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AP Microeconomics Structured Practice Paper (10 Questions, 100 Marks)
AP Microeconomics
AP Microeconomics structured practice paper: 10 original questions, 100 marks in 60 minutes, covering price elasticity and total revenue.
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Paper details Level: S6 (AP) | Subject: Economics | Time: 60 minutes | Marks: 100 | Questions: 10
Section A Demand, Elasticity and Market Equilibrium (50 marks)
Questions 1-3
| # | Question | Answer and marking notes |
|---|---|---|
| 1 | (Price elasticity of demand) The price of a drink falls from HK$40 to HK$36 a cup and daily sales rise from 200 to 260 cups. (a) Calculate the percentage changes in price and in quantity. (2 marks) (b) Calculate the price elasticity of demand and state whether demand is elastic or inelastic. (3 marks) (c) Calculate total revenue before and after the price cut and explain the link between the revenue change and elasticity. (3 marks) (d) State one factor that would make demand for this drink less elastic. (2 marks) |
(a) Price change = (36 – 40) / 40 x 100 = -10.0 per cent; quantity change = (260 – 200) / 200 x 100 = +30.0 per cent. (b) PED = 30.0 / (-10.0) = -3.0, absolute value 3.0. Demand is elastic because the value exceeds 1. (c) Revenue before = 40 x 200 = HK$8,000; after = 36 x 260 = HK$9,360, a rise of HK$1,360 (17.0 per cent). With elastic demand, price and total revenue move in opposite directions because the quantity gain outweighs the price cut. (d) Any one: few close substitutes; the drink is a necessity; spending on it is a small share of income; buyers have little time to adjust. Marking note: part (b) must show the sign or state that the absolute value is taken; part (c) must give both revenue figures. |
| 2 | (Market equilibrium) In a market, demand is Qd = 120 – 2P and supply is Qs = 3P – 30, where price is in dollars. (a) Find the equilibrium price and quantity. (3 marks) (b) Calculate the consumer surplus at equilibrium. (3 marks) (c) Calculate the producer surplus at equilibrium. (2 marks) (d) Calculate total surplus and explain what the vertical intercept of the demand curve means. (2 marks) |
(a) Setting 120 – 2P equal to 3P – 30 gives 150 = 5P, so P = 30 and Q = 60. (b) Demand intercept on the price axis = 120 / 2 = 60; consumer surplus = 0.5 x (60 – 30) x 60 = 900. (c) Supply intercept = 30 / 3 = 10; producer surplus = 0.5 x (30 – 10) x 60 = 600. (d) Total surplus = 900 + 600 = 1,500. The intercept is the maximum price consumers would pay, i.e. the marginal benefit when quantity is zero. Marking note: parts (b) and (c) need the triangle formula and the equilibrium quantity. |
| 3 | (Profit maximisation) A firm faces demand P = 100 – Q and total cost TC = 200 + 40Q + 0.5Q squared. (a) State the marginal revenue (MR) and marginal cost (MC) functions. (3 marks) (b) Find the profit-maximising quantity and price. (3 marks) (c) Calculate the profit at that quantity. (2 marks) (d) Calculate average total cost (ATC) and average variable cost (AVC) at that quantity and decide whether the firm should keep producing. (2 marks) |
(a) TR = P x Q = (100 – Q)Q, so MR = 100 – 2Q; MC = dTC/dQ = 40 + 1.0Q. (b) Setting MR = MC: 100 – 2Q = 40 + 1.0Q gives Q = 20 and P = 80. (c) TR = 1,600; TC = 1,200; profit = 400. (d) ATC = 60 and AVC = 50. Since price exceeds both AVC and ATC the firm should keep producing and earns supernormal profit. Marking note: part (a) needs MR with twice the slope of demand; part (d) must compare P with AVC. |
Questions 4-5
| # | Question | Answer and marking notes |
|---|---|---|
| 4 | (Specific tax) In a market, demand is Qd = 200 – 4P and supply is Qs = 2P – 40. The government imposes a specific tax of 9 per unit on sellers. (a) Find the equilibrium price and quantity before the tax. (2 marks) (b) Find the price paid by buyers, the net price received by sellers and the quantity traded after the tax. (4 marks) (c) Calculate tax revenue and the deadweight loss. (2 marks) (d) Explain how the tax burden is shared between buyers and sellers. (2 marks) |
(a) 200 – 4P = 2P – 40 gives P = 40 and Q = 40. (b) The new supply is Qs = 2(P – 9) – 40. Solving gives buyer price P = 43, quantity 28 and sellers keep 34. (c) Tax revenue = 252; deadweight loss = 0.5 x 9 x (40 – 28) = 54. (d) Buyers pay 3 more and sellers receive 6 less, a 1 to 2 split, so sellers bear more of the burden because supply is less elastic than demand at the new equilibrium. Marking note: part (b) needs all three figures; part (d) needs an elasticity explanation. |
| 5 | (Price ceiling) In a market, demand is Qd = 300 – 5P and supply is Qs = 4P – 60. The government sets a price ceiling of 32. (a) Find the free-market equilibrium price and quantity. (3 marks) (b) Calculate quantity supplied and quantity demanded under the ceiling. (3 marks) (c) Calculate the shortage. (2 marks) (d) State two forms of non-price rationing the ceiling may cause. (2 marks) |
(a) 300 – 5P = 4P – 60 gives P = 40 and Q = 100. (b) At the ceiling of 32, quantity supplied = 68 and quantity demanded = 140. (c) Shortage = 72 units. (d) Any two: queues and waiting lists; ration coupons; black market trading; sellers choosing buyers or bundling. Marking note: in part (b) the quantity traded is set by supply, so it is 68, not the quantity demanded. |
