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# Price Elasticity - How to Use Cross Price and Own Price Elasticity

### Price Elasticity - The Scenario:

A market research firm 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. The price of margarine is 25 cents per kilo with sales of 3500 kilos per month. The 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?

### Cross Price Elasticity - What Does it Mean?:

The article Cross-Price Elasticity of Demand gives the following explanation: "The Cross-Price Elasticity of Demand measures the rate of response of quantity demanded of one good, due to a price change of another good. If two goods are substitutes, we should expect to see consumers purchase more of one good when the price of its substitute increases..." The formula for the Cross-Price Elasticity of Demand (CPEoD) is given by:

CPEoD = (% Change in Quantity Demand for Good X)/(% Change in Price for Good Y)

### Cross Price Elasticity - Answering the Question:

We saw that the price of butter dropped 10% from 60 cents to 54 cents. 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 for margarine was originally 3500 kilos - it is now 16% less or 2940 kilos. (3500 * (1 - 0.16)) = 2940.

### Own Price Elasticity - What Does it Mean?:

The article Price Elasticity of Demand gives the following explanation: "The Price Elasticity of Demand (commonly known as just price elasticity) measures the rate of response of quantity demanded due to a price change. The formula for the Price Elasticity of Demand (PEoD) is":

PEoD = (% Change in Quantity Demanded)/(% Change in Price)

### Own Price Elasticity - Answering the Question:

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 for butter was originally 1000 kilos - it is now 30% less or 1300 kilos.

### Cross Price-Elasticity: Effect on Revenue of Margarine Sellers:

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-Elasticity: Effect on Revenue of Butter Sellers:

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.

### Cross Price and Own Price Elasticity - Have any Questions?:

If so, feel free to leave them at this blog entry.
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