets \( P < P^* \). Creates shortage. Quantity traded falls to \( Q_s \). DWL appears.
Price Floor
Sets \( P > P^* \). Creates surplus. Quantity traded falls to \( Q_d \). DWL appears.
Taxes
Drives a wedge between buyer's price and seller's price. Reduces quantity traded. DWL appears.

Why Equilibrium Is Efficient

1
Every unit traded has a buyer whose willingness to pay exceeds the seller's cost. Both gain surplus.
2
No additional unit beyond \( Q^* \) can be traded profitably: for units past \( Q^* \), cost exceeds willingness to pay.
3
Producing fewer than \( Q^* \) units leaves mutually beneficial trades unrealized, creating DWL.
4
Producing more than \( Q^* \) units means some units cost more to produce than buyers value them: also DWL.

How Shifts Affect Surplus

Q P S
\(D_1\)
\(D_2\)
\(E_1\)
\(E_2\)

Common Mistakes

Confusing Surplus with Profit
Producer surplus is not the same as profit. PS measures the gain above the marginal cost curve, not above total cost (which includes fixed costs).
Mislocating CS and PS
CS is below demand and above price. PS is above supply and below price. Mixing these up reverses the answer.
Ignoring DWL Direction
DWL arises whenever the quantity traded differs from \(Q^*\) (whether under- or over-production). A binding price control always creates DWL.

Summary of Key Concepts

Concept Formula Graph Area
Equilibrium \( Q_d = Q_s \) Intersection of S and D
Consumer Surplus \( \frac{1}{2} Q^*(P_{\max} - P^*) \) Triangle below D, above \(P^*\)
Producer Surplus \( \frac{1}{2} Q^*(P^* - P_{\min}) \) Triangle above S, below \(P^*\)
Total Surplus \( CS + PS \) Full area between S and D
Deadweight Loss \( TS_{\text{eq}} - TS_{\text{actual}} \) Triangle of lost trades

Question 1 of 5

At market equilibrium, which of the following is true?

Question 2 of 5

If \( Q_d = 80 - 4P \) and \( Q_s = 2P - 10 \), what is the equilibrium price \( P^* \)?

Question 3 of 5

Consumer surplus is best described as the area:

Question 4 of 5

A binding price ceiling set below \( P^* \) will cause:

Question 5 of 5

If the equilibrium price increases due to a rightward shift of the supply curve, what happens to producer surplus?