Question

The demand function for a certain make of ink-jet cartridge is the following where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. $ p = - {\color{black}0.07} x^2 -{\color{black}0.7} x +6$ Compute the elasticity of demand when x = 5. (Round your answer to two decimal places.)

Answer 1

Answer:

The answer to the following question is: (-9.34)

Explanation:

Given that:

p = -0.07 x^2 - 0.7x  + 6

The price elasticity of demand = ( change in quality / change in price)

     =   (dp / dx)  (x/p)

     =   d / dx   (-0.07 x^2 - 0.7x  + 6)   x / p

     =   (-0.14x - 0.7)  x/ (-0.07 x^2 - 0.7x  + 6)

elasticity = (-0.14x^2 - 0.7x) / (-0.07 x^2 - 0.7x  + 6)

at x=5;

elasticity = (-0.14(5)^2 - 0.7(5)) / (-0.07 (5)^2 - 0.7(5)  + 6)

              = (-3.5 - 3.5) / (-1.75 - 3.5 + 6)

              =  -7/ 0.75 = -9.333

              = -9.34