(1). Suppose that a department store is selling a popular brand of dress shirt f
ID: 2902445 • Letter: #
Question
(1). Suppose that a department store is selling a popular brand of dress shirt for $109 each. During the first two weeks, the store sold 100 shirts, and in order to boost sale and clear the isles for new product, it declared a sale "buy one get one free". This resulted in sale of 500 shirts in one week, and the isles were cleared.
(a). Calculate the price elasticity of demand.
(b). Interpret your result. Specifically, what type of demand elasticity is it and what does the co-efficient of elasticity indicate when price went down?
Explanation / Answer
Price(OLD)=109
Price(NEW)=109/2 = 54.5
QDemand(OLD)=100
QDemand(NEW)=500
To calculate the price elasticity, we need to know what the percentage change in quantity demand is and what the percentage change in price is. It's best to calculate these one at a time.
Calculating the Percentage Change in Quantity Demanded
The formula used to calculate the percentage change in quantity demanded is:
[QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)
By filling in the values we wrote down, we get:
[500 - 100] / 100 = (400/100) = 4
We note that % Change in Quantity Demanded = 4. Now we need to calculate the percentage change in price.
Calculating the Percentage Change in Price
Similar to before, the formula used to calculate the percentage change in price is:
[Price(NEW) - Price(OLD)] / Price(OLD)
By filling in the values we wrote down, we get:
[54.5 - 109] / 109 = (1/9) = -0.496
Final Step of Calculating the Price Elasticity of Demand
We go back to our formula of:
PEoD = (% Change in Quantity Demanded)/(% Change in Price)
We can now fill in the two percentages in this equation using the figures we calculated earlier.
PEoD = (4)/(-0.496) = -8.06
PEod (percentage of elasticity on demand) = -8.06
2) A good economist is not just interested in calculating numbers. The number is a means to an end; in the case of price elasticity of demand it is used to see how sensitive the demand for a good is to a price change. The higher the price elasticity, the more sensitive consumers are to price changes. A very high price elasticity suggests that when the price of a good goes up, consumers will buy a great deal less of it and when the price of that good goes down, consumers will buy a great deal more. A very low price elasticity implies just the opposite, that changes in price have little influence on demand.
If PEoD > 1 then Demand is Price Elastic (Demand is sensitive to price changes)
If PEoD = 1 then Demand is Unit Elastic
If PEoD < 1 then Demand is Price Inelastic (Demand is not sensitive to price changes)
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