Does a discount increase revenue? Calculating the price elasticity of demand and checking profit
A coffee shop offered a 15% discount on coffee. We calculate elasticity in two scenarios, show when revenue rises and when it falls, and check why profit may fall even if revenue rises.
At the "Kunduz Kofe" coffee shop a cup of coffee costs 20 000 soum, and 500 cups are sold a week. The owner, Dilshod, wants to announce a 15% discount: the price falls to 17 000 soum. He believes: "If it's cheaper, people will buy more and revenue will rise". Whether this is true or not is decided by one indicator: the price elasticity of demand.
How is elasticity calculated?
Elasticity shows by how many percent the quantity sold changes when the price changes by 1 percent:
When the price falls, the quantity rises, so the result comes out negative. Usually its absolute value (the value without the sign) is looked at:
| Absolute value | Type of demand | Meaning |
|---|---|---|
| Greater than 1 | Elastic | The buyer is price-sensitive, the quantity changes more strongly than the price |
| Equal to 1 | Unit elasticity | The quantity changes by the same percentage as the price |
| Less than 1 | Inelastic | Quantity changes less than the price, the buyer is not very price-sensitive |
One subtle point: if you calculate the percentage from the starting point, you get different results when the price falls and when it rises again. To avoid this, economists use the midpoint method: the change is divided by the average of the old and new values.
When does a discount increase revenue?
Suppose Dilshod tested the discount for two weeks. Let us compare two scenarios (figures hypothetical):
| Indicator | Before the discount | Scenario A | Scenario B |
|---|---|---|---|
| Price, soum | 20 000 | 17 000 | 17 000 |
| Weekly sales, cups | 500 | 650 | 550 |
| Change in quantity | — | +30% | +10% |
| Elasticity (simple percentage) | — | 30 ÷ (−15) = −2.0 | 10 ÷ (−15) = −0.67 |
| Weekly revenue, soum | 10 000 000 | 11 050 000 | 9 350 000 |
In scenario A demand is elastic: the quantity changed twice as strongly as the price, and revenue rose by 1 050 000 soum. In scenario B demand is inelastic: buyers paid almost no attention to the discount, and revenue fell by 650 000 soum.
With the midpoint method, scenario A: quantity 150 ÷ 575 = 26.1%, price 3 000 ÷ 18 500 = 16.2%, elasticity ≈ −1.61. The figure is different, but the conclusion does not change: the absolute value is greater than 1.
The rule is: if demand is elastic, a discount increases revenue; if it is inelastic, it reduces it. Elasticity is usually higher when there are many close substitutes (other coffee shops nearby), when the product takes a noticeable share of the buyer's budget and when the buyer is given time to adjust.
If revenue rises, does profit rise too?
This is where many people stop and make a mistake. The variable cost of each cup (coffee beans, milk, the cup) is a hypothetical 9 000 soum. With the discount this cost does not fall; only the money left from each cup falls.
| Indicator | Before the discount | Scenario A |
|---|---|---|
| Amount left from one cup (price − 9 000) | 11 000 | 8 000 |
| Sales, cups | 500 | 650 |
| Weekly contribution margin, soum | 5 500 000 | 5 200 000 |
Revenue rose by 1 050 000 soum, but the amount left after deducting variable costs fell by 300 000 soum. Dilshod worked more and earned less.
How many cups must be sold to keep the profit? 5 500 000 ÷ 8 000 = 687.5, i.e. at least 688 cups, sales must rise by 37.6%. This corresponds to an elasticity of about −2.5. So for the discount to pay off, demand must not just be elastic but very elastic.
What to do in practice: 1. Before a discount, calculate its "break-even point": current contribution margin ÷ amount left from one unit at the new price. 2. Test the discount on a few days of the week or in one branch and compare sales with a period without the discount. 3. Judge the result not by revenue but by the amount left after variable costs.
Test yourself
5 questions on this topic: pick an option or reveal the answer.
When the price of samsa at a cafe rose by 10%, the quantity sold fell by 20%. What is the price elasticity of demand coefficient (in absolute value) and the type of demand?
Dilnoza quit a job paying 6 mln soums a month and opened a flower shop. The shop's monthly revenue is 25 mln soums, and its expenses paid in cash are 15 mln soums. Taking opportunity cost into account, what is the monthly economic profit?
When the real income of a city's population rose by 10%, the quantity demanded of taxi services rose by 15% (prices unchanged). What is the income elasticity of demand, and what type of good is this service?
In a city market, the demand function for melons is Qd = 100 − 2P and the supply function is Qs = 20 + 2P (P is the price in thousand soums; Q is in units). What are the equilibrium price and equilibrium quantity?
In the city's cafes the price of coffee rose by 10%, and over the same period the quantity of tea demanded increased by 5% (other conditions unchanged). What is the cross elasticity of demand, and what is the relationship between these two goods?
Answered: 0 / 50 of 5 correct
All tests →See also
Sources
- General concept of economic theory: price elasticity of demand · the definition, the midpoint method and the relationship between elasticity and revenue are given as general knowledge
- Example, amounts and calculations · compiled by the author, hypothetical