Principles of Microeconomics - ECON 221

[Virtual Presenter] Principles of Microeconomics ECON 221 Carlos Molina Lecture 5: Price Elasticity of Demand.

[Audio] Back to last class: how much do sellers receive? 10 Last class gave us S (P∗, Q∗) = ($5, 50). E 5 D Price per cup ($) P × Q 0 Revenue is the amount buyers pay and sellers receive: Revenue = P × Q. 0 50 100 Cups of coffee per week, Q Revenue = $5 × 50 = $250 . Revenue is not profit: costs have not been subtracted. 2 / 28.

[Audio] Four shifts, one revenue question Curve shift P∗ Q∗ Revenue Demand increases ↑ ↑ ↑ Demand decreases ↓ ↓ ↓ Supply increases ↓ ↑ ? Supply decreases ↑ ↓ ? When price and quantity move together, revenue moves with them. When they move in opposite directions, direction alone is not enough. 3 / 28.

[Audio] The same price increase can raise or lower revenue Smaller quantity response Larger quantity response 10 10 DB : P = 10 − 0.1Q DA : P = 26 − 0.5Q E2 E2 B B 6 7 6 7 E1 E1 Price ($) Price ($) C A A C 0 0 38 40 0 20 60 0 20 30 40 60 Quantity, Q Quantity, Q P : $6 → $7, Q : 40 → 38 Revenue: $240 → $266 ↑ P : $6 → $7, Q : 40 → 30 Revenue: $240 → $210 ↓ Both prices rise by $1. The size of the quantity response determines whether sellers receive more or less. 4 / 28.

[Audio] Price elasticity of demand The price elasticity of demand measures the percentage response of quantity demanded to a percentage change in the good's own price, holding other demand determinants fixed. εD = %∆Q %∆P . Because this is demand, the explicit notation is QD; we use Q when there is no ambiguity. Economists often report price elasticity as |εD|, focusing on responsiveness rather than direction. Elasticity is unit-free: it compares percentage changes. 5 / 28.

[Audio] Percentages make markets comparable A $1 price increase has very different meanings for different goods. Initial price New price Percentage increase Cup of coffee $2 $3 50% Concert ticket $100 $101 1% The same logic applies to quantity. A decline of 100 units is large in a market selling 200 units and small in a market selling 100,000. Percentage changes put price and quantity responses on a common scale. 6 / 28.

[Audio] Formula to calculate elasticity between two points Let E1 = (P1, Q1) and E2 = (P2, Q2) denote two market equilibria on one demand curve. %∆P = P2 − P1 ¯P × 100, %∆Q = Q2 − Q1 ¯Q × 100, ¯P = P1 + P2 2 , ¯Q = Q1 + Q2 2 . Therefore, εD = %∆Q %∆P = (Q2 − Q1)/¯Q ∆P ¯P ¯Q . (P2 − P1)/¯P = ∆Q This formula gives the same elasticity whether we move from point 1 to point 2 or in reverse. Optional: revenue formula Optional: revenue percentages Optional: choice of base 7 / 28.

[Audio] Classify demand using elasticity's magnitude For ordinary downward-sloping demand over an interval: Value Absolute value Classification Quantity response If price rises εD < −1 |εD| > 1 Elastic Larger percentage change than price Revenue falls εD = −1 |εD| = 1 Unit elastic Equal percentage change Revenue is unchanged εD > −1 |εD| < 1 Inelastic Smaller percentage change than price Revenue rises 8 / 28.

[Audio] Price elasticity in the examples from slide 4 For both demand curves, E1 = ($6, 40) and P2 = $7. DA: smaller response, Q2 = 38 DB: larger response, Q2 = 30 εD = −2/39 εD = −10/35 1/6.5 = −1 3 1/6.5 = −13 7 Inelastic demand Elastic demand 3 7 ∆R = 39(1) � 1 − 1 ∆R = 35(1) � 1 − 13 � = +26 � = −30 Revenue rises: $240 → $266 Revenue falls: $240 → $210 The formula gives the same +$26 and −$30 revenue changes shown in slide 4. 9 / 28.

[Audio] What the two elasticity estimates mean DA: smaller response DB: larger response εD = −1 εD = −13 3 ≈ −0.33 7 ≈ −1.86 A 1% increase in price is associated with approximately a 0.33% decrease in quantity demanded. A 1% increase in price is associated with approximately a 1.86% decrease in quantity demanded. The quantity response is small enough that revenue rises in this example. The quantity response is large enough that revenue falls in this example. The same price increase produces a much larger percentage quantity response on DB. 10 / 28.

