MATH SOLVE

3 months ago

Q:
# Suppose that the demand equation for a certain item is 1p+1x2β160=0. evaluate the elasticity at 65:

Accepted Solution

A:

Price elasticity is defined as [tex]\frac{\Delta(quantity)}{\Delta(price)}[/tex].

Here, the question has omitted to define variables, so we will ASSUME

p=price

x=variable,

and we're given

p+x^2-160=0

We calculate

[tex]\delta{x}/\delta{p}[/tex] by implicit differentiation with respect to p:

1+2x (dx/dp)=0

=>

E(x)=(dx/dp)=-1/(2x)

Therefore the price elasticity at x=65 is

E(65)=1/(2*65) =-1/130 (approximately -0.00769)

Here, the question has omitted to define variables, so we will ASSUME

p=price

x=variable,

and we're given

p+x^2-160=0

We calculate

[tex]\delta{x}/\delta{p}[/tex] by implicit differentiation with respect to p:

1+2x (dx/dp)=0

=>

E(x)=(dx/dp)=-1/(2x)

Therefore the price elasticity at x=65 is

E(65)=1/(2*65) =-1/130 (approximately -0.00769)