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**Microeconomics.**

The price elasticity of demand which is popularly just referred to as price elasticity is a measure of the rate of response of quantity demanded when price changes (Backman ,1953). We have the following data to work with.

Old price of a gallon of paint=$3.00

New price of a gallon of paint =$3.50

Old quantity demanded= 35 gallons of paint per month.

New quantity demanded= 20 gallons of paint per month.

Calculation of elasticity entails first a computation of percentage change in quantity demanded per month and percentage change in price.

## Calculating the percentage change in quantity demanded per month

The formula used to calculate the percentage change in quantity demanded is

**[ Quantity demanded ( New) -Quantity demanded (Old) ] / Quantity demanded (old)** . (Backman, 1953)

Substituting values:

[20-35] / 35 = -15/35 = -0.4286

**The percentage change in quantity demanded is thus = -0.4286 in decimal form. This translates to -42.86% . **

** Calculating the percentage change in price:**

**[Price (New) - price(Old)] / Price (Old).**

**[3.**

**50 - 3.00] / 3.00 = ( 0.50/3.00) = 0.1667. = 16.67%**

Since we have already calculated the percentage change in quantity demanded and the percentage change in price , we now calculate the price elasticity of demand.

** Calculating the price Elasticity of demand.**

**Price elasticity of demand = (% Change in Quantity Demanded) / (% Change in Price). **(Backman ,1953)

Substituting using the calculated values**:**

**PEOD = - 0.4286/0.1667 = - 42.86% /16.67% = -2.5711.**

When analyzing price elasticity , we take the absolute value hence we ignore the negative sign**. Thus in our case , the price elasticity of demand when the price increases from $3.00 to $3.50 is 2.5711. **

If price Elasticity of demand > 1 then Demand is price Elastic ( Demand is responsive to price changes).

If price Elasticity of Demand = 1 then Demand is said to be Unit Elastic.

If Price Elasticity of demand is < 1 then Demand is price Inelastic (Demand is not responsive to price changes) . (Backman ,1953)

In our calculation we have obtained a price elasticity of demand = 2.

5711. which is greater than 1 . This shows that our Demand for paint is price Elastic.

** Interpretation of the price Elasticity of Demand.**

Since we have obtained an high price Elasticity of Demand, our Demand for paint is very sensitive to price changes. When the price of paint goes up , a great deal less of it is bought and when the price goes down , a great deal more of it is bought.