The consumer demand curve for tissues is given by
$q = ( 92 - p ) ^ { 2 }$
Where p is the price per case of tissues and q is the demand in weekly sales. Determine the elasticity of demand E when the price is set at $30.

Round the answer to the nearest hundredth.

A)0.01
B) 0.48
C) 1.94
D) 0.97
E) 0.65

Question

The consumer demand curve for tissues is given by 
 $q = ( 92 - p ) ^ { 2 }$  
Where p is the price per case of tissues and q is the demand in weekly sales. Determine the elasticity of demand E when the price is set at $30.
 
Round the answer to the nearest hundredth.
 
A)0.01
B) 0.48
C) 1.94
D) 0.97
E) 0.65

Quizplus · Accepted Answer

The elasticity of demand (E) is calculated using the formula $E = \frac{p}{q} \times \frac{dq}{dp}$. First, find $q$ when $p = 30$: $q = (92 - 30)^2 = 62^2 = 3844$. Then, find $\frac{dq}{dp}$ by differentiating $q$ with respect to $p$: $\frac{dq}{dp} = 2(92 - p)(-1) = -2(92 - 30) = -124$. Substitute $p = 30$ and $q = 3844$ into the elasticity formula: $E = \frac{30}{3844} \times (-124) = -0.97$. The negative sign indicates that the relationship between price and demand is inversely proportional, but for elasticity, we consider the absolute value, so $E = 0.97$.

The Consumer Demand Curve for Tissues Is Given By q=(92−p)2q = ( 92 - p ) ^ { 2 }q=(92−p)2

The Consumer Demand Curve for Tissues Is Given By $q = ( 92 - p ) ^ { 2 }$