The Price-Revenue Puzzle: Why Some Price Hikes Work and Others Backfire
Building Blocks: Demand, Revenue, and Elasticity
Before solving the puzzle, we need to understand the three key pieces: Demand, Total Revenue, and Elasticity.
1. Demand: This is the relationship between the price of a good and the quantity of it that consumers are willing and able to buy. The law of demand states that, all else being equal, as price goes up, the quantity demanded goes down, and vice versa. This is usually shown as a downward-sloping line on a graph.
2. Total Revenue (TR): This is the total amount of money a seller receives from sales. It is calculated simply as:
$ TR = Price \ (P) \times Quantity \ Sold \ (Q) $
For example, if a lemonade stand sells 50 cups at $2 each, the total revenue is $2 × 50 = $100.
3. Price Elasticity of Demand (PED): This measures how much the quantity demanded responds to a change in price. It's not enough to know that quantity goes down when price goes up; we need to know by what percentage. PED is calculated as:
$ PED = \frac{\%\ Change \ in \ Quantity \ Demanded}{\%\ Change \ in \ Price} $
Because price and quantity demanded move in opposite directions (one goes up, the other goes down), the PED value is almost always a negative number. However, economists often refer to its absolute value (ignoring the minus sign) when describing how "elastic" demand is.
The Five Faces of Elasticity
The numerical value of PED tells us the "type" of demand. We can classify it into five categories, which are summarized in the table below.
| Type of Demand | PED (Absolute Value) | Meaning | Example |
|---|---|---|---|
| Perfectly Inelastic | $ PED = 0 $ | Quantity demanded does not change at all when price changes. | Life-saving medicine with no substitutes. |
| Inelastic | $ 0 < |PED| < 1 $ | Quantity demanded changes by a smaller percentage than the price change. | Gasoline, basic food items (salt, bread), cigarettes. |
| Unit Elastic | $ |PED| = 1 $ | Quantity demanded changes by the exact same percentage as the price change. | A theoretical midpoint. Revenue remains unchanged when price changes. |
| Elastic | $ |PED| > 1 $ | Quantity demanded changes by a larger percentage than the price change. | Restaurant meals, brand-name soda, vacations, movie tickets. |
| Perfectly Elastic | $ PED = \infty $ | Consumers will buy any quantity at one specific price, but none at a higher price. | A farmer selling identical wheat in a huge competitive market. |
Solving the Puzzle: The Golden Rule of PED and Revenue
Now we can connect elasticity to total revenue ($ TR = P \times Q $). A price change has two opposing effects on revenue:
1. The Price Effect: A higher price increases the revenue you get per unit sold.
2. The Quantity Effect: A higher price decreases the number of units sold, which decreases revenue.
The type of elasticity determines which effect is stronger.
The Golden Rule:
- If demand is ELASTIC ($ |PED| > 1 $): The Quantity Effect > Price Effect. A price increase causes a large drop in sales, so Total Revenue FALLS. A price decrease causes a large jump in sales, so Total Revenue RISES.
- If demand is INELASTIC ($ |PED| < 1 $): The Price Effect > Quantity Effect. A price increase causes only a small drop in sales, so Total Revenue RISES. A price decrease causes only a small increase in sales, so Total Revenue FALLS.
- If demand is UNIT ELASTIC ($ |PED| = 1 $): The two effects perfectly balance each other. Total Revenue REMAINS UNCHANGED when the price changes.
Think of it like a seesaw with Price (P) and Quantity (Q) on either end. Elastic demand means the Q end is very heavy—move it a little (change price), and it swings a lot (revenue moves opposite to price). Inelastic demand means the P end is heavy—move it, and it controls the motion (revenue moves with price).
Real-World Scenarios: From Gas Stations to Movie Theaters
Let's apply the golden rule to concrete examples.
Scenario 1: Inelastic Demand – Gasoline Price Hike.
Imagine the price of gasoline rises by 20%. For most drivers, gasoline is a necessity for commuting; there are few good short-term substitutes (like electric cars or buses). The quantity demanded might only fall by, say, 5%. $ PED = \frac{-5\%}{+20\%} = -0.25 $ The absolute value is 0.25 ($ |PED| < 1 $), so demand is inelastic. According to the rule, a price increase should raise total revenue for gas stations. Let's check: If original revenue was $P \times Q$, the new price is 1.2P and the new quantity is 0.95Q. New Revenue = 1.2P × 0.95Q = 1.14PQ. Revenue increased by 14%!
