Week 5 — Practice Exercises · Elasticity

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 3 · Ungraded — for self-study and exam preparation
6 exercises, answer key below — try each before peeking.

Every number below is pre-computed and verified. Calculator and scratch paper recommended.

Exercise 1 — PED via midpoint formula (inelastic case)

The price of a commuter train pass rises from $4 to $6 per trip, and daily ridership falls from 80 to 60 trips.

(a) Compute PED using the midpoint formula. Show all steps.
(b) Classify as elastic, inelastic, or unit-elastic.
(c) Does total revenue for the transit authority rise or fall? Calculate both TR values to confirm.

Exercise 2 — PED via midpoint formula (elastic case)

A boutique coffee brand raises its price from $10 to $12 per bag, and weekly sales fall from 100 to 70 bags.

(a) Compute PED using the midpoint formula. Show all steps.
(b) Classify as elastic, inelastic, or unit-elastic.
(c) Does total revenue rise or fall? Confirm with TR calculations.

Exercise 3 — Elasticity ≠ slope

The demand for coffee cups follows Qd = 120 − 10P.

(a) Compute PED at the point where P = $2, Q = 100 (use a $1 price change: from P=2 to P=3, Q goes from 100 to 90). Use the midpoint formula.
(b) Now compute PED at the point where P = $8, Q = 40 (from P=8 to P=9, Q=40 to Q=30). Use the midpoint formula.
(c) The slope of the demand curve is constant (−1/10). Did PED change between parts (a) and (b)? What does that tell you about the relationship between slope and elasticity?

Exercise 4 — The TR test

For each situation, use the TR test only (no formula needed) to predict whether total revenue rises, falls, or stays the same:

(a) Demand is inelastic; the seller lowers price.
(b) Demand is elastic; the seller raises price.
(c) Demand is unit-elastic; the seller raises price.
(d) Demand is inelastic; the seller raises price.

Exercise 5 — Income elasticity (YED)

When household income rises from $50,000 to $70,000 per year, a household's annual demand for restaurant meals rises from 60 to 90 meals.

(a) Compute YED using the midpoint formula.
(b) Classify: normal good, inferior good, necessity, or luxury?

Exercise 6 — Cross-price elasticity (XED) and determinants

(a) When the price of butter rises from $3 to $5, the quantity of margarine demanded rises from 40 to 60 units per week. Compute XED and classify the relationship.

(b) For each pair of goods, predict the sign of XED and the relationship type:
- Netflix and a movie theater ticket
- Printer ink and a printer
- Apples and bananas

(c) Which determinant of elasticity explains why the short-run demand for gasoline is more inelastic than the long-run demand?

Answer Key (instructor + self-check)

Exercise 1

(a) %ΔQ = (60 − 80)/((80+60)/2) = −20/70 = −2/7; %ΔP = (6−4)/((4+6)/2) = 2/5; PED = (−2/7)÷(2/5) = −5/7 ≈ −0.71.
(b) |PED| = 0.71 < 1 → inelastic.
(c) TR₁ = $4×80 = $320; TR₂ = $6×60 = $360. TR rises (same direction as price) → confirms inelastic. ✓

Exercise 2

(a) %ΔQ = (70−100)/((100+70)/2) = −30/85 = −6/17; %ΔP = (12−10)/((10+12)/2) = 2/11; PED = (−6/17)÷(2/11) = −33/17 ≈ −1.94.
(b) |PED| = 1.94 > 1 → elastic.
(c) TR₁ = $10×100 = $1,000; TR₂ = $12×70 = $840. TR falls (opposite direction to price) → confirms elastic. ✓

Exercise 3

(a) P=2→3, Q=100→90: %ΔQ = −10/95 ≈ −0.1053; %ΔP = 1/2.5 = 0.4; PED = −0.1053/0.4 ≈ −0.26 (inelastic at the lower-price/high-Q end).
(b) P=8→9, Q=40→30: %ΔQ = −10/35 ≈ −0.2857; %ΔP = 1/8.5 ≈ 0.1176; PED = −0.2857/0.1176 ≈ −2.43 (elastic at the higher-price/low-Q end).
(c) Yes — PED changed dramatically even though the slope (−10 in ΔQ/ΔP, or −1/10 in ΔP/ΔQ) stayed constant. Elasticity is not slope: the same absolute price change is a very different percentage depending on where you are on the curve.

Exercise 4

(a) Inelastic + price ↓ → TR ↓ (same direction). Falls.
(b) Elastic + price ↑ → TR ↓ (opposite direction). Falls.
(c) Unit elastic + price ↑ → TR unchanged.
(d) Inelastic + price ↑ → TR ↑ (same direction). Rises.

Exercise 5

(a) %ΔQ = (90−60)/((60+90)/2) = 30/75 = 2/5; %ΔY = (70k−50k)/((50k+70k)/2) = 20k/60k = 1/3; YED = (2/5)÷(1/3) = 6/5 = 1.2.
(b) YED = +1.2 > 1 → normal good, luxury range (quantity rises faster than income). ✓

Exercise 6

(a) %ΔQ_marg = (60−40)/((40+60)/2) = 20/50 = 2/5; %ΔP_butter = (5−3)/((3+5)/2) = 2/4 = 1/2; XED = (2/5)÷(1/2) = 4/5 = 0.8 > 0 → substitutes. ✓
(b) Netflix and theater ticket: XED > 0, substitutes (streaming substitutes for movies). Printer ink and printer: XED < 0, complements (need both together). Apples and bananas: XED > 0, substitutes (both are fruits).
(c) Adjustment time (the "T" in SLAT): in the short run drivers can't easily switch cars or routes, so demand is inelastic. In the long run they can buy fuel-efficient vehicles, carpool, or move closer to work → more elastic.