Question

Difficulty: MediumMarket Equilibrium Price and Quantity

In a domestic agricultural market, the weekly demand function for palm oil is given by Qd=80020PQ_d = 800 - 20P and the supply function is given by Qs=100+10PQ_s = -100 + 10P, where PP is the price per litre in Naira and QQ 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 (Qd=QsQ_d = Q_s). Setting 80020P=100+10P800 - 20P = -100 + 10P yields 30P=90030P = 900, which gives an equilibrium price of P=30P = 30 Naira. Substituting P=30P = 30 into the demand function Qd=80020(30)Q_d = 800 - 20(30) gives an equilibrium quantity of 200200 litres.

Step-by-Step Solution

1
Equate the demand function QdQ_d and the supply function QsQ_s to find the market equilibrium condition.
80020P=100+10P800 - 20P = -100 + 10P
At market equilibrium, quantity demanded equals quantity supplied.
2
Rearrange the equation to isolate PP and calculate the equilibrium price.
30P=900    P=3030P = 900 \implies P = 30
Adding 20P20P and 100100 to both sides groups variable terms and constant terms together.
3
Substitute the equilibrium price (P=30P = 30) into the demand equation to determine the equilibrium quantity.
Q=80020(30)=200Q^* = 800 - 20(30) = 200
Evaluating QdQ_d at P=30P = 30 gives the total quantity traded at equilibrium.

Key Concept

Market Equilibrium Price and Quantity
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