00:01
Let's suppose our price demand equation is defined by p, which is equal to the square root of 176 minus 2x.
00:10
Now, elasticity is given by e, which is equal to negative price p over the quantity x times the derivative of the quantity x.
00:23
Since our price demand is written as a function of p in terms of x, you will have to rewrite that.
00:30
Now, p equals a square root of 176 minus 2x, that's p squared equal to 176 minus 2x, which means that 2x equals 176 minus p squared.
00:47
Or if we divide it by 2, x is equal to 88 minus 1 half of p squared.
00:56
So if you take the derivative of x with respect to p, we have x prime that's equal to negative 1 half times 2p or that's negative p.
01:10
Thus, e is equal to negative p over x times x prime, which is negative, of p.
01:20
So it'll be p squared over x.
01:24
But p squared is 176 minus 2x, so this is just 176 minus 2x over x.
01:33
Because you want the elasticity to be elastic, we want it to be greater than 1.
01:38
So if is greater than 1, then 176 minus 2x over x should be greater than 1, which implies that 176 minus 2x over x minus 1 is greater than 0.
01:56
It'll be 176 minus 2x minus x over x greater than 0 or that 176 minus 3x over x is greater than 0...