Consider a two-period consumption-saving model. The consumer's preferences are represented by the utility function

U(c,c')=c^0.5+b*c'^0.5

where the discount factorb=0.4.You need to use this expression for the utility function in answering all subquestions of this question. The consumer receives exogenous income in the current and in the future periods,y=270 andy'=500and pays lump-sum taxest =95 andt'=85. As usual,candc'denote current and future consumption. Assume that the credit market is perfect: the consumer can borrow and lend at the real interest rater=0.05.

Derive the two conditions that define the optimal choice of consumption in the current and in the future periods. You can use the method of Lagrange or a graphical approach to explain your derivations. Interpret (i.e. explain in words) the meaning of each of the two optimality conditions.