Suppose you are given the utility function:
U space equals space ln space c space plus space left parenthesis 0.25 right parenthesis space ln space c apostrophe
and the budget constraint:
c space plus thin space fraction numerator c apostrophe over denominator 1 space plus space r space end fraction space equals space y space plus space fraction numerator y apostrophe over denominator 1 space plus space r end fraction
where y = 100, y' = 120, and the interest rate r = 0.05.
What is the optimal value of current consumption c*? Show all steps.