Tags: price elasticity of demand, elastic, inelastic, demand curve, demand shifters, complements, substitutes, price discrimination, first degree, second degree, hurdle model, markup, margin, optimal pricing, network externalities, information goods, Texas A&M, microeconomic theory
This section covers the determinants of demand (what shifts the curve vs. what moves you along it), how to measure and interpret price elasticity, and how firms use elasticity to set optimal prices. It also covers price discrimination (first-degree, second-degree, and segment-based), the markup rule, and special pricing topics like information goods and network externalities.
Price elasticity of demand (Ep)
The percentage change in quantity demanded divided by the percentage change in price. Measures how responsive buyers are to price changes. Expressed as an absolute value in most applied contexts.
Elastic demand
|Ep| > 1. Quantity responds more than proportionally to a price change. A price increase causes total revenue to fall.
Inelastic demand
|Ep| < 1. Quantity responds less than proportionally to a price change. A price increase causes total revenue to rise.
Completely inelastic demand
Ep = 0. A vertical demand curve. Quantity does not change at all when price changes. The slope of the curve is infinite, so 1/slope = 0.
Demand curve shift vs. movement along the curve
A change in the good's own price causes a movement along the demand curve (upward for a price increase, downward for a decrease). A change in income, the price of related goods, tastes, or other external factors causes the entire curve to shift.
Substitute goods
Goods where an increase in the price of one leads to an increase in demand for the other. The cross-price coefficient in the demand equation is positive.
Complementary goods
Goods where an increase in the price of one leads to a decrease in demand for the other. The cross-price coefficient in the demand equation is negative. Example: motorcycles and motorcycle helmets.
First-degree price discrimination (perfect price discrimination)
The seller charges each individual customer a different price, extracting the maximum each is willing to pay.
Second-degree price discrimination
The seller offers a menu of different prices for different quantities, and customers self-select the package that suits them best. Think: bulk discounts, tiered pricing plans.
Third-degree price discrimination (segment pricing)
The seller identifies distinct market segments with different elasticities and charges different prices to each. Requires the ability to distinguish segments and prevent resale.
Hurdle model
A pricing approach used when it is difficult to distinguish between customer groups directly. A "hurdle" (e.g. a coupon, rebate, or waiting period) separates willing-to-pay-more customers from price-sensitive ones. Only applicable when you cannot easily identify segments.
Markup
(P – MC) / MC. The percentage by which price exceeds marginal cost, expressed relative to cost.
Margin
(P – MC) / P. The percentage of price that represents profit above marginal cost.
Information good
A product characterised by high fixed costs of creation but low or negligible marginal costs of reproduction (e.g. software, digital media, databases).
Network externalities (positive)
A good becomes more valuable to each user as the total number of users grows. Example: an online dating service, a social network, a messaging platform.
Own price changes cause movement along the demand curve, not a shift.
A price increase → upward movement along the curve (higher P, lower Q).
Demand curve shifts are caused by changes in: income, prices of related goods, consumer tastes, population, expectations.
In the equation Q = 60 – 60P + 2Y, a $2 price increase reduces Q by 120, while an $80 income increase raises Q by 160. Net effect: +40 units.
If increased demand for motorcycles increases demand for helmets, they are complements.
In the demand equation for helmets, the coefficient on the price of motorcycles will be negative (higher motorcycle prices → fewer motorcycles bought → fewer helmets demanded).
Positive coefficient on a related good's price → substitute. Negative coefficient → complement.
Q = 1,000 – 240P + 80Pc (Pc = competitor's price)
At P = 1.50 and Pc = 1.20: Q = 1,000 – 360 + 96 = 736
Demand curve for Pc = 1.20: Q = 1,096 – 240P
If Pc rises to 1.50: demand shifts right to Q = 1,120 – 240P (substitute effect)
QM = 1,200 – 8PM + 4PS
At PM = 200, PS = 300: QM = 1,200 – 1,600 + 1,200 = 800
Demand curve with PS = 300: QM = 2,400 – 8PM
Inverse demand: PM = 300 – (1/8)QM
Direct (arc) method: Ep = (%ΔQ) / (%ΔP)
Price of X goes from $5 to $8, Q falls from 100 to 80.
%ΔP = (8 – 5)/5 = 60%
%ΔQ = (80 – 100)/100 = –20%
|Ep| = 20/60 = 0.33 → inelastic (less than 1)
Point-slope method for inverse demand P = a – bQ:
Ep = (1/slope of inverse) × (P/Q) = (–1/b) × (P/Q)
Take absolute value
Worked example (JIF peanut butter):
P = 32 – 3Qd
At PUS = $3: Qd = 29/3 ≈ 9.67
At PUK = $10: Qd = 22/3 ≈ 7.33
Direct method: %ΔQ = –2.33/9.66 = –0.24, %ΔP = 7/3 = 2.33. |Ep| = 0.24/2.33 = 0.10
Point-slope at UK price: Ep = (1/3) × 10/(22/3) = |–0.46| = 0.46
If demand is elastic (|Ep| > 1): a price increase reduces total revenue (quantity drops more than proportionally).
If demand is inelastic (|Ep| < 1): a price increase raises total revenue.
A vertical demand curve has infinite slope → 1/slope = 0 → completely inelastic.
