Question

help

Answer 1

This is definitely not my area. But according to wikipedia
Price elasticity is the percentage change in quantity demanded in response to a one percent change in price

So using this definition, we can first find the quantity when price=34 (P=34)
Q= (95-P)^2 = (95-34)^2= 61^2= 3721

Now find the quantify Q when we increase the price by 1% (multiply 34*1.01)
Q2= (95-34*1.01)= 3679.64
The percent change is
\[ 100\cdot \frac{Q2-Q}{Q} = 100\cdot \frac{3679.64-3721}{3721}= -1.11 \% \]
They say it is often treated as a positive number, though it is negative?

Wikipedia also gives a formula
price elasticity is equal to the absolute value of the first derivative of quantity with respect to price (dQd/dP) multiplied by the point's price (P) divided by its quantity (Qd).

\[ E= \frac{P}{Q} \frac{dQ}{dP} \]

starting with
Q= (95-P)^2
we find dQ/dP = -2(95-P)= 2P-190
when P=34, dQ/dP = 68-190= -122
using the absolute value dQ/dP= 122

with P=34 and Q= 3721 (see above), and dQ/dP= 122, the equation for E gives
34*122/3721= 1.11 which matches above.