Question 1 Consider a two-period model in which an agent needs to decide how much to consume today, 01 and how much to consume tomorrow, c2. They begin in period 1 with some wealth, W, and receives income in both periods, y1 and y2. They can borrow or lend at rate r and their utility function is given by: u(c1,c2)=14-ln(c1)+ll -ln(c2) A) Derive an algebraic expression for the optimal present and future consumption, c1 and c2, as a function of the present value of lifetime resources (PVLR). B) Assume W=500, y1=2000, y2=1200, and r=20%. Find the numerical values for c1 and c2 using the formulas found in a). Is the representative agent a saver or a borrower? C) Suppose a financial crisis hits the economy and the agent's wealth melt to zero (Vi/=0). Find the new optimal consumption bundle (c1 and c2). Is the agent's saving status the same as in part b)? Explain why. D) Seeing the negative shock from part c), the central bank decides to decrease the real interest rate (r) in the economy to 5%. Find the new optimal consumption bundle (c1 and c2), and discuss the substitution and income effects at play