[Audio] What makes demand more or less elastic? Examples from Mankiw (2027): Close substitutes. Oat and almond milk are close substitutes; eggs have fewer. But what about iPhones and Android phones? Necessity or luxury. Sailboats tend to be more elastic than doctor visits. But what about a specific limited-production Ferrari model? Market definition. Vanilla ice cream tends to be more elastic than ice cream overall or food. But what about Pfizer–BioNTech when it was the only U.S.-authorized COVID-19 vaccine? Time horizon. Gasoline demand becomes more elastic as buyers gain time to adjust. But what if new-car prices rise? These are tendencies, not universal rules. 11 / 28.

[Audio] How elastic is demand for familiar goods? Inelastic Elastic Housing Transatlantic air travel (economy) -0.12 -0.12 -0.15 Rail transit (rush hour) -0.20 -0.22 -0.35 Electricity Taxi cabs Gasoline -0.40 Transatlantic air travel (first class) Wine Beef Transatlantic air travel (business class) Kitchen and household appliances -0.55 -0.59 -0.62 -0.63 -0.64 Chicken Cable TV (basic, rural) -0.69 -0.70 Soft drinks -0.80 Beer -0.87 New vehicle -1.00 Rail transit (off-peak) -1.44 Computer -1.51 Cable TV (basic, urban) -1.77 Cable TV (premium) -2.27 Restaurant meals -2.5 -2.0 -1.5 -1.0 -0.5 0.0 Price elasticity of demand Illustrative estimates reported in Shapiro et al. (2022), Table 5.2. 12 / 28.

[Audio] Slope and elasticity are not the same But they are closely connected Elasticity over an interval εD = ∆Q Slope on the graph ∆P ∆Q ∆P ¯P ¯Q With price on the vertical axis, slope is measured in dollars per unit of quantity. Slope depends on the units used; elasticity has no units, so it is better for measuring and comparing responsiveness. Because ¯P > 0 and ¯Q > 0, elasticity and slope have the same sign. For a downward-sloping demand curve, both are negative. 13 / 28.

[Audio] Elasticity changes along a linear demand curve 10 elastic The slope is constant everywhere. 8 unit elastic 5 Price ($) inelastic 2 D At high prices and low quantities, the percentage quantity response is large relative to the percentage price change. 0 0 20 50 80 100 Quantity, Q The reverse is true near the quantity intercept. One straight demand curve can contain elastic, unit-elastic, and inelastic regions. 14 / 28.

[Audio] A supply increase can raise or lower revenue Both examples move along the same unchanged demand curve, P = 10 − 0.1Q. Elastic part of demand Inelastic part of demand Supply increase: ($7, 30) → ($6, 40) Supply increase: ($3, 70) → ($2, 80) Quantity: +28.6%; price: −15.4% Quantity: +13.3%; price: −40.0% εD ≈ −1.86 εD ≈ −0.33 Revenue: $210 → $240 ↑ Revenue: $210 → $160 ↓ The direction of a supply shift does not determine the direction of revenue; demand elasticity over the movement does. 15 / 28.

[Audio] Check your understanding Elasticity along a linear demand curve Consider the generic inverse demand curve P = a − bQ, a > 0, b > 0. On the economically relevant portion of the curve, 0 < Q < a b. For which values of Q is demand elastic, unit elastic, or inelastic? 16 / 28.

[Audio] Check your understanding Both demand curves pass through the same point, E. PE E Price, P DA DB QE Quantity, Q At this point, can we say that one demand curve is more elastic than the other? 17 / 28.

[Audio] Two extremes anchor the elasticity scale Perfectly inelastic demand: εD = 0 Perfectly elastic demand: εD → −∞ D : Q = 50 6 5 D : P = 5 Price Price 4 50 25 75 Quantity, Q Quantity, Q Quantity does not respond to price. Buyers are extremely sensitive around one price. 18 / 28.

[Audio] Elasticity when demand is not linear Special case: constant elasticity Any demand function of the form Q = kPη, where k > 0 and η < 0 are constants, has constant price elasticity along the entire curve. In this family, the exponent η is the price elasticity: εD = η. Imagine that we set k = 100 and η = −1. The equation becomes Q = 100P−1 = 100 P . Since η = −1, demand is unit elastic—neither elastic nor inelastic. 19 / 28.

