See Attachment. I am the TA for a macroeconomics course. My professor provided me with the answer for this problem (3a.) but I am having a difficult time deriving it using the partial derivatives of the current period C(t) and future period C(t+1). The Euler equation format she has taught the students to use is u'(c1)= (1+r)B*u'(c2) where B is the discount rate and r is the interest rate. Please help!!
I have been finding the derivative of t=1 and t=2 and then trying to plug these into the Euler equation. For t=1 I get Ct^(-omega) and for t=2 I get B(Ct+1)^(-omega). Plugging these into the Euler equation gives me a B^2 term, which I know is not correct.