The market demand and supply functions for a staple food item are given as Q_d = 100 - 4P … — JAMB UTME

The market demand and supply functions for a staple food item are given as $Q_d = 100 - 4P$ and $Q_s = 20 + 4P$ , where $P$ is the price in Naira, $Q_d$ is the quantity demanded, and $Q_s$ is the quantity supplied. If the government fixes a maximum price ceiling of $\text{N}5$ , what will be the resulting market situation?

An excess demand of 40 unitsAnswer
B
An excess supply of 40 units
C
An excess demand of 20 units
D
An excess supply of 20 units

Answer

An excess demand of 40 units

Substituting

P = 5

into the demand function yields

Q_d = 80

units and into the supply function yields

Q_s = 40

units. Because quantity demanded exceeds quantity supplied by 40 units (

80 - 40 = 40

), the policy creates an excess demand (shortage) of 40 units.

Step-by-Step Solution

Calculate quantity demanded (

Q_d

) at the price ceiling of

P = 5

Q_d = 100 - 4(5) = 100 - 20 = 80

units

Substitute the maximum price set by the government into the demand equation.

Calculate quantity supplied (

Q_s

) at the price ceiling of

P = 5

Q_s = 20 + 4(5) = 20 + 20 = 40

units

Substitute the maximum price set by the government into the supply equation.

Determine the market imbalance by calculating

Q_d - Q_s

80 - 40 = 40

units of excess demand (shortage)

Since quantity demanded exceeds quantity supplied (

Q_d > Q_s

), a shortage occurs.

Key Concept

Price Ceiling and Market Shortage

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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