intertemporal utility function usage : calculating consumption I have encountered this a lot in my exams and can not seem to understand how to use these functions here is an easy exemple :

A consumer who will only live 2 periods receives 1000€ in the first period and 5000€ in the second period, if the interest is at 0% how much will he consume in both periods knowing that his utility function is :


  U(C¹,C²) = 3×C¹×C²


Where C¹ is the consommation of first period and C² of second.

How do I make use of this utility function to calculate the consumption in both periods  ?
This is the two-period budget constraint:


  C1 + C2/(1+r) = Y1 + Y2/(1+r)


Derivation is straightforward. On the LHS, you have the present value of consumption (considered during period 1), and on the RHS you have the present value of income. 

Intuitively, think about 1/(1+r) on the LHS as the price ratio between Good 1 and Good 2. Now you can solve the u-max problem as per usual.