Drawing and interpretation of equilibrium using demand and supply curves

Published by Patrick Mutisya · 14 days ago

IGCSE Economics 0455 – The Allocation of Resources: Price Determination

The Allocation of Resources – Price Determination

Learning Objective

Students will be able to draw and interpret market equilibrium using demand and supply curves.

1. The Demand Curve

The demand curve shows the relationship between the price of a good (P) and the quantity demanded (Qd). It is generally downward‑sloping because of the law of demand.

  • Higher price → lower quantity demanded.

  • Lower price → higher quantity demanded.

Typical linear demand function:

\$Q_d = a - bP\$

where a is the intercept (quantity demanded when price is zero) and b is the slope (change in quantity demanded per unit change in price).

2. The Supply Curve

The supply curve shows the relationship between the price of a good (P) and the quantity supplied (Qs). It is generally upward‑sloping because of the law of supply.

  • Higher price → higher quantity supplied.

  • Lower price → lower quantity supplied.

Typical linear supply function:

\$Q_s = c + dP\$

where c is the intercept (quantity supplied when price is zero) and d is the slope (change in quantity supplied per unit change in price).

3. Market Equilibrium

Equilibrium occurs where the quantity demanded equals the quantity supplied:

\$Qd = Qs\$

Substituting the linear functions gives:

\$a - bP = c + dP\$

Solving for the equilibrium price (P*):

\$P^* = \frac{a - c}{b + d}\$

Substituting P* back into either the demand or supply equation gives the equilibrium quantity (Q*):

\$Q^* = a - bP^* = c + dP^* = \frac{ad + bc}{b + d}\$

Suggested diagram: Plot the demand curve (downward‑sloping) and the supply curve (upward‑sloping) on the same axes. Mark the equilibrium point where they intersect and label the equilibrium price (P*) and quantity (Q*).

4. Shifts in the Curves

Changes in factors other than price cause the whole curve to shift.

FactorEffect on Demand CurveEffect on Supply Curve
Change in consumer income (normal good)Shift right (increase)–
Change in consumer income (inferior good)Shift left (decrease)–
Change in production technology–Shift right (increase)
Change in input prices–Shift left (decrease) if input price rises
Government tax on producers–Shift left (decrease)
Government subsidy to producers–Shift right (increase)

5. Interpreting New Equilibria

  1. Identify which curve has shifted and in which direction.

  2. Redraw the curves on the same axes.

  3. Locate the new intersection point.

  4. Read the new equilibrium price (Pnew) and quantity (Qnew).

  5. Compare with the original equilibrium to determine the direction of change in price and quantity.

6. Worked Example

Suppose the demand for a product is given by \$Qd = 120 - 2P\$ and the supply by \$Qs = 20 + 3P\$.

Find the equilibrium price and quantity.

  1. Set \$Qd = Qs\$:

    2. \$120 - 2P = 20 + 3P\$

  2. Solve for \$P\$:

    3. \$120 - 20 = 3P + 2P\$

    \$100 = 5P\$

    \$P^* = 20\$

  3. Substitute \$P^*\$ into either equation to find \$Q^*\$:

    4. \$Q^* = 120 - 2(20) = 80\$

  4. Interpretation:

    • At a price of $20 per unit, the market clears with 80 units bought and sold.

    • If a tax of \$5 per unit is imposed on producers, the supply equation becomes \$Q_s = 20 + 3(P-5) = 5 + 3P$.

    • New equilibrium: \$120 - 2P = 5 + 3P \Rightarrow 115 = 5P \Rightarrow P^* = 23\$ and \$Q^* = 120 - 2(23) = 74\$.

    • Result: price to consumers rises, quantity falls.

7. Summary Checklist

  • Know the shape and slope of demand and supply curves.

  • Be able to write and rearrange linear demand and supply equations.

  • Identify equilibrium where \$Qd = Qs\$.

  • Understand how shifts affect equilibrium price and quantity.

  • Practice drawing diagrams and labeling key points.