A general exponential demand function has the form to follow. $q = A e ^ { - m q }$ (A, m - nonzero constants)

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

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

Question

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

Quizplus · Accepted Answer

The elasticity of demand, $E$, is defined as the percentage change in quantity demanded ($q$) for a one percent change in price ($p$). Mathematically, it is given by $E = \frac{d q / q}{d p / p}$. However, the provided demand function is in terms of $q$ and not directly in terms of $p$. To find the elasticity in terms of $p$, we need to understand the relationship between $q$ and $p$, which is not directly provided in the question. However, in general, for exponential demand functions, the elasticity can be related to the price ($p$) and the parameters of the function. Given the lack of direct relationship between $q$ and $p$ in the question, the correct answer involves understanding that elasticity is directly proportional to the price ($p$) in many demand functions, especially when considering the general form and properties of exponential functions. The correct choice, therefore, involves recognizing that elasticity varies with price, and without the explicit function linking $p$ and $q$, the most straightforward relationship reflecting the direct proportionality to $p$ and the parameter $m$ (which typically represents the sensitivity of the demand to changes in price) is the correct approach. Hence, $E = m p$ is the correct formula for elasticity in this context, reflecting the direct impact of price changes on demand elasticity in a general exponential demand function scenario.

A General Exponential Demand Function Has the Form to Follow q=Ae−mqq = A e ^ { - m q }q=Ae−mq

A General Exponential Demand Function Has the Form to Follow $q = A e ^ { - m q }$