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.)

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