In a local agricultural market, the daily demand function for inorganic fertilizer is give… — JAMB UTME

In a local agricultural market, the daily demand function for inorganic fertilizer is given by $Q_d = 600 - 15P$ and the supply function is given by $Q_s = -150 + 10P$ , where $P$ represents the price per bag in Naira ( $\text{N}$ ). What is the market equilibrium price in Naira?

Answer: 30 Naira

Answer

The market equilibrium price is 30 Naira.

At market equilibrium, quantity demanded equals quantity supplied (

Q_d = Q_s

). Equating

600 - 15P

and

-150 + 10P

gives

750 = 25P

, which solves to an equilibrium price of 30 Naira.

Step-by-Step Solution

Equate the demand function and the supply function to set the market equilibrium condition.

Q_d = Q_s \implies 600 - 15P = -150 + 10P

Market equilibrium occurs precisely where the quantity buyers wish to purchase equals the quantity sellers wish to supply.

Collect constants on one side and terms with the variable

P

on the other side.

600 + 150 = 10P + 15P \implies 750 = 25P

Transposing

-150

and

-15P

across the equals sign changes their signs to positive.

Solve for the equilibrium price

P

by dividing the total constant by the coefficient of

P

P = \frac{750}{25} = 30

Dividing 750 by 25 yields the price per bag at which the market clears.

Key Concept

Market Equilibrium Price

Estimated Time:1m 30s

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