Maximisation of a utility function: two period intertemporal model

[johnnykim]

I'm working on a two period intertemporal model. I have managed to find the utility function but I seem to have problems finding the first order and maximising it. The utility function is:

. . .

I just need help finding the first order with respect to C1 where

and maximising it.

Thanks

 

[stapel]

I'm working on a two period intertemporal model. I have managed to find the budget constraint and the objective function but I seem to have problems finding the first order and maximising it. The objective function is:

. . . . .\(\displaystyle \large \dfrac{C_1^{1-\gamma}}{1\, -\, \gamma}\, +\, \delta\, \dfrac{\left\{(1\, +\, r)\, (A_1\, -\, C_1)\right\}^{1 - \gamma}}{1\, -\, \gamma} \)

To be a "function", there needs to be an "equals" sign and the functional statement ("f(x)", "U(C₁, C₂)", etc) on the other side.

When you reply with that information, please provide a clear listing of your thoughts and efforts so far, keeping in mind that folks here are likely only to know about the math. Any assumptions, definitions, relationships, etc, implicit in your economics modelling will need to be stated, as necessary, in order for us to know what's going on. Thank you!