Price determination — practice questions

Step 1 — Demand shift: Health report → demand shifts right → P↑, Q↑.

Step 2 — Supply shift: Good harvest → supply shifts right → P↓, Q↑.

Step 3 — Combined effect on Q: Both shifts raise quantity → Q definitely increases.

Step 4 — Combined effect on P: Demand raises P; supply lowers P → P is ambiguous — depends on relative shift magnitudes.

If demand shift is larger → net P rises. If supply shift is larger → net P falls.

Diagram: Draw D₁→D₂ (right) and S₁→S₂ (right). Mark E₁ and E₂. Label Q₂ > Q₁ clearly.

Part (a): Calculate Equilibrium

Step 1: Set quantity demanded equal to quantity supplied (Qd = Qs) to find the equilibrium price (P). 2,000 - 10P = 500 + 5P

Step 2: Solve for P. Add 10P to both sides: 2,000 = 500 + 15P Subtract 500 from both sides: 1,500 = 15P Divide by 15: P = $100$

Step 3: Substitute the equilibrium price (P = $100) back into either the demand or supply equation to find the equilibrium quantity (Q). Using the demand equation: Qd = 2,000 - 10(100) = 2,000 - 1,000 = 1,000 units. Using the supply equation (to check): Qs = 500 + 5(100) = 500 + 500 = 1,000 units.

Answer (a): The equilibrium price is $100 and the equilibrium quantity is 1,000 headphones.

**Part (b): Calculate Disequilibrium at P = $80**$

**Step 1: Calculate quantity demanded (Qd) at P = $80.**$ Qd = 2,000 - 10(80) = 2,000 - 800 = 1,200 units.

**Step 2: Calculate quantity supplied (Qs) at P = $80.**$ Qs = 500 + 5(80) = 500 + 400 = 900 units.

Step 3: Compare Qd and Qs to determine the disequilibrium. At P = $80, Qd (1,200) > Qs (900). This is a situation of excess demand, or a shortage.

Step 4: Calculate the size of the shortage. Shortage = Qd - Qs = 1,200 - 900 = 300 units.

Answer (b): At a price of $80, there is an excess demand (shortage) of 300 headphones.