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# Price Elasticity of Demand-Economists' Approach to Pricing:

Learning Objective of the Article:

1. Define and explain the term "Price elasticity of demand".
2. 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 traded-off 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.

## Elasticity of Demand--Definition and Explanation:

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.

## Formula and Example of Price Elasticity of Demand:

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 apple-almond 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 apple-almond 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 apple-almond 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.

## Profit Maximizing Price:

Under certain conditions, it can be shown that the profit-maximizing price can be determined by marking up variable cost using the following formula:

*[Profit-maximizing 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:

[Profit-maximizing 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:

 Apple-Almond 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 unit--given (b) \$2.00 \$0.40 Markup, (a) × (b) 2.82 0.30 ------------ ----------- Profit maximizing price \$4.82 \$0.70 ======= =======

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 apple-almond 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 factors--the 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 ===== =====

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.

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