maximize u(x) = ln x - 1/a x

Question

individual utility function: u(x) = ln x - 1/a x, where a > 0

a) what is the utility- maximization choice of x?

b) what is the maximized value of utility?

Answer 1

u(x)=ln(x)-x/a, u'(x)=1/x-1/a=(a-x)/(ax)=0, x=a at extremum.

u(a)=ln(a)-1, u"(a)=-1/a²<0⇒(a,ln(a)-1) is a maximum. 

(a) x=a

(b) ln(a)-1