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Zorluk: OrtaMarket Equilibrium Price and Quantity

In a regional market for palm oil, the weekly quantity demanded is expressed as Qd=400−8PQ_d = 400 - 8P and the quantity supplied is expressed as Qs=−80+12PQ_s = -80 + 12P, where PP represents the price per liter in Naira (₦₦). If the government fixes a price ceiling of ₦15₦15 per liter, what is the resulting market condition?

  1. A shortage of 180 litersCevap
  2. B
    A surplus of 180 liters
  3. C
    A shortage of 280 liters
  4. D
    Market equilibrium with 208 liters traded

Cevap

A shortage of 180 liters
Evaluating both market equations at the controlled price ceiling of P=₦15P = ₦15 yields a quantity demanded of Qd=400−8(15)=280Q_d = 400 - 8(15) = 280 liters and a quantity supplied of Qs=−80+12(15)=100Q_s = -80 + 12(15) = 100 liters. Subtracting quantity supplied from quantity demanded (280−100280 - 100) leaves an excess demand of 180180 liters, which constitutes a market shortage.

Adım Adım Çözüm

1
Calculate the market equilibrium price to determine if the price ceiling is binding.
400−8P=−80+12P⇒480=20P⇒P∗=₦24400 - 8P = -80 + 12P \Rightarrow 480 = 20P \Rightarrow P^* = ₦24. Since ₦15<₦24₦15 < ₦24, the price ceiling is binding.
A price ceiling set below the equilibrium price restricts the market price legally.
2
Calculate the quantity demanded (QdQ_d) at the price ceiling of P=₦15P = ₦15.
Qd=400−8(15)=400−120=280Q_d = 400 - 8(15) = 400 - 120 = 280 liters.
Determines how much consumers wish to buy at the controlled price.
3
Calculate the quantity supplied (QsQ_s) at the price ceiling of P=₦15P = ₦15.
Qs=−80+12(15)=−80+180=100Q_s = -80 + 12(15) = -80 + 180 = 100 liters.
Determines how much producers are willing to supply at the controlled price.
4
Compute the difference between quantity demanded and quantity supplied.
Qd−Qs=280−100=180Q_d - Q_s = 280 - 100 = 180 liters (Shortage).
When quantity demanded exceeds quantity supplied below equilibrium, the market experiences an excess demand or shortage.

Anahtar Kavram

Market Disequilibrium and Price Ceiling Impact
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Konular

Market Equilibrium Price and Quantity

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