# 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.

## Expert Answers

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"!

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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.

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