Please help me with this basic problem that I cannot solve;
Consider the following equation
U=(H-h) * (I^(1-e))/1-e
and the following identity
and the following condition
I want to solve for e when U is at its maximum. By guess is to transform to
U=(H-h) * ((hw)^(1-e))/1-e
and differentiate wrt to h , then set dU/dh to zero and solve. This method should work as it is an inverted U shaped function.
or alternatively express as I
U=(H-I/w) * (I^(1-e))/1-e
and differentiate wrt to I.
The expected result is e=H/(H-h), but I cannot do the proof !
Thanks in advance, my maths is very rusty, and i cannot get any further, unfortunately.