Section B Firm Behaviour, Market Structure and Trade (50 marks)
Questions 6-8
| # | Question | Answer and marking notes |
|---|---|---|
| 6 | (Negative externality) A chemical product has marginal private cost MPC = 20 + Q, marginal external cost MEC = 0.5Q and marginal social benefit MSB = 100 – Q. (a) Find the market equilibrium quantity and price. (3 marks) (b) Find the socially optimal quantity and price. (3 marks) (c) Calculate the deadweight loss at the market equilibrium. (2 marks) (d) Find the per-unit Pigouvian tax at the optimal quantity and explain why. (2 marks) |
(a) Market equilibrium: 100 – Q = 20 + Q gives Q = 40 and P = 60. (b) Social optimum: MSB = MPC + MEC, i.e. 100 – Q = 20 + 1.5Q, giving Q = 32 and P = 68. (c) MEC at the market quantity = 20; deadweight loss = 0.5 x (40 – 32) x 20 = 80. (d) Pigouvian tax = MEC at the optimal quantity = 16 per unit, which internalises the external cost so that private cost equals social cost and output falls to the social optimum. Marking note: the triangle height in part (c) uses MEC at the market quantity, not at the optimum. |
| 7 | (Shutdown decision) A perfectly competitive firm has total cost TC = 400 + 20Q + 2.0Q squared, and the market price is 60. (a) State the MC function and find the profit-maximising quantity. (3 marks) (b) Calculate total revenue, total cost and profit at that quantity. (3 marks) (c) Calculate AVC at that quantity and decide whether the firm should shut down in the short run. (2 marks) (d) Find the shutdown price. (2 marks) |
(a) MC = 20 + 4.0Q. Setting P = MC gives Q = 10. (b) TR = 600; TVC = 400, TFC = 400, TC = 800, so profit = -200 (a loss). (c) AVC = 40, which is below the price of 60, so the firm should keep producing in the short run because it covers all variable cost and part of fixed cost. (d) The shutdown price is the minimum AVC. Since TVC starts at the origin, AVC tends to 20 as Q tends to zero, so the shutdown price is 20. Marking note: part (c) must compare price with AVC; a loss alone does not imply shutdown. |
| 8 | (Mark-up pricing) A firm charges HK$50 for its product and has marginal cost of HK$30. (a) Calculate the Lerner index. (3 marks) (b) Use (a) to infer the absolute value of the price elasticity of demand the firm faces. (3 marks) (c) If in another market the absolute elasticity is 2.0 and MC is HK$30, what price follows from the same mark-up rule? (2 marks) (d) Explain why the mark-up is smaller when demand is more elastic. (2 marks) |
(a) Lerner index = (P – MC) / P = (50 – 30) / 50 = 0.40 (40 per cent). (b) The Lerner index equals 1 divided by the absolute elasticity, so the elasticity is 1 / 0.40 = 2.5. (c) Mark-up = 1 / 2.0 = 0.50, so P = MC / (1 – mark-up) = 30 / 0.50 = HK$60. (d) The more elastic the demand, the larger the sales lost when price rises, so the price can exceed marginal cost by less and the mark-up is smaller. Marking note: part (b) needs the relation between the Lerner index and elasticity. |
Questions 9-10
| # | Question | Answer and marking notes |
|---|---|---|
| 9 | (International trade) A country has demand Qd = 500 – 10P and domestic supply Qs = 20P – 100. The world price is 12 and the country is a price taker. (a) Find domestic output, quantity demanded and imports under free trade. (3 marks) (b) The government imposes a tariff of 3 per unit. Find the new domestic output, quantity demanded and imports. (3 marks) (c) Calculate tariff revenue and the fall in imports. (2 marks) (d) State two effects of the tariff on domestic consumers. (2 marks) |
(a) At the world price of 12: Qd = 380, Qs = 140 and imports are 240. (b) After the tariff the domestic price is 15: Qd = 350, Qs = 200 and imports are 150. (c) Tariff revenue = 450; imports fall by 90. (d) Any two: a higher price reduces consumer surplus; consumption falls from 380 to 350; fewer varieties; some consumers are priced out of the market. Marking note: in part (b) the domestic price equals the world price plus the tariff. |
| 10 | (Three elasticities) The price of a good falls by 5 per cent and quantity demanded rises by 12 per cent. In the same period consumer income rises by 10 per cent and quantity demanded of the good rises by 25 per cent. The price of a related good rises by 8 per cent and quantity demanded of this good falls by 4 per cent. (a) Calculate the price elasticity of demand and state whether demand is elastic or inelastic. (3 marks) (b) Calculate the income elasticity and state whether the good is a necessity or a luxury. (3 marks) (c) Calculate the cross price elasticity and state whether the two goods are substitutes or complements. (2 marks) (d) If a firm faces elastic demand, what happens to total revenue when it cuts price? Explain. (2 marks) |
(a) PED = (+12 per cent) / (-5 per cent) = 2.4. Its absolute value exceeds 1, so demand is elastic. (b) YED = (+25 per cent) / (+10 per cent) = 2.5. It is above 1, so the good is a normal good and a luxury. (c) XED = (-4 per cent) / (+8 per cent) = -0.5. It is negative, so the two goods are complements. (d) With elastic demand a price cut raises total revenue because the percentage rise in quantity is larger than the percentage fall in price, so the quantity effect dominates. Marking note: part (a) needs the absolute value and a judgement; part (c) must keep the negative sign. |
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