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Zorluk: OrtaMarket Equilibrium Price and Quantity

In a regional commodity market, the monthly demand function for cocoa beans is given by Qd=250−4PQ_d = 250 - 4P and the supply function is given by Qs=−50+6PQ_s = -50 + 6P, where PP represents the price per bag in thousands of Naira (₦), QdQ_d is the quantity demanded in bags, and QsQ_s is the quantity supplied in bags. What is the equilibrium quantity of cocoa beans traded in this market?

Cevap: 130 bags

Cevap

The equilibrium quantity of cocoa beans is 130 bags.
Market equilibrium occurs at the price where quantity demanded equals quantity supplied (Qd=QsQ_d = Q_s). Setting 250−4P=−50+6P250 - 4P = -50 + 6P yields 10P=30010P = 300, so the equilibrium price P∗=30P^* = 30. Substituting P∗=30P^* = 30 into the demand function gives Q∗=250−4(30)=130Q^* = 250 - 4(30) = 130 bags.

Adım Adım Çözüm

1
Equate the demand function and supply function
250−4P=−50+6P250 - 4P = -50 + 6P
Market equilibrium occurs at the price level where quantity demanded equals quantity supplied.
2
Solve for equilibrium price (P∗P^*)
P∗=30P^* = 30
Rearranging 300=10P300 = 10P yields the equilibrium price of ₦30 thousand per bag.
3
Calculate equilibrium quantity (Q∗Q^*)
Q∗=130Q^* = 130
Substituting P=30P = 30 into Qd=250−4(30)Q_d = 250 - 4(30) gives 130 bags.

Anahtar Kavram

Market Equilibrium Price and Quantity
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Market Equilibrium Price and Quantity

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