Given the demand function for a commodity as Q_d = 100 - 5P and the supply function as Q_s… — JAMB UTME

Given the demand function for a commodity as $Q_d = 100 - 5P$ and the supply function as $Q_s = 20 + 3P$ , where $P$ represents the price in Naira ( $₦$ ), calculate the equilibrium quantity.

Answer: 50 units

Answer

The equilibrium quantity is 50 units.

At market equilibrium, quantity demanded equals quantity supplied (

Q_d = Q_s

). Setting

100 - 5P = 20 + 3P

gives

80 = 8P

, which solves to

P = 10

. Substituting

P = 10

into

Q_d = 100 - 5(10)

gives the equilibrium quantity of 50 units.

Step-by-Step Solution

Equate quantity demanded to quantity supplied to find the equilibrium condition

100 - 5P = 20 + 3P

Market equilibrium occurs where quantity demanded equals quantity supplied.

Solve for the equilibrium price (P)

P = 10 Naira

Group like terms: 100 - 20 = 5P + 3P => 80 = 8P, yielding P = 10.

Substitute the equilibrium price into the demand function to find equilibrium quantity

Q = 50 units

Qd = 100 - 5(10) = 50 units.

Key Concept

Market Equilibrium Price and Quantity

Question

Answer

Step-by-Step Solution

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