# Elasticity on demand, breakeven analysis and pricing decisions

Elasticity on demand, breakeven analysis and pricing decisions

Harlow, Jonathan

When a firm changes prices, the effect on profits is more important than the effect on revenue. There is a simple formula to calculate

the critical Price Elasticity of demand which is just sufficient to maintain the contribution to overheads and profits. This will be greater than that required to maintain revenue.

A common issue in business and in business studies is whether a firm should change the prices at which products are offered. The calculations begin with estimates of the reaction of customers to the new prices. This reaction is represented as Price Elasticity of Demand (PED), the ratio of the proportionate changes in volume and price.

Students are always told – and some students even remember that Elastic Demand (PED >1) means more revenue from a lower price and less from a higher one; and Inelastic Demand (PED

But who wants the same revenue with lower profits? Any change in price will have a much bigger impact, proportionately, on the contribution per item for the firm than on the asking price to the customer. It follows that an increase in price may succeed in raising profits, even though revenue falls; and that a lower price may reduce profits even though revenue increases. So the critical question is not whether the PED is greater or less than one, but whether it is sufficiently high (for a lower price) or sufficiently low (for a price increase) to improve profits.

The critical level of PED can be found by an application of breakeven analysis. We can take the current level of contribution to overheads and profit; and ask what the volume (units sold) must be to give the same level of contribution at the alternative price.

Having found this critical volume, we can then compute what the PED would be to give us this volume at the new price, compared with the existing price and quantity. This then will be the Critical Price Elasticity of Demand (CPED). If we are raising prices, any PED less than CPED will increase profits; if we are lowering price, we want PED to be more than CPED. And while there is no way, short of trying the price change, to know what the PED actually is, a firm may well have sensible ideas about the likelihood of its being significantly greater or less than a specified value.

It may seem that calculating the CPED is rather a waste of time, since we should have to calculate the required change in quantity first; and might just as well reckon our chances of getting this volume after our price change, without entering into Elasticity computations at all. However it turns out that there is a very simple formula for calculating the CPED. For a single product/price the formula is P^sub o^ / C, where P^sub o^ is the original Price and C, is the Contribution per item at the new price. (Direct cost per unit is assumed to remain constant.)

For example, a firm sells 2,500 items, with a direct cost of L5.45 each, at a price of L9.95, for a total contribution of L11,250. It considers a price rise to L10.95. The CPED is 1.81: the PED must be less than this to increase profits. Note that it is a much less inelastic response, than that required to maintain revenue. Or the firm might consider a price cut to L8.95. This would give a CPED of at least 2.84, a great deal more elastic than the revenue-maintaining PED.

This simple case can be generalised to cover the situation where a range of products are sold under a common Markup (MU) applied as a percentage to Direct Cost. In this case the CPED by which to test a different markup policy is found as (100 + MU^sub o^) / MU^sub 1^ where MU^sub o^ is the original and MU^sub i^ the proposed markup. The figure charts the CPEDs for a range of Markups against an existing 100% rule.

Jonathan Harlow