Assume that when the price of good X is $12,quantity demanded is 32.When price is decreased to $9,quantity demanded increases to 45.Over this range,the arc elasticity of demand is 1.182.

Question

Quizplus · Accepted Answer

The formula for arc elasticity of demand is:
Arc elasticity of demand = (percentage change in quantity demanded) / (percentage change in price)

Using the given values, we can calculate the percentage change in quantity demanded:
[(45-32)/32] x 100% = 40.63%

And the percentage change in price:
[(9-12)/12] x 100% = -25%

Now we can substitute these values into the formula for arc elasticity of demand:
1.182 = 40.63% / -25%

Solving for the missing variable, we get:
-25% x 1.182 = -29.55%

So the arc elasticity of demand over this range is -29.55%. Since it is negative, we know that the good is price elastic. Therefore, a decrease in price leads to a proportionally larger increase in quantity demanded. This is consistent with the given information that a 25% decrease in price led to a 40.63% increase in quantity demanded. Therefore, the statement is true and the answer is A.

Assume That When the Price of Good X Is $12,quantity