[Audio] Elasticity when demand is not linear Special case: unit elastic demand 10 Here Q = 100P−1, so η = −1. P Q Revenue Price 4 5 D 2 10 20 25 50 $0.5 200 $100 $2 50 $100 $4 25 $100 $5 20 $100 $10 10 $100 Quantity, Q Every movement along this curve has εD = −1, so demand is unit elastic and revenue is constant. 20 / 28.

[Audio] Elasticity when demand is not linear Special case: constant elasticity Same k = 100 and same five prices in Q = 100Pη. Compare the curves Inelastic demand: η = −0.5 Elastic demand: η = −2 P Q Revenue P Q Revenue $0.5 141.4 $70.7 $2 70.7 $141.4 $4 50.0 $200.0 $5 44.7 $223.6 $10 31.6 $316.2 $0.5 400.00 $200 $2 25.00 $50 $4 6.25 $25 $5 4.00 $20 $10 1.00 $10 As price rises, revenue rises. As price rises, revenue falls. When −1 < η < 0, price and revenue move together; when η < −1, they move in opposite directions. At η = −1, revenue is constant. 21 / 28.

[Audio] Check your understanding A productive harvest can reduce farm revenue Suppose improved growing conditions shift the market supply of a staple crop to the right. 1. Equilibrium crop price falls and equilibrium quantity rises. 2. Demand for a basic staple may be inelastic over the relevant range. 3. The percentage fall in price then exceeds the percentage increase in quantity. 4. Buyers' spending, which is also sellers' revenue, falls. What is good news for physical production can be bad news for market revenue. Can this information alone determine what happens to profit? 22 / 28.

[Audio] Check your understanding Can elasticity predict revenue? A theater estimates demand elasticity over a proposed price interval as εD = −0.6. It is considering a 5% increase in ticket price. Approximately how much does ticket quantity fall? Does ticket revenue rise or fall? Can this information alone determine what happens to the theater's profit? 23 / 28.

[Audio] Three applications: why elasticity matters Examples from Mankiw (2027), Section 5.3 Organization of the Petroleum Exporting Countries (OPEC). Application What changes? Why elasticity matters Farming A productivity gain shifts crop supply to the right. With inelastic demand, the percentage fall in price exceeds the percentage rise in quantity, so farm revenue falls. Drug policy Interdiction shifts supply left; prevention or treatment shifts demand left. With inelastic demand, interdiction can raise spending even as use falls. Demand reduction lowers price, quantity, and spending. OPEC and oil OPEC cuts oil supply. Less elastic short-run demand implies a large price rise; more elastic long-run demand weakens the price effect. 24 / 28.

[Audio] Oil prices show both OPEC's power and its limits World crude oil price, 1970–1990 1973--74 1979--80 60 First oil shock Second oil shock 40 1973–74: Arab OPEC producers cut output and imposed an embargo. The nominal annual oil price rose from $2.81 to $10.97 per barrel—almost fourfold. 20 U.S. dollars per barrel 1978–85: The Iranian Revolution and Iran–Iraq War produced a second shock. OPEC then cut output, especially in Saudi Arabia, to defend high prices. 1985--86 Price collapse 0 1970 1975 1980 1985 1990 Nominal dollars Real 2010 dollars 1985–86: Conservation and expanding non-OPEC production weakened OPEC's price power. Quota discipline eroded, Saudi Arabia stopped acting as the swing producer, and the nominal annual price fell by 47% in 1986. Sources: World Bank (2026); EIA (2026); EIA (1986). World Bank real prices use the Manufacturers Unit Value Index (2010=100). 25 / 28.

[Audio] Why OPEC's price power weakens over time The same supply cut meets more elastic demand in the long run DSR S1 OPEC cut ESR S0 ELR E0 Short run: demand is inelastic. The price rises substantially, while quantity falls only slightly. DLR Price of oil, P Quantity of oil, Q Long run: demand is more elastic. The price rises less, while quantity falls more. 26 / 28.

[Audio] What we discussed today? 1. Price elasticity of demand measures percentage responsiveness and is unit-free: εD = %∆Q/%∆P. 2. For ordinary downward-sloping demand, demand is elastic if εD < −1, unit elastic if εD = −1, and inelastic if −1 < εD < 0. 3. Elasticity is not slope: a linear demand curve has constant slope but changing elasticity. 4. Along unchanged demand, price and revenue move oppositely when demand is elastic, together when demand is inelastic, and revenue is unchanged when demand is unit elastic. 27 / 28.

