Elasticity, the Total Revenue Test, and Classifying Goods

Objectives

• Students will be able to calculate price elasticity of demand using the midpoint formula and classify demand as elastic, inelastic, or unit elastic.
• Students will be able to apply the total revenue test to predict how a price change affects total revenue.
• Students will be able to calculate and interpret the sign of cross-price and income elasticity to classify goods as substitutes or complements and normal or inferior.
• Students will be able to explain the determinants of elasticity: availability of substitutes, share of budget, necessity vs luxury, and time horizon.

Materials (all free, no student accounts needed)

• Elasticity module lesson
• Elasticity sandbox graph
• Elasticity practice set
• Flashcards for spaced review
• AP Micro cram sheet

Five-minute warm-up, no prep

Open one of these on the projector. Students say what they think happens to price and quantity before anything moves, lock it in, and then the graph plays out step by step. No accounts, nothing graded or stored.

• Tea Gets Pricier
• Coffee Beans Get Expensive
• Printers Get Pricier, Ink Suffers

Warm-up (10 min)

• Do Now: "Insulin and movie tickets both go up 20% in price. For which one does quantity demanded barely move, and why?"
• Think-pair-share, then cold-call. Write the two words that will run the whole lesson on the board next to each good: inelastic (insulin) and elastic (movie tickets).

Direct instruction (25 min)

• Project the Price Elasticity of Demand and Total Revenue sections of the module lesson. Write the midpoint formula and work one full calculation, emphasizing that AP reports PED as an absolute value so the negative sign is dropped.
• Classify the result: greater than 1 is elastic, less than 1 is inelastic, equal to 1 is unit elastic. Anchor each to the warm-up goods.
• Teach the total revenue test as a two-column decision: if demand is elastic, price and total revenue move opposite ways; if inelastic, they move together.
• Introduce cross-price elasticity (positive means substitutes, negative means complements) and income elasticity (positive means normal, negative means inferior). Stress that the SIGN carries the meaning here.
• List the four determinants of elasticity and give a one-line example of each.

Guided practice (30 min)

• Project /sandbox/elasticity. Point out that along a single straight-line demand curve elasticity is not constant. Drag the point into the upper region and cold-call: "Elastic or inelastic here?" Then drag to the lower region and ask again.
• At each point, have the class read the total revenue box and predict, before you move the price, whether revenue rises or falls. Confirm with the total revenue test on the board.
• Whiteboard round: give two price/quantity pairs and have every student compute PED with the midpoint formula and hold up elastic or inelastic. Reveal, then have one student walk through the arithmetic.
• Rapid classification: read these five scenarios and have students hold up the answer and justify it by the sign of the elasticity. (1) A 10% rise in the price of tea raises the quantity of coffee demanded: positive cross-price elasticity, substitutes. (2) Incomes fall and bus ridership rises: negative income elasticity, inferior good. (3) The price of printers drops and ink-cartridge sales rise: negative cross-price elasticity, complements. (4) Incomes rise and demand for restaurant steak dinners increases: positive income elasticity, normal good. (5) The price of gasoline rises and demand for large SUVs falls: negative cross-price elasticity, complements.

Independent practice (25 min)

• Students complete the Elasticity practice set, taking the midpoint-calculation and total-revenue-test items first.
• Each student computes one cross-price and one income elasticity from a short data prompt and writes the good classification with a one-sentence justification.

Exit ticket

• When price rises from $8 to $12 quantity demanded falls from 100 to 60. Use the midpoint formula to compute PED and classify demand as elastic, inelastic, or unit elastic.
• A coffee shop is deciding whether to raise prices. Its demand is inelastic. Will total revenue rise or fall, and how do you know?
• The cross-price elasticity between two goods is -1.5. Are they substitutes or complements? What single feature of the number told you?

Homework

• Finish the Elasticity practice set and review the elasticity terms on /flashcards for five minutes.
• Write two real product examples, one you expect to be price elastic and one inelastic, each with a one-sentence reason from the four determinants.

Differentiation

• Early finishers: hand them a linear demand schedule and ask them to find the single price where demand is unit elastic and total revenue is maximized.
• Support: provide a formula reference card with the midpoint formula pre-written and one worked example so students focus on plugging in, not recalling the setup.
• Reteach group: pull students who inverted the total-revenue-test logic and drill four elastic/inelastic cards asking only "same direction or opposite?"

Misconceptions to head off

• Belief: elasticity is the same as the slope of the demand curve. Correction: elasticity is based on percentage changes, so it varies along a straight-line demand curve even though the slope is constant.
• Belief: because demand elasticity is negative you report it as a negative number. Correction: AP reports price elasticity of demand as its absolute value; the negative sign is understood and dropped.
• Belief: a steeper demand curve is more elastic. Correction: a steeper (closer to vertical) curve is more inelastic; flatter is more elastic.
• Belief: a negative cross-price elasticity means an inferior good. Correction: a negative cross-price elasticity means the goods are complements; it is the INCOME elasticity sign that distinguishes inferior (negative) from normal (positive).