Scenario 2: Elastic Demand – Movie Ticket Price Hike.
Now, imagine a local cinema raises ticket prices by 20%. For many people, movies are a treat with many substitutes: streaming at home, video games, or other entertainment. Customers are sensitive to the price. The quantity demanded might fall by 30%. $ PED = \frac{-30\%}{+20\%} = -1.5 $ The absolute value is 1.5 ($ |PED| > 1 $), so demand is elastic. The rule says a price increase should lower total revenue. Check: New price = 1.2P, new quantity = 0.7Q. New Revenue = 1.2P × 0.7Q = 0.84PQ. Revenue decreased by 16%. The cinema would have been better off lowering prices to attract more viewers.
Scenario 3: The Farmer's Dilemma – A Bountiful Harvest Can Be Bad News.
This is a classic application. Basic food crops like wheat or corn have inelastic demand—people need to eat roughly the same amount regardless of price. If farmers have a fantastic harvest, the market is flooded with supply, causing the price to fall dramatically. Because demand is inelastic, the percentage increase in quantity sold is much smaller than the percentage drop in price. Following the inelastic rule (price down → revenue down), the farmers' total income can actually decrease despite having more crops to sell. This explains why governments sometimes intervene to support farm prices.
What Makes Demand Elastic or Inelastic?
Several factors determine whether a product faces elastic or inelastic demand:
| Factor | Makes Demand More ELASTIC | Makes Demand More INELASTIC |
|---|---|---|
| Availability of Substitutes | Many close substitutes (e.g., different brands of soda, types of fruit). | Few or no substitutes (e.g., insulin for diabetics, gasoline in the short run). |
| Necessity vs. Luxury | Luxury goods (e.g., vacations, designer clothes). | Necessities (e.g., basic food, medicine, utilities). |
| Time Horizon | Long run (consumers have time to find alternatives, e.g., switching from gas to electric car). | Short run (consumers are "stuck" with current habits and products). |
| Share of Budget | Large portion of income (e.g., cars, rent). | Small portion of income (e.g., salt, matches). |
| Addiction/Habit | Non-addictive goods. | Addictive goods (e.g., cigarettes, coffee for regular drinkers). |
Important Questions
No, not always. This is the key mistake the article warns against. The correct strategy depends entirely on the elasticity of demand for the product. If demand is inelastic, a price rise will increase revenue. However, if demand is elastic, a price rise will decrease revenue. A smart business must first estimate whether its product faces elastic or inelastic demand before making a pricing decision.
Because the demand for these goods is relatively inelastic. Smokers and drivers need them in the short run and have few immediate alternatives. When the government imposes a tax that raises the price, the quantity sold doesn't fall by much. This means the government collects a lot of tax revenue (the sellers' revenue increases from the price hike, and the government takes a share via tax). Additionally, for cigarettes, the goal is also to discourage smoking, but the inelastic nature means heavy taxes are very effective at raising funds.
Yes, absolutely. Elasticity is not a fixed number. It can change based on the factors in the table above. For example, the demand for gasoline is inelastic in the short run (you're stuck with your car). But over a long period (years), it becomes more elastic as people can buy fuel-efficient cars, move closer to work, or use public transportation. Also, if the price range considered changes, elasticity can vary along a demand curve.
The relationship between Price Elasticity of Demand and Total Revenue is a cornerstone of practical economics. The simple rule—elastic demand means price and revenue move in opposite directions, inelastic demand means they move together—provides a powerful lens to understand diverse real-world phenomena. It explains why Apple carefully tests prices for new iPhones (likely elastic demand), why utility companies are heavily regulated (inelastic demand for essential services), and why a bumper crop can be a curse for farmers. By analyzing the availability of substitutes, necessity, and time horizon, anyone can make better predictions about market behavior and smarter personal or business decisions. Mastering this concept is the first step to thinking like an economist.
Footnote
[1] PED (Price Elasticity of Demand): A numerical measure of the responsiveness of the quantity demanded of a good to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.