Drawing and interpretation of disequilibrium using demand and supply curves

Allocation of Resources – Price Determination

Learning Objective

Students will be able to draw and interpret disequilibrium situations using demand and supply curves.

Key Concepts

• Demand curve – relationship between price (\$P\$) and quantity demanded (\$Q_d\$).
• Supply curve – relationship between price (\$P\$) and quantity supplied (\$Q_s\$).
• Market equilibrium – where \$Qd = Qs\$ at the equilibrium price \$P_e\$.
• Disequilibrium – any point where \$Qd \neq Qs\$.
• Surplus – \$Qs > Qd\$ (price above equilibrium).
• Shortage – \$Qd > Qs\$ (price below equilibrium).

Equilibrium Diagram (Suggested)

Drawing Disequilibrium

1. Start with the equilibrium diagram described above.
2. Choose a price level above \$P_e\$:

   • Draw a horizontal line at the chosen price (\$P_{high}\$).
   • From this line, read off the quantity supplied (\$Qs\$) on the supply curve and the quantity demanded (\$Qd\$) on the demand curve.

3. Label the resulting gap between \$Qs\$ and \$Qd\$ as a surplus.
4. Repeat the process for a price level below \$Pe\$ (\$P{low}\$) to illustrate a shortage.

Interpretation of Disequilibrium

When a market is not in equilibrium, market forces tend to move it back toward equilibrium:

• Surplus: Excess supply puts downward pressure on price. Sellers lower prices, increasing quantity demanded and reducing quantity supplied until \$Qd = Qs\$.
• Shortage: Excess demand puts upward pressure on price. Buyers are willing to pay more, encouraging producers to increase output, reducing the gap until equilibrium is restored.

Effects of Shifts in Demand and Supply

Mathematical Representation

Demand and supply functions can be expressed as:

\$\$

Q_d = a - bP \qquad\text{(downward‑sloping demand)}

\$\$

\$\$

Q_s = c + dP \qquad\text{(upward‑sloping supply)}

\$\$

Equilibrium is found by setting \$Qd = Qs\$:

\$\$

a - bPe = c + dPe \;\Longrightarrow\; P_e = \frac{a - c}{b + d}

\$\$

Any price \$P \neq P_e\$ creates disequilibrium. The size of the surplus or shortage is:

\$\$

\text{Surplus} = Qs - Qd = (c + dP) - (a - bP) = (c - a) + (b + d)P

\$\$

When \$P > Pe\$, the expression is positive (surplus); when \$P < Pe\$, it is negative (shortage).

Worked Example

Suppose the demand for a good is \$Qd = 200 - 4P\$ and the supply is \$Qs = 20 + 2P\$.

1. Find the equilibrium price and quantity.
2. Show the surplus that would exist if the price were set at \$P = 30\$.

Solution:

\$\$

200 - 4P = 20 + 2P \;\Longrightarrow\; 180 = 6P \;\Longrightarrow\; P_e = 30

\$\$

\$\$

Qe = 20 + 2(30) = 80 \quad\text{or}\quad Qe = 200 - 4(30) = 80

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At \$P = 30\$, the market is actually at equilibrium, so there is no surplus. If the price were \$P = 40\$:

\$\$

Qd = 200 - 4(40) = 40,\qquad Qs = 20 + 2(40) = 100

\$\$

\$\$

\text{Surplus} = 100 - 40 = 60 \text{ units}

\$\$

Exam‑Style Question

Using a diagram, explain what happens to the market for oranges when a sudden frost reduces the supply of oranges.

• Identify the initial equilibrium.
• Show the leftward shift of the supply curve.
• Label the new equilibrium price and quantity.
• Explain the temporary shortage that occurs if the price is kept at the original equilibrium level.

Summary Checklist

1. Can you draw the demand and supply curves correctly?
2. Do you know how to locate equilibrium (\$Pe\$, \$Qe\$)?
3. Can you illustrate a surplus (price above \$Pe\$) and a shortage (price below \$Pe\$)?
4. Are you able to explain the market forces that move the price back toward equilibrium?
5. Do you understand how shifts in demand or supply create new disequilibrium situations?