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2281 · 2.6

Price changes — practice questions

Practice and worked examples for 2281 Price changes. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

In the market for coffee, a health report increases demand while good weather simultaneously increases supply.

Analyse the effect on equilibrium price and quantity.

Show solution outline

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.

Worked example 2

The market for a standard smartphone has the following demand and supply functions: Demand: Qd = 500 - 2P Supply: Qs = 100 + 2P Where P is the price in dollars ($) and Q is the quantity in thousands of units.

a) Calculate the equilibrium price and quantity. b) If the government imposes a maximum price of $80, calculate the resulting shortage or surplus.

Show solution outline

Part a) Calculating Equilibrium

Step 1: Set quantity demanded equal to quantity supplied. To find the equilibrium, we set Qd = Qs. 500−2P=100+2P500 - 2P = 100 + 2P

Step 2: Solve for the equilibrium price (P). Rearrange the equation to solve for P. 500−100=2P+2P500 - 100 = 2P + 2P 400=4P400 = 4P P=400/4P = 400 / 4 P = 100100

Step 3: Solve for the equilibrium quantity (Q). Substitute the equilibrium price (P = $100) into either the demand or supply equation. Using the demand equation: Qd=500−2(100)=500−200=300Qd = 500 - 2(100) = 500 - 200 = 300 Using the supply equation: Qs=100+2(100)=100+200=300Qs = 100 + 2(100) = 100 + 200 = 300 So, the equilibrium quantity is 300,000 units.

Equilibrium: Price = $100, Quantity = 300,000 units.

Part b) Calculating Disequilibrium at a Maximum Price

**Step 1: Calculate quantity demanded at the maximum price of 80.∗∗80.** Substitute P = $80 into the demand equation. Qd=500−2(80)=500−160=340Qd = 500 - 2(80) = 500 - 160 = 340 At $80, the quantity demanded is 340,000 units.

**Step 2: Calculate quantity supplied at the maximum price of 80.∗∗80.** Substitute P = $80 into the supply equation. Qs=100+2(80)=100+160=260Qs = 100 + 2(80) = 100 + 160 = 260 At $80, the quantity supplied is 260,000 units.

Step 3: Determine the shortage or surplus. Compare Qd and Qs. Since Qd (340,000) > Qs (260,000), there is an excess demand (shortage). Shortage=Qd−Qs=340,000−260,000=80,000Shortage = Qd - Qs = 340,000 - 260,000 = 80,000

Result: At a maximum price of $80, there is a shortage of 80,000 smartphones.

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