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Difficulty: Very hardMarket Equilibrium Price and Quantity

In a regional agricultural market for cashew nuts, total market demand consists of domestic processing demand (Qdd=500−8PQ_{dd} = 500 - 8P) and export demand (Qdx=300−4PQ_{dx} = 300 - 4P), where PP is the price per bag in thousands of Naira (\text{N}). The market supply from producer cooperatives is given by Qs=−100+8PQ_s = -100 + 8P. What is the equilibrium market quantity of cashew nuts in bags?

Answer: 260 bags

Answer

260 bags
Total market demand is obtained by adding domestic processing demand and export demand (Qd=800−12PQ_d = 800 - 12P). Equating total demand to market supply (800−12P=−100+8P800 - 12P = -100 + 8P) yields an equilibrium price of P∗=45P^* = 45 (in thousands of Naira). Substituting P∗=45P^* = 45 into the supply function yields the equilibrium quantity Q∗=−100+8(45)=260Q^* = -100 + 8(45) = 260 bags.

Step-by-Step Solution

1
Aggregate domestic and export demand functions to derive the total market demand function.
Qd=(500−8P)+(300−4P)=800−12PQ_d = (500 - 8P) + (300 - 4P) = 800 - 12P
Total market demand represents the horizontal sum of all demand sectors at any given price level.
2
Set total market demand equal to market supply to find the equilibrium price (P∗P^*).
800−12P=−100+8P  ⟹  20P=900  ⟹  P∗=45800 - 12P = -100 + 8P \implies 20P = 900 \implies P^* = 45
Market equilibrium requires total quantity demanded to equal total quantity supplied.
3
Substitute the equilibrium price (P∗=45P^* = 45) into the market supply function to solve for the equilibrium quantity (Q∗Q^*).
Q∗=−100+8(45)=260Q^* = -100 + 8(45) = 260 bags
Evaluating supply at the equilibrium price yields the final market equilibrium quantity.

Key Concept

Market Equilibrium Price and Quantity with Aggregated Demand Sectors
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Topics

Market Equilibrium Price and Quantity

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