Answer to Question #129095 in Microeconomics for Javeria Hashmi

Question

Demand curve of a software development firm digisign is qd= -16p^2 -4p + 250 .Carry out analysis of demand function and find out elasticity of demand Ed At p=25.
Draw pertinent conclusions .

Answer 1

Analysis

The demand function given by

$qd = -16p^2 - 4p + 250$ is nonlinear. It is a quadratic demand function. The demand function is defined only in the positive quadrant.

When p = $0, $qd = -16(0^2) - 4(0) + 250$

$=250 \space units$

When qd = 0 units,

$=> 0 = -16p^2 - 4p + 250$

$=> 16p^2 + 4p - 250 = 0$

Reducing the equation by 2 gives:

$8p^2 + 2p - 125 =0$

Using the quadratic formula to find $p$ gives:

$p =\dfrac { -(2) \pm \sqrt {2^2 -4(8)(-125)}} {2(8)}$

$p =\dfrac { -2 \pm \sqrt {4 004}} {16}$

$p = 3.8298230049$

$=\$3.83$

$Thus, \space qd = -16p^2 - 4p + 250 \space, \\for \space \$0 \le p \le \$3.83$

When p > $3.83, qd becomes negative. A negative quantity demanded do not make sense and hence the qd function will be undefined on price ranges that give a negative qd.

Calculating Ed

from the above analysis, the demand function is undefined when $p = \$25$ because qd will be negative. Thus,

$qd = -16(25^2) - 4(25) + 250$

$= -9,850 \space units$

Thus, we can conclude that the elasticity of demand when $p = \$25$ cannot be found since such point do not exist on the given demand function.