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# Demand #### November 22, 2009

The total revenue of any product or service is a function of the price and the quantity sold. The “law of demand” states that there exists a negative relationship between price and quantity demanded. That means, if the price goes up, less will be demanded, as the price goes down, more will be demanded.

When shown on a graph for a range of prices, total revenue appears as a parabola or an inverted letter U. At one extreme where the price is very high, there will be no sales and thus no revenue. At the other extreme where the price is 0, there will also be no revenue. The maximum total revenue is achieved at some point in between.

Determining demand at different pricing levels, the “demand curve”, will enable a business to price their products to achieve maximum revenue. Economists have chosen to gage this relationship between price and quantity with a measurement called “elasticity”.

Price elasticity of demand can be defined as the ratio of the percentage change in quantity demanded to the corresponding percentage change in price. Examine, for example, the percentage change in quantity demanded when there is a price change of one percent. If the quantity demanded changes by the same one percent, the elasticity is said to be “unitary”. If the quantity demanded changes by more than one percent, up or down, the demand is considered “elastic”. If the percent change is less than one percent, the demand is considered to be “inelastic”.

Since determining the “elasticity” of demand is the key to maximizing revenue, let’s use rubber bands for a demonstration. The area inside the rubber bands will represent total revenues, price x units sold. Rubber band #1 will represent total revenues when prices are decreasing and #2 will represent revenues when prices are increasing.

The total revenue for rubber band #1 will increase as prices are decreased from an excessively high level. Expand the area within the band with the pressure of your fingers representing the increased units demanded by lower prices. The “demand” curve in this situation is considered by economists to be “elastic”. Maximum revenue, that point at which the area within the band will no longer expand as a result of lowering prices, is achieved just prior to the point of “inelasticity”.

The total revenue for rubber band #2 will increase as prices are increased from a starting level of zero. Expand the area within the band to represent the expansion of total revenues brought about by increasing prices. When the total revenues increase as a result of increasing prices, the demand curve is considered by economists to be “inelastic”. Again, maximum revenue, that point at which the area within the band will no longer expand as a result of increasing prices, is achieved just prior to the point of “elasticity”.

With both of the rubber bands, we have approached the point of “unitary elasticity”. Total revenue is maximized at this point. Locating this point is probably only theoretically possible. However, as a practical matter, the closer your pricing policy comes to this point, the greater the profits. There is perhaps no more important decision that a business makes than the pricing of its products. Too often, too little time and attention is given to this most important decision.

When the demand is elastic, a price decrease results in a more than proportionate increase in quantity. So total revenue will increase with price decreases when the demand is “elastic”. When a decrease in price results in a less than proportionate increase in quantity, the demand is defined as “inelastic”. Total revenue will decline with a further price reduction when the demand is inelastic. Total revenue will be enhanced, however, with a price increase in a situation with inelastic demand.

Understanding of the demand curve and the concept of “elasticity” are valuable to decision makers in both the public and private sector.

The frequently discussed “Laffer Curve” is utilized to explain how total tax revenues will change when tax rates are changed.

The Laffer Curve represents total tax revenues and takes the parabolic shape of the inverted U. At one extreme where the tax rate is 100%, there would be no revenue because there would be no incentive to produce. At the other extreme the rate would be zero and that too would result in no tax revenue.

As tax rates decreased from 100%, total tax revenue will increase while the demand curve remains “elastic”. As rates are increased from 0, total tax revenues will also increase during the “inelastic” segment of the demand curve.

The point that economist Arthur Laffer was making is that at some point, an increase in tax rates actually will end up reducing total tax revenues. Determining that point of “unitary elasticity” has been elusive for public policy makers.

If the demand for your product is “elastic”, a lowering of your prices may increase your total revenues. If the demand for your product is “inelastic”, an increase in price will enhance total revenue. Because its your business, create the pressure to expand the area within your rubber band.

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