I've been given the Cobb-Douglas utility function:
$\ u(q_1, q_2)=alnq_1+blnq_2=q_1^aq_2^b \ $$\ u(q_1, q_2)=a\ln q_1+b\ln q_2=q_1^aq_2^b \ $
If I want to prove homothetic preferences, I use the following condition:
$\ u(\lambda q_1, \lambda q_2)=\lambda u(q_1,q_2) \ $
According to my calculation, this yields:
$\ u(\lambda q_1, \lambda q_2)=(\lambda q_1)^a(\lambda q_2)^b \ $
$\ =\ \lambda^{a+b}q_1^aq_2^b \ $
Is it correct to say that as a result, preferences are homothetic if and only if $\ a+b=1 \ $?