Price determination — practice questions

Step 1 — Equilibrium (a): where quantity demanded equals quantity supplied → $8 and 600 pizzas per week.

Step 2 — At $12 (b): Qs = 800 but Qd = 400 → excess supply (surplus) of 400. Unsold pizzas lead sellers to cut prices; as price falls, quantity demanded extends and quantity supplied contracts until the market returns to $8.

Step 3 — At $6 (c): Qd = 700 but Qs = 500 → excess demand (shortage) of 200. Queues and sell-outs lead sellers to raise prices; quantity demanded contracts and quantity supplied extends until the market returns to $8.

Step 4 — Diagram: draw D (downward) and S (upward) crossing at (600, $8). Mark the surplus gap at $12 and the shortage gap at $6.

Key point: surpluses push the price down and shortages push it up, so the price settles where there is no pressure to change — the equilibrium.

Step 1 — Equilibrium (a): 2 000 − 10P = 500 + 5P → 1 500 = 15P → P = $100. Quantity = 2 000 − 10(100) = 1 000 headphones. Check: Qs = 500 + 500 = 1 000.

Step 2 — At $80 (b): Qd = 2 000 − 800 = 1 200; Qs = 500 + 400 = 900. Quantity demanded exceeds quantity supplied by 300 — a shortage (excess demand).

Step 3 — Back to equilibrium (c): at $80 the headphones sell out and some buyers are turned away. Sellers raise the price. As it rises towards $100, quantity demanded contracts (from 1 200 towards 1 000) and quantity supplied extends (from 900 towards 1 000). At $100 the shortage is gone and the price stops rising.

Step 4 — Interpret: the shortage is the signal; the rising price both rations the limited headphones and gives the producer an incentive to supply more.