Unit 7 The firm and its customers
7.5 Demand, elasticity, and revenue
 differentiated product
 A product produced by a single firm that has some unique characteristics compared to similar products of other firms.
Beautiful Cars is an example of a firm producing a differentiated product. Not all cars are the same. Each make and model is produced by just one firm, and has some unique characteristics of design and performance that differentiate it from the cars made by other firms.
When a firm sells a differentiated product, it faces a downwardsloping demand curve. Section 7.2 gives an empirical example of a demand curve, for Apple Cinnamon Cheerios (another differentiated product). If the price of a Beautiful Car is high, demand will be low because the only consumers who will buy it are those who strongly prefer Beautiful Cars to all other makes. As the price falls, more consumers, who might otherwise have purchased a Ford or a Volvo, will be attracted to a Beautiful Car.
The demand curve
For any product that consumers might wish to buy, the product demand curve is a relationship that tells you the number of items (the quantity) they will buy at each possible price. For a simple model of the demand for Beautiful Cars, imagine that there are 100 potential consumers who would each buy one Beautiful Car today, if the price were low enough.
 willingness to pay (WTP)
 An indicator of how much a person values a good, measured by the maximum amount they would pay to acquire a unit of the good. See also: willingness to accept.
Each consumer has a willingness to pay (WTP) for a Beautiful Car, which depends on how much the customer personally values it (given the resources to buy it, of course). A consumer will buy a car if the price is less than or equal to his or her WTP. Suppose we line up the consumers in order of WTP, with the highest first, and plot a graph to show how the WTP varies along the line (Figure 7.9). Then if we choose any price, say P = $32,800, the graph shows the number of consumers whose WTP is greater than or equal to P. In this case, 18 consumers are willing to pay $32,800 or more, so the demand for cars at a price of $32,800 is 18.
The Law of Demand dates back to the seventeenth century, and is attributed to Gregory King (1648–1712) and Charles Davenant (1656–1714). King was a herald at the College of Arms in London, who produced detailed estimates of the population and wealth of England. Davenant, a politician, published the Davenant–King Law of Demand in 1699, using King’s data. It described how the price of corn would change depending on the size of the harvest. For example, he calculated that a ‘defect’, or shortfall, of onetenth (10%) would raise the price by 30%.
If P is lower, there is a larger number of consumers willing to buy, so the demand is higher. Demand curves are often drawn as straight lines, as in this example, although there is no reason to expect them to be straight in reality: the demand curve for Apple Cinnamon Cheerios was not straight. But we do expect demand curves to slope downward: as the price rises, the quantity that consumers demand falls. Conversely, when the available quantity is low, it can be sold at a high price. This relationship between price and quantity is sometimes known as the Law of Demand.
Question 7.6 Choose the correct answer(s)
The diagram depicts two alternative demand curves, D and D′, for a product. Based on this graph, read the following statements and choose the correct option(s).
 On demand curve D, when the price is £5,000, the firm can sell 10 units.
 When Q = 70, the corresponding price on D′ is £3,000.
 D′ is a rightward shift of D, by 40 units. So for any price, the firm can sell 40 more units on D′ than on D.
 With an output of 30 units, the firm can charge £4,000 more on D′ than on D.
The elasticity of demand
The demand curve represents the tradeoff the firm has to make between price and quantity. To maximize profit, it would like both to be as high as possible—but if it raises the price, fewer consumers will want to buy. So the firm’s choice of price depends on the slope of the demand curve—that is, on how much demand will change if the price changes. If the demand curve is steep, the firm can raise the price without reducing sales very much.
 price elasticity of demand
 The percentage change in demand that would occur in response to a 1% increase in price. We express this as a positive number. Demand is elastic if this is greater than 1, and inelastic if less than 1.
The price elasticity of demand is a measure of the responsiveness of consumers to a price change. It is defined as the percentage change in demand that would occur in response to a 1% increase in price. For example, suppose that the price of a product increases by 10%, and we observe a 5% fall in the quantity sold. We calculate the elasticity, ε, as follows:
\[\varepsilon = \frac{\% \text{ change in demand}}{\% \text{ change in price}}\]ε is the Greek letter epsilon, which is often used to represent elasticity. For a demand curve, quantity falls when price increases. So the change in demand is negative if the price change is positive, and vice versa. The minus sign in the formula for the elasticity ensures that we get a positive number as our measure of responsiveness. In this example, we get:
\[\begin{align*} \varepsilon &= \frac{5}{10} \\ &= 0.5 \end{align*}\]If the demand curve is almost flat, quantity changes a lot in response to a change in price, so the elasticity is high. Conversely, a steeper demand curve corresponds to a lower elasticity. But they are not the same thing. We will explain why the elasticity changes as we move along the demand curve, even if the slope doesn’t.
Suppose Beautiful Cars produces 18 cars per day and sells them at a price of $32,800 (point K in Figure 7.9). To calculate the elasticity of demand at this point, we work out how Q and P would change if the firm moved a small distance along the demand curve—for example to another point, L, where Q = 19. The demand curve has a constant slope of –400 (you can check this from the points where it crosses the axes) so when we move from K to L, the price falls to $32,400.
The table in Figure 7.10 shows the calculation. The move down the demand curve represents a 5.56% increase in Q, and a 1.22% decrease in P. Taking the ratio of the percentage changes gives an elasticity of 4.56.
Point K  Point L  change  % change  elasticity  

