In a domestic agricultural market, the weekly demand function for palm oil is given by Q_d… — JAMB UTME

In a domestic agricultural market, the weekly demand function for palm oil is given by $Q_d = 800 - 20P$ and the supply function is given by $Q_s = -100 + 10P$ , where $P$ is the price per litre in Naira and $Q$ is the quantity in litres. What is the equilibrium quantity in litres?

Answer: 200 litres

Answer

The equilibrium quantity is 200 litres.

Market equilibrium occurs where quantity demanded equals quantity supplied (

Q_d = Q_s

). Setting

800 - 20P = -100 + 10P

yields

30P = 900

, which gives an equilibrium price of

P = 30

Naira. Substituting

P = 30

into the demand function

Q_d = 800 - 20(30)

gives an equilibrium quantity of

200

litres.

Step-by-Step Solution

Equate the demand function

Q_d

and the supply function

Q_s

to find the market equilibrium condition.

800 - 20P = -100 + 10P

At market equilibrium, quantity demanded equals quantity supplied.

Rearrange the equation to isolate

P

and calculate the equilibrium price.

30P = 900 \implies P = 30

Adding

20P

and

100

to both sides groups variable terms and constant terms together.

Substitute the equilibrium price (

P = 30

) into the demand equation to determine the equilibrium quantity.

Q^* = 800 - 20(30) = 200

Evaluating

Q_d

P = 30

gives the total quantity traded at equilibrium.

Key Concept

Market Equilibrium Price and Quantity

Question

Answer

Step-by-Step Solution

Key Concept

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