A general hyperbolic demand function has the form to follow. $q = \frac { m } { p ^ { z } }$ (s, m - nonzero constants)

Obtain a formula for the elasticity of demand at a unit price of p.

A) $E = s m p$
B) $E = m$
C) $E = s$
D) $E = \frac { s p } { m }$
E) $E = - m p$

Question

A general hyperbolic demand function has the form to follow.   $q = \frac { m } { p ^ { z } }$ (s, m - nonzero constants)
 
Obtain a formula for the elasticity of demand at a unit price of p.
 
A) $E = s m p$
B) $E = m$
C) $E = s$
D) $E = \frac { s p } { m }$
E) $E = - m p$

Quizplus · Accepted Answer

The elasticity of demand, $E$, is defined as the percentage change in quantity demanded ($q$) divided by the percentage change in price ($p$). Mathematically, it can be represented as $E = \frac{p}{q} \cdot \frac{dq}{dp}$. Given the demand function $q = \frac{m}{p^z}$, we differentiate $q$ with respect to $p$ to find $\frac{dq}{dp}$. The derivative of $q$ with respect to $p$ is $\frac{dq}{dp} = -z \cdot \frac{m}{p^{z+1}}$. Substituting $q$ and $\frac{dq}{dp}$ into the elasticity formula gives $E = \frac{p}{\frac{m}{p^z}} \cdot \left(-z \cdot \frac{m}{p^{z+1}}\right) = -z \cdot \frac{p \cdot p^{z}}{m} \cdot \frac{m}{p^{z+1}} = -z$. The question mistakenly uses $s$ instead of $z$ in the options, assuming $s$ represents the elasticity coefficient (which should be $z$), the correct interpretation based on the provided options would be $E = s$, indicating a typo or misunderstanding in the formulation of the question and options.

A General Hyperbolic Demand Function Has the Form to Follow q=mpzq = \frac { m } { p ^ { z } }q=pzm​

A General Hyperbolic Demand Function Has the Form to Follow $q = \frac { m } { p ^ { z } }$