Question

Consider a two-period economy discussed in Chapter 9. Suppose there are only two households, and each household's utility function and endowment are given as follows. u' (C1,C2) = (C122) and e' = (18,4). u? (C1,C2) = Incı + 2 Inc and e? = (3,6). el denote the allocation of endowment income for household i. For simplicity, there is no government, and therefore no tax in both periods. There is a perfectly competitive credit (financial market in which they can buy and sell bonds. 1. Based on what you learned in Chapter 9, write down each household's budget constraint for period by period. Using these, write down each household's lifetime budget constraint. 2. Using the lifetime budget constraint in 1, solve each household's optimization problem and derive the optimal demand function for c c ) as a function of the real interest rate r. 3. Then, find the optimal saving/borrowing function in terms of r) for each household 4. Using the credit market clearing condition, determine the equilibrium real interest rate. 5. Can you say anything about the efficiency" of the equilibrium outcome? Discuss.

Answer 1

1 Endger Contralur you inter rempont choice : of or C liv & C2 Yo (110 + 12 for hegnetold tillit ca = 18 (1tv + 1- howtwold 2 Colt - 3(1+r) 16 (11) fornelold 2 quilibrium: Mrser or (11) I kootund I quilitlum Me Sego (11) Or, 2002 C -cler | 20. ova, 4010 | Seeting in (1) 1. 5/2 = 3(117)+ 6 Or, &* 2(11) 19 (1) 4 2.0 , | Raviny/Lormwing X 5) Swiy/Powe

- 10 9 Bewiva / Baring 72 - 6 Loving / Burrsing 12- 62 = 6- 2(14)- 4 = 2-2(lt) 72) = 6 - 28 - 6 - 2-q[1+r) - - 7-av- 2 زور را ر و ز رو را زد و از روتور سواری کا دور دو ر از تروا Jundian cua aquel 1.2, at = 1

5) However, r = 1 is ineffecient, as a 100% real interest rate means consumers do not consume anything in period 1, i.e., c₁ = 0, which is not an efficient solution.