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    Question

    Given the demand function QD=100−2P and the supply

    function QS=3P−50, where QD is the quantity demanded, QS is the quantity supplied, and P is the price. What are the equilibrium price and quantity in this market?
    A Equilibrium Price = 20, Equilibrium Quantity = 60 Correct Answer Incorrect Answer
    B Equilibrium Price = 30, Equilibrium Quantity = 40 Correct Answer Incorrect Answer
    C Equilibrium Price = 30, Equilibrium Quantity = 20 Correct Answer Incorrect Answer
    D Equilibrium Price = 50, Equilibrium Quantity = 50 Correct Answer Incorrect Answer

    Solution

    To find the equilibrium price and quantity, we set the quantity demanded equal to the quantity supplied (QD=QS). • Set Demand equal to Supply: 100−2P=3P−50 • Solve for P (Price): Add 2P to both sides: 100=5P−50 Add 50 to both sides: 150=5P Divide by 5:  P=150/5  P=30 So, the equilibrium price is 30. • Substitute P back into either the Demand or Supply equation to find Q (Quantity): Using the Demand function: QD=100−2P  QD=100−2(30)  QD=100−60  QD=40 Using the Supply function (to verify): QS=3P−50  QS=3(30)−50  QS=90−50  QS=40 Both equations yield an equilibrium quantity of 40. Therefore, the equilibrium price is 30 and the equilibrium quantity is 40.

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