If the price elasticity of demand for a product is 2.5, then a price cut from $2.00 to $1.80 will:
a) Increased the quantity demanded by about 2.5 percent
b) Decreased the quantity demanded by about 2.5 percent
c) Increased the quantity demanded by about 25%
d) Increased the quantity demanded by about 250%
Please show working for problem.
The correct answer to this is C. This change in price should lead to a 25% increase in quantity demanded.
In order to understand why this is so, let us start with the equation for finding the elasticity coefficient. That equation is:
Elasticity coefficient = percentage change in quantity demanded / percentage change in price
We are already given the elasticity coefficient so we know that
2.5 = percentage change in quantity demanded / percentage change in price
Furthermore, we know how much the price has changed. We know that the price was originally $2 and it dropped to $1.80. That is a 20 cent drop on an original price of $2.00. 20/200 = .1 so the percentage change in price is 10 (because the price dropped by 10 percent).
We are now left with the equation:
2.5 = percentage change in quantity demanded / 10
Using algebra, we multiply both sides by 10. That gives us 25% = percentage change in quantity demanded.
Thus, we can see that C is the correct answer. The drop in price leads to a 25% change in quantity demanded.
Let's first identify the information that has already been presented to us in the problem:
- We know that the elasticity coefficient (Ed) is 2.5 since the problem tells us that the price elasticity for demand of the product is 2.5.
- We know that the price change is that of $0.20, since the starting price of the product was $2.00 and the price cut resulted in the product costing $1.80. This translates to a percentage change in price of 10%.
With this information in mind, we can now consider the formula necessary to solve this problem:
Ed = percentage change in Qd / percentage change in Price
Let's plug in the numbers we have:
2.5 = percentage change in Qd / 10
When we solve for the percentage change in quantity demanded, we find that there has been a 25% change. In other words, the correct answer would be "C"!