# Homework Help: Logarithmic elasticities

1. Sep 19, 2011

### elfy

1. The problem statement, all variables and given/known data
Find an expression (in terms of x and y) for the elasticity of y wrt x:
ln(y) = 10 + 0.9x - 0.6x^2

2. Relevant equations
ln(y) = 10 + 0.9x - 0.6x^2

3. The attempt at a solution
I first tried the normal way of doing elasticities:

ElxY = (x/y)*y'(x) which I got to:

[x / 10 + 0.9x - 0.6x^2] * (0.9 - 1.2x) --> 0.9x - 1.2x^2 / (10 + 0.9x -0.6x^2)

Furthermore, the log stated on the left-hand side is somewhat worrying me so I also tried the logarithmic rule in relation to elasticities:
ElxY = dlnY/dlnX but I got a really wierd answer when I started to differentiate wrt x.

Could someone just point me in the right direction so that I could have an attempt at the problem? I would very much appriciate any help I can get!

EDIT: If that one is too complex to explain I also have a simpler version which is similar:
lny=ax + bx
ElxY = (x/ax + bx) * a + bx ---> ax / ax = 1.
However, the same problem happens here with regards to the lny, which I assume makes my answer incorrect.

Last edited: Sep 19, 2011