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## The representative agent is endowed with incomes Y1 in first

Paper help Economics The representative agent is endowed with incomes Y1 in first

# The representative agent is endowed with incomes Y1 in first

The representative agent is endowed with incomes Y1 in first period and Y2 in second period. The ag… Show more The representative agent is endowed with incomes Y1 in first period and Y2 in second period. The agent does not choose how much time to spend working or enjoy as leaisure. Price level in first period is P1 and in second period is P2. Nominal interest rate is constant at i…1\$ saving in period 1 has a return of i dollars in period 2, so the consumer would have \$(1 + i) in second period. A0 = 0, wealth at the beginner of period 1 is equal to 0. Life time utility of the representative agent is u(c1, c2) = ln(c1) + Bln(c2) where C1 is consumption in period 1, c2 is consumption in period 2, and 0 < B < 1 is the future discount rate. The representative agent lives only for 2 periods and knows he dies at the end of period 2. Net inflation in period is defined as pi2 = P2/P1 - 1. Finally, there is no liquidity constraint--the representative agent can borrow as much as he likes in period 1 as long as he does not die with debt ( A2 >= 0, and since he would not want to die with positive wealth, A2 = 0 will hold). a) Write down the life time budget constraint of the representative agent. b) Using lagrangian, derive the consumers optimal period 1 and period 2 consumption condition (Use LBC as constraint in lagrange forumla). c) Combining the LBC derived in part a and the optimality condition derived in part b, derive the closed form solutions for c1 and c2 (derive c1 and c2 as a function of Y1, Y2, i, B, P1, and P2 only) d) Using your results in part c, explain what happens to c1 and c2 when…i) Discount rate B increases. ii) Price level in period 1, P1, increases. iii) Price level in period 2, P2, increases. iv) Nominal interest rate i increases. • Show less

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