*Q* *P* 
18 32,800 
19 32,400 
∆Q = 1 ∆P = −400 
$$ \frac{100×\Delta Q}{18} = 5.56\% $$ $$ \frac{100× \Delta P}{32,800} = −1.22\% $$ 
$$ \varepsilon = \frac{5.56}{1.22} = 4.56 $$ 
The elasticity tells us that when Beautiful Cars is operating at point K, raising (or lowering) the price by 1% would lead to a 4.56% fall (or rise) in the quantity of cars sold.
There are several different ways to calculate elasticity from the changes in P and Q, summarized in the table in Figure 7.11. They are all equivalent—you can use whichever you like.
Suppose that if price changes by ΔP, demand changes by ΔQ. Then the elasticity of demand can be written in four different ways: 


$$ − \frac{\% \text{ change in } Q}{\% \text{ change in } P} $$  $$ \varepsilon = − \frac{100 \Delta Q}{Q} / \frac{100 \Delta P}{P} $$  
$$ − \frac{\text{ proportional change in } Q}{\text{ proportional change in } P} $$  $$ \varepsilon = − \frac{\Delta Q}{Q} / \frac{\Delta P}{P} $$  
The fraction can be simplified to get:  $$ \varepsilon = − \frac{P}{Q} \frac{\Delta Q}{\Delta P} $$  
And since \( \dfrac{\Delta P}{\Delta Q} \) is the slope of the demand curve:  $$ \varepsilon = − \frac{P}{Q} \frac{1}{\text{ slope}} $$ 
Figure 7.12 uses the fourth expression to calculate the elasticity at other points on the demand curve for Beautiful Cars. This demand curve has a constant slope; as we move down it P falls and Q rises, so the elasticity falls. When prices are low, demand is less elastic.
$$ \varepsilon = − \frac{P}{Q} \frac{1}{\text{ slope}} $$  
A  B  C 

Q  20  40  70 
P  $32,000  $24,000  $12,000 
slope  −400  −400  −400 
elasticity  4.00  1.50  0.43 
We say that demand is elastic if the price elasticity is higher than 1: that is, a 1% increase in price would lead to a fall of more than 1% in the quantity sold. If the elasticity is less than 1, we say that demand is inelastic. For Beautiful Cars, demand is elastic at A and B, but inelastic at C.
Why is the price elasticity of demand important to the firm?
The firm’s price elasticity of demand will depend on how much competition it faces from other firms. If lots of firms sell similar cars that customers would consider as potential alternatives, the demand for Beautiful Cars will be more elastic. Then if it raises the price, consumers will search for alternative sellers, and many of them may decide to buy elsewhere. In this situation, competition from rival products with similar characteristics will limit the firm’s ability to raise its price.
But if Beautiful Cars’ product has unique qualities that appeal to consumers and are not available elsewhere, its price elasticity of demand will be lower (demand will be less elastic). Then it can benefit from a high price. Sales will remain high, and it will make a higher profit on every unit it sells.
 total revenue, revenue
 A firm’s total revenue is the number of units sold times the price per unit.
There is a direct relationship between the elasticity of demand and how the firm’s revenue changes as quantity increases. Figure 7.13 shows a firm producing at a point on its demand curve where Q = 5 and P = 20. Its revenue (price × quantity) is represented by the area of the rectangle under the demand curve. Work through the figure to understand that if it increases quantity, revenue will rise or fall depending on whether demand is elastic or inelastic.
 marginal revenue
 The change in revenue obtained by increasing the quantity sold by one unit.
The change in revenue when output is increased by one unit is called the marginal revenue. In Figure 7.13:
 Marginal revenue is positive when demand is elastic (\(\varepsilon>1\)); the firm can increase revenue by raising output because prices fall only a little.
 Marginal revenue is negative when demand is inelastic; the firm can increase revenue by decreasing output because prices rise a lot.
The extension at the end of this section demonstrates that this result is true for all demand curves. In subsequent sections, we will show that firms facing little competition and less elastic demand curves will set higher prices.
Question 7.7 Choose the correct answer(s)
A shop sells 20 hats per week at $10 each. When it increases the price to $12, the number of hats sold falls to 15 per week. Based on this information, read the following statements and choose the correct option(s).
 When the price increases from $10 to $12, demand decreases by 100 × (20 –15)/20 = 25%.
 The percentage price increase is 100 × 2/10 = 20%. It causes a percentage decrease in demand of 100 × 5/20 = 25%.
 Using the figures to estimate the price elasticity of demand gives a value greater than 1, so demand is elastic.
 The percentage price increase is 100 × 2/10 = 20%; the percentage decrease in demand is 100 × 5/20 = 25%. So the elasticity can be estimated as 25/20 = 1.25.
Question 7.8 Choose the correct answer(s)
The figure depicts two demand curves, D_{1} and D_{2}.
Based on this figure, read the following statements and choose the correct option(s).
 At E, the price and quantity are the same on both demand curves, but D_{1} is steeper, so it is less elastic than D_{2}.
 The slope is the same at A and C, but at A the price is higher and quantity is lower, so the elasticity is higher.
 Demand curve D_{1} is less elastic than D_{2}, so the firm with demand curve D_{1} likely faces less competition than the firm with demand curve D_{2}.
 The slope is the same at E and B. But at E the price is higher and quantity is lower, so the elasticity is higher.