In a competitive market for cassava flour, the weekly demand function is given by Q_d = 32… — JAMB UTME

In a competitive market for cassava flour, the weekly demand function is given by $Q_d = 320 - 15P$ and the supply function is $Q_s = -40 + 10P$ , where $P$ is the price in Naira per kilogram, $Q_d$ is the quantity demanded in kilograms, and $Q_s$ is the quantity supplied in kilograms. What is the magnitude of the excess demand (shortage) in kilograms when the market price is fixed at $₦12$ per kilogram?

Answer: 60 kg

Answer

The magnitude of excess demand (shortage) at

₦12

per kilogram is

60

kg.

At a disequilibrium price of

₦12

, quantity demanded (

Q_d = 140

kg) is greater than quantity supplied (

Q_s = 80

kg). Subtracting quantity supplied from quantity demanded yields an excess demand (shortage) of

60

kg.

Step-by-Step Solution

Substitute

P = 12

into the demand function

Q_d = 320 - 15P

Q_d = 320 - 15(12) = 320 - 180 = 140

To find the total quantity consumers are willing to purchase at the specified price level.

Substitute

P = 12

into the supply function

Q_s = -40 + 10P

Q_s = -40 + 10(12) = -40 + 120 = 80

To find the total quantity producers are willing to bring to the market at the specified price level.

Calculate the difference between quantity demanded and quantity supplied (

Q_d - Q_s

)

Excess Demand =

140 - 80 = 60

Because the market price (

₦12

) is below the equilibrium price (

₦14.40

), quantity demanded exceeds quantity supplied, creating a shortage.

Key Concept

Market Equilibrium and Disequilibrium Shortage

Question

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