Determining Price Elasticity

How to Use Cross-Price and Own-Price of Demand

The Cross-Price and Own-Price Elasticity of Demand are essential to understanding the market exchange rate of goods or services because the concepts determine the rate the quantity demanded of a good fluctuates due to the price change of another good involved in its manufacturing or creation.

In this, cross-price and own-price go hand-in-hand, conversely affecting the other wherein cross-price determines the price and demand of one good when another substitute's price changes and the own-price determines the price of a good when the quantity demanded of that good changes.

As is the case with most economic terms, the elasticity of demand is best demonstrated through an example. In the following scenario, we'll observe the market elasticity of demand for butter and margarine by examining a decrease in the price of butter.

An Example of the Market Elasticity of Demand

In this scenario, a market research firm that reports to a farm co-operative (which produces and sells butter) that the estimate of the cross-price elasticity between margarine and butter is approximately 1.6%; the co-op price of butter is 60 cents per kilo with sales of 1000 kilos per month; and the price of margarine is 25 cents per kilo with sales of 3500 kilos per month wherein the own-price elasticity of butter is estimated to be -3. 

What would be the effect on the revenue and sales of the co-op and margarine sellers if the co-op decided to cut the price of butter to 54p?

The article "Cross-Price Elasticity of Demand" assumes that "if two goods are substitutes, we should expect to see consumers purchase more of one good when the price of its substitute increases," so according to this principle, we should see a decrease in revenue since the price is expected to drop for this particular farm.

Cross-Price Demand of Butter and Margarine

We saw that the price of butter dropped 10% from 60 cents to 54 cents, and since the cross-price elasticity margarine and butter is approximately 1.6, suggesting that the quantity demanded of margarine and the price of butter are positively related and that a drop in the price of butter by 1% leads to a drop in the quantity demanded of margarine of 1.6%.

Since we saw a price drop of 10%, our quantity demanded of margarine has dropped 16%; the quantity demanded margarine was originally 3500 kilos — it is now 16% less or 2940 kilos. (3500 * (1 - 0.16)) = 2940.

Before the change in the price of butter, margarine sellers were selling 3500 kilos at a price of 25 cents a kilo, for a revenue of $875. After the change in the price of butter, margarine sellers are selling 2940 kilos at a price of 25 cents a kilo, for a revenue of $735 — a drop of $140.

Own-Price Demand of Butter

We saw that the price of butter dropped 10% from 60 cents to 54 cents. The own price elasticity of butter is estimated to be -3, suggesting that the quantity demanded of butter and the price of butter are negatively related and that a drop in the price of butter by 1% leads to a rise in the quantity demanded of butter of 3%.

Since we saw a price drop of 10%, our quantity demanded of butter has risen 30%; the quantity demanded butter was originally 1000 kilos, whereas it is now 30% less at 1300 kilos.

Before the change in the price of butter, butter sellers were selling 1000 kilos at a price of 60 cents a kilo, for a revenue of $600. After the change in the price of butter, margarine sellers are selling 1300 kilos at a price of 54 cents a kilo, for a revenue of $702 — an increase of $102.