The Lerner index / inverse elasticity rule links elasticity to optimal pricing:
(P – MC) / P = 1 / |Ep|
Worked example: |Ep| = 3, MC = 20
(P – 20)/P = 1/3
P – 20 = P/3
(2/3)P = 20
P = 30
Margin = (30 – 20)/30 = 33%
Markup = (30 – 20)/20 = 50%
Worked example: |Ep| = 4, MC = 2
(P – 2)/P = 1/4
P – 2 = P/4
(3/4)P = 2
P = 8/3 ≈ 2.67
Margin = (2.67 – 2)/2.67 = 25%
Markup = (2.67 – 2)/2 = 33%
Finding MC from price and elasticity:
If P = 5 and |Ep| = 3: (5 – MC)/5 = 1/3 → MC = 10/3 ≈ 3.33
If demand is inelastic at the current output and MR < MC, the firm should decrease output. Revenue rises (inelastic means higher price boosts revenue), costs fall (less production). Profit increases.
At the profit-maximising point, MR = MC.
If you know the elasticity and the firm is already optimising, you can back out the price from the markup rule.
First-degree: charge each customer their maximum willingness to pay. Captures all consumer surplus.
Second-degree: offer a price schedule (quantity discounts, tiers) and let customers self-select.
Segment (third-degree): identify groups with different elasticities, charge different prices. Requirements:
Ability to distinguish the groups
Prevention of resale between groups
Groups must have different price elasticities
When practising segment pricing, charge a higher price to the segment with more inelastic demand.
Examples: academic journals charging different rates to libraries vs. individuals, airline tickets for business vs. leisure travellers.
In the parking garage problem, to maximise revenue across two segments, set prices so that marginal revenues from the segments are equal.
The hurdle model is for situations where you cannot easily identify which group a customer belongs to.
If you can easily distinguish customers (libraries vs. individuals), you do not need a hurdle. You simply charge different prices directly.
Characterised by high fixed costs and low or negligible marginal costs.
This does not mean they should be priced at zero or at average fixed cost.
Profit-maximising pricing still applies, informed by demand and elasticity.
A good with positive network externalities becomes more valuable as more people use it.
Example: an online dating service (more users → more matches → more value for each user).
Not the same as bundling (shaving cream + razor blades) or capacity constraints (waiting lists).
If |Ep| = 1.5 and price drops from $20 to $17.50 (a 12.5% decrease):
Expected %ΔQ = 1.5 × 12.5% = 18.75% increase
Price elasticity (direct/arc method): Ep = (%ΔQ) / (%ΔP)
Point elasticity (from inverse demand P = a – bQ): |Ep| = (1/b) × (P/Q)
Lerner index / optimal pricing rule: (P – MC) / P = 1 / |Ep|
Margin: (P – MC) / P
Markup: (P – MC) / MC
⚠️ A change in own price moves you along the curve. A change in income or the price of a related good shifts the curve. This distinction is tested frequently.
⚠️ Complements have a negative cross-price coefficient. Substitutes have a positive one. Motorcycles and helmets are complements (negative coefficient on motorcycle price in the helmet demand equation).
⚠️ Elastic demand: price up → revenue down. Inelastic demand: price up → revenue up. This is one of the most commonly tested relationships.
⚠️ A vertical demand curve is completely inelastic (Ep = 0), not perfectly elastic.
⚠️ The markup rule (P – MC)/P = 1/|Ep| is central to optimal pricing problems. Know how to solve for P, MC, margin, and markup from this equation.
⚠️ When practising price discrimination across segments, charge more to the segment with more inelastic demand.
⚠️ The hurdle model only applies when you cannot easily identify customer groups. If identification is easy, use direct segment pricing.
⚠️ To maximise revenue across segments, equalise marginal revenues, not total revenues or average revenues.
⚠️ Point elasticity problems: %ΔQ = |Ep| × %ΔP. Watch the direction of the price change.
Q: If demand is elastic and the firm raises its price, what happens to total revenue?
A: Revenue decreases. Quantity falls by a larger percentage than the price increase.
Q: A vertical demand curve has what type of elasticity?
A: Completely inelastic (Ep = 0). The slope is infinite, so 1/slope = 0.
Q: The price of good X rises from $5 to $8 and quantity falls from 100 to 80. Is demand elastic or inelastic?
A: Inelastic. %ΔP = 60%, %ΔQ = 20%. Since 20% < 60%, |Ep| < 1.
Q: If |Ep| = 3 and MC = $20, what is the optimal price?
A: (P – 20)/P = 1/3 → P = $30.
Q: What is the margin and markup at P = 30, MC = 20?
A: Margin = (30 – 20)/30 = 33%. Markup = (30 – 20)/20 = 50%.
Q: What defines second-degree price discrimination?
A: The seller offers different prices for varying amounts purchased, and customers choose the price-quantity combination that best suits them.
Q: When a firm price-discriminates across two segments, where does it charge the higher price?
A: In the segment with more inelastic demand.
Q: What is true of information goods?
A: They are characterised by high fixed costs but low or negligible marginal costs.
Q: An online dating service is an example of what?
A: A good with positive network externalities. It becomes more valuable as more users join.
Q: A firm's demand is Q = 60 – 60P + 2Y. Price rises by $2 and income rises by $80. What is the net change in Q?
A: ΔQ = –60(2) + 2(80) = –120 + 160 = +40 units.
Q: In a parking garage with short-term and long-term segments, what condition maximises revenue?
A: Set prices so that marginal revenues from the two segments are equal.
Q: If |Ep| = 1.5 and price falls from $20 to $17.50, what is the expected percentage increase in quantity?
A: %ΔP = 12.5%. Expected %ΔQ = 1.5 × 12.5% = 18.75%.
Q: When is the hurdle model used for price discrimination?
A: When the firm cannot easily distinguish between customer groups. If groups are easily identifiable, direct segment pricing is used instead.
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