Price Elasticity of DemandEconomists' Approach to Pricing:
Learning Objective of the Article:
 Define and
explain the term "Price elasticity of demand".
 Calculate profit
maximizing price of a product of service using the price elasticity of
demand and variable cost.
If a company raises the price of a product,
unit sales ordinarily falls. Because of this, pricing is a delicate
balancing act in which the benefits of higher revenues per unit are tradedoff against the lower volume that results from charging higher prices. The
sensitivity of unit sales to changes in prices is called the price
elasticity of demand.

Definition and explanation of price elasticity of demand

Formula of Price elasticity of demand

Profit
maximizing price
A product's price elasticity should be a key
element in setting its price. The price elasticity of demand measures
the degree to which the unit sales of a product or service are affected by a
change in price. Demand for a product is said to be inelastic if a
change in price has little effect on the number of units sold. The demand
for designer perfumes sold by trained personnel at cosmetic counters in
department stores is relatively inelastic. Lowering prices on these luxury
goods has little effect on sales volume; factors other than price are more
important in generating sales. On the other hand, demand for a product is
said to be elastic if a change in price has a substantial effect on
the volume of units sold. An example of a product whose demand is
elastic is gasoline. If a gas station raises its prices for gasoline, there
will usually be a substantial drop in volume as customers seek lower prices
elsewhere.
Price elasticity is very important in
determining prices. Managers should set higher markups over cost where
customers are relatively insensitive to price (i.e., demand is inelastic)
and lower markups where customers are relatively sensitive to price (i.e.,
demand is elastic). This principle is followed in departmental stores.
Merchandise sold in the bargain basement has a much lower markup than
merchandise sold elsewhere in the store because customers who shop in the
bargain basement are much more sensitive to price i.e., demand is
elastic.
Price elasticity of demand for a product or
service can be estimated using the following formula:
[Price
Elasticity of Demand = In(1+ % Change in quantity sold) / In(1 + % Change in
price)]
 The
term In( ) is the natural log function. You can compute natural log of
any number using the LN or lnx key on your calculator. For example,
ln(0.85) = –0.1625
 This
formula assumes that the price elasticity of demand is constant. This
occurs when the relationship between the selling price, P, and the unit
sales, q, can be expressed in the following form: ln(q) = a + elasticity
of demand ln(p). Even if this is not precisely true, the formula
provides a useful way to estimate a product's real price elasticity.

For example, suppose that the managers of
Nature's Garden Inc. believe that every 10% increase in the selling price of
their applealmond shampoo will result in a 15% decrease in the number of
bottles of shampoo sold. The Calculation of the price elasticity of demand for this product
would be as follows:
Price elasticity of Demand
= In(1 + ( – (0.15)) / In(1 + (1.10))
In(0.85) / In(1.10)
= – 1.71
 The estimated
change in unit sales should take into account competitor's responses to a
price change.

For comparison purposes, the managers of
Nature's Garden Inc. believe that another product, strawberry glycerin soap, will
experience 20% drop in unit sales if its price is increased by 10%.
(Purchasers of this product are more sensitive to price than the
purchasers of the applealmond shampoo). The calculation of the price elasticity of demand for
the strawberry glycerin soap is:
Price elasticity of Demand
= In(1 + ( – (0.20)) / In(1 + (1.10))
In(0.80) / In(1.10)
= – 2.34
Both of these products, like other normal
products, have a price elasticity that is less than – 1. Not also
that the price elasticity of demand for the strawberry glycerin soap is
larger (in absolute value) that the price elasticity of demand for the
applealmond shampoo. The more sensitive customers are to price, the larger
(in absolute value) in the price elasticity of demand. In other words, a
larger (in absolute value) price elasticity of demand indicates a product
whose demand is more elastic. The price elasticity of demand will be used to
calculate selling price that maximizes the profits of the company.
Under certain conditions, it can be shown
that the profitmaximizing price can be determined by marking up
variable cost using the following formula:
*[Profitmaximizing markup on variable cost = (Price elasticity of demand / 1
+ Price elasticity of demand) – 1]
*The
formula assumes that:
 The price elasticity of demand is
constant.
 Total cost = Total fixed cost +
Variable cost per unit × q
 The price of the product has no effect
on the sales or costs of any other product. The formula can be derived
using calculus.

Using the above markup is equivalent to
setting the selling price using this formula:
[Profitmaximizing price = (Price elasticity of demand / 1 + Price
elasticity of demand) Variable cost per unit]
The profit maximizing prices for two Nature's
Garden products are computed below using these formulas:

AppleAlmond Shampoo 
Strawberry Glycerin Soap 
Price
elasticity of demand 
– 1.71 
– 2.34 
Profit
maximizing markup on variable cost (a) 
(– 1.71 / – 1.71 + 1) – 1 
(– 2.34 / – 2.34 + 1) – 1 

2.41 – 1 = 1.41 or 141% 
1.75 – 1 = 0.75 or 75% 
Variable
cost per unitgiven (b) 
$2.00 
$0.40 
Markup, (a)
× (b) 
2.82 
0.30 

 
 
Profit
maximizing price 
$4.82 
$0.70 

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Note that the 75% markup for the strawberry
glycerin soap is lower that 140% markup for the apple almond shampoo. The
reason for this is that the purchasers of strawberry glycerin soap are more
sensitive to price than the purchasers of applealmond shampoo. This could
be because strawberry glycerin soap is a relatively common product with
close substitutes available in nearly every grocery store.
Caution is advised when using these formulas
to establish a selling price. The assumptions underlying the formulas are
probably not completely valid, and the estimate of the percentage change in
unit sales that would result from a given percentage change in price is
likely to be inexact. Nevertheless, the formulas can provide valuable clues
regarding whether prices should be increased or decreased. Suppose, for
example, that the strawberry glycerin soap is currently being sold for $0.60
per bar. The formula indicates that the profit maximizing price is $0.70 per
bar. Rather than increasing the price by $0.10, it would be prudent to
increase the price by a more modest amount to observe what happens to unit
sales and to profits.
The formula for the profit maximizing price
also convey a very important lesson. The optimal selling price should depend
on two factorsthe variable cost per unit and how sensitive unit sales are
to changes in price. In particular, fixed costs play no role in setting the
optimal price. If the total fixed costs are the same whether the company
charges $0.60 or $0.70, they cannot be relevant in the decision of which
price to charge for the soap. Fixed costs are relevant when deciding whether
to offer a product but are not relevant when deciding how much to charge for
the period.
Incidentally we can directly verify that an
increase in selling price for the strawberry glycerin soap from the current
price of $0.60 per bar is warranted, based just on the forecast that a 10%
increase in selling price would lead to a 20% decrease in unit sales.
Suppose, for example, that Nature's Garden is currently selling 200,000 bars
of the soap per year at the price of $0.60 a bar. If the change in price has
no effect on the company's fixed costs or on other products, the effect on
profits of increasing the price by 10% can be computed as follows:

Percent Price 
Higher Price 
Selling
price 
$0.60 
$0.60 + (0.10 $0.60) = $0.66 
Unit sales 
200,000 
200,000 (0.20 200,000) = 160,000 
Sales 
$120,000 
$105,600 
Variable
cost 
80,000 
64,000 

 
 
Contribution margin 
$40,000 
$41,600 

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Despite the apparent optimality of prices
based on marking up variable costs according to the price elasticity of
demand, surveys consistently reveal that most managers approach the pricing
problem from a completely different perspective. They prefer to mark up some
version of full, not variable, costs, and the markup is based on desired
profits rather than on factors related to demand.