[Audio] For next class Next topic Income elasticity, cross-price elasticity, and price elasticity of supply. Preparation For next class, review the percentage-change method and the assigned elasticity reading: Chapter 5 of the main book (Mankiw 2027), or Sections 5.1–5.2 and the revenue subsection of Section 5.3 of the free book (Shapiro et al. 2022). You do not need to read both. 28 / 28.

[Audio] Appendix: Deriving the revenue formula Let ∆P = P2 − P1 and ∆Q = Q2 − Q1. The midpoint definitions imply 2 , ¯Q + ∆Q 2 (P2, Q2) = � ¯P + ∆P � , 2 , ¯Q − ∆Q 2 (P1, Q1) = � ¯P − ∆P � . Therefore, ∆R = P2Q2 − P1Q1 2 2 2 2 = � ¯P + ∆P � � ¯Q + ∆Q � − � ¯P − ∆P � � ¯Q − ∆Q � = ¯Q∆P + ¯P∆Q. The elasticity formula can be rearranged as εD = ∆Q/¯Q ∆P/¯P =⇒ ¯P∆Q = ¯Q∆P εD. Substituting this expression into the last line above gives ∆R = ¯Q∆P + ¯Q∆P εD = ¯Q∆P(1 + εD). Back.

[Audio] Appendix: Midpoint versus initial-value methods Why the percentage-change base matters The midpoint method divides each change by the average of the two endpoints. The initial-value method uses the starting value, so reversing direction generally changes the result. For small changes, the two are usually close. Demand Midpoint εD Initial-value εD Classification DA: 40 → 38 −0.33 −0.30 Inelastic under both DB: 40 → 30 −1.86 −1.50 Elastic under both With initial-value percentages, the exact revenue formula is more complicated. Reusing the previous formula gives the approximations DA : ∆R ≈ 39(1)(1 − 0.30) = +27.3 instead of + 26, DB : ∆R ≈ 35(1)(1 − 1.50) = −17.5 instead of − 30. Larger movements can even change the classification. See an example Back.

[Audio] Appendix: Revenue-growth approximation Using Ri = PiQi and midpoint bases, write the proportional changes as decimals: gP = ∆P 2 . ¯P , gQ = ∆Q ¯Q , gR = ∆R ¯R , ¯R = R1 + R2 The midpoint identities give ∆R = ¯P∆Q + ¯Q∆P = ¯P ¯Q(gP + gQ), 4 ¯R = ¯P ¯Q � 1 + gPgQ � . Therefore, gR = gP + gQ 1 + gPgQ/4 ≈ gP + gQ ⇐⇒ %∆R ≈ %∆P + %∆Q . The approximation treats 1 + gPgQ/4 as 1; the product is small when the price and quantity changes are modest. Back.

[Audio] Appendix: How η changes demand η = −0.5 η = −1 η = −2 P = $2 2 With the same k = 100, all three curves meet only at (P, Q) = (1, 100). 1.5 At P = $2 η Q 1 Price, P 0.5 −0.5 70.7 −1 50 −2 25 0 0 25 50 70.7 100 150 200 Quantity, Q Larger |η| means a larger quantity response to the same price change. Back to the tables.

[Audio] Appendix: When the base matters A classification reversal Consider a relatively large movement along one demand curve: E1 = (P1, Q1) = ($10, 4), E2 = (P2, Q2) = ($6, 6). Midpoint values E1 as the base εinitial D = 2/4 εD = 2/5 −4/10 = −1.25 −4/8 = −0.80 Elastic Inelastic . ∆R = 36 − 40 = 5(−4)(1 − 0.80) = −4 � �� � exact , � ∆R = 5(−4)(1 − 1.25) = +5 � �� � initial-base approximation The initial-value calculation changes both the classification and the predicted direction of revenue. Back to initial values.

[Audio] References Mankiw, N. G. (2027). Principles of Microeconomics. 11th ed. Cengage. Shapiro, D., D. MacDonald, and S. A. Greenlaw (2022). Principles of Microeconomics 3e. Licensed under CC BY 4.0. Houston, TX: OpenStax. U.S. Energy Information Administration (Jan. 1986). Short-Term Energy Outlook. U.S. Department of Energy. — (2026). Oil Prices and Outlook. url: https://www.eia.gov/energyexplained/oil-and-petroleum-products/prices-and-outlook.php (visited on 09/01/2026). World Bank (Jan. 6, 2026). World Bank Commodity Price Data (The Pink Sheet): Annual Prices, 1960 to Present. url: https://thedocs.worldbank.org/en/doc/18675f1d1639c7a34d463f59263ba0a20050012025/related/CMO-Historical-Data-Annual.xlsx (visited on 09/01/2026)..