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.

1. Compute the lifetime wealthweof the consumer.
2. Define thelifetime(intertemporal)budget constraint of the consumer. What is the economic meaning of the lifetime budget constraint?
3. Plot the lifetime budget constraint on a diagram withcon the horizontal axis andc'on a vertical axis. Indicate the endowment point. What are the values of the intercepts with the horizontal and vertical axes? What is the value of the slope of the budget constraint?