I am trying to prove the following theorem (Danthine and Donaldson- Intermediate Financial Theory 3rd edition, p. 121) but haven't been successful.
Theorem 5.5 (Arrow, 1971): If, for all wealth levels Y,
i. R'(Y)= 0 (CRRA) then η=1
ii. R'(Y)<0 (DRRA) then η>1
iii. R'(Y)>0 (IRRA) then η<1
where R'(Y) is the first derivative of Arrow's relative risk aversion measure, Y is wealth, and η(Y,a*)= (Y/a*)/(da*/dY) i.e., the wealth elasticity of investment in the risky asset (a* is the optimal amount invested in the risky asset).
How would you proceed with the proof?