13. (Use this information to answer qustion 13 - 16) Suppose a household solves the following two-period consumption-savings problem max u(c₁) + Bu(c2) {C1,C2} s.t. aw Y1 - C1 C2y2 (1+r)a with u(c) = √c where c₁ is consumption at time 1, c2 is consumption at time 2, y₁ is houshold income at time 1, 2 is houshold income at time 2 and w is the initial wealth. Suppose the incomes of the household are $50 in time 1 and $210 in time 2. The initial wealth is $100, the discount factor is 0.975 and interest rate is 5%. Solve for the household's choice of C1. (a) 125.12 (b) 126.58 (c) 175.16 (d) 341.88 14. Now a government wants to introduce income tax in both time 1 and time 2 {1, 2} to finance a construction project that costs $50 in time 1 and another $52.5 in time 2. Which ones of the following are the household intertemporal budget constraints. (a) y1 + 1/2 =C1+ 1+1 Y2 (b) w+y1 + = C₁ + 1+r 1+r (c) wy1T1 + Y2 T2 1+r Y2 1+r = €1 + 12 1+r (d) wy171 + =C1+ 1+r C2 (1+72) 1+r 15. Solve for the household's choice of consumption in time 1 (c₁) if tax in time 1 (71) is $30. (a) 100.76 (b) 125.12 (c) 160.97 (d) 175.16 16. Solve for the private saving. (a) 19.24 (b) -5.76 (c) -40.97 (d) -75.76
13. (Use this information to answer qustion 13 - 16) Suppose a household solves the following two-period consumption-savings problem max u(c₁) + Bu(c2) {C1,C2} s.t. aw Y1 - C1 C2y2 (1+r)a with u(c) = √c where c₁ is consumption at time 1, c2 is consumption at time 2, y₁ is houshold income at time 1, 2 is houshold income at time 2 and w is the initial wealth. Suppose the incomes of the household are $50 in time 1 and $210 in time 2. The initial wealth is $100, the discount factor is 0.975 and interest rate is 5%. Solve for the household's choice of C1. (a) 125.12 (b) 126.58 (c) 175.16 (d) 341.88 14. Now a government wants to introduce income tax in both time 1 and time 2 {1, 2} to finance a construction project that costs $50 in time 1 and another $52.5 in time 2. Which ones of the following are the household intertemporal budget constraints. (a) y1 + 1/2 =C1+ 1+1 Y2 (b) w+y1 + = C₁ + 1+r 1+r (c) wy1T1 + Y2 T2 1+r Y2 1+r = €1 + 12 1+r (d) wy171 + =C1+ 1+r C2 (1+72) 1+r 15. Solve for the household's choice of consumption in time 1 (c₁) if tax in time 1 (71) is $30. (a) 100.76 (b) 125.12 (c) 160.97 (d) 175.16 16. Solve for the private saving. (a) 19.24 (b) -5.76 (c) -40.97 (d) -75.76
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Transcribed Image Text:13. (Use this information to answer qustion 13 - 16) Suppose a household
solves the following two-period consumption-savings problem
max u(c₁) + Bu(c2)
{C1,C2}
s.t. aw Y1 - C1
C2y2
(1+r)a
with u(c) = √c where c₁ is consumption at time 1, c2 is consumption at
time 2, y₁ is houshold income at time 1, 2 is houshold income at time
2 and w is the initial wealth. Suppose the incomes of the household are
$50 in time 1 and $210 in time 2. The initial wealth is $100, the discount
factor is 0.975 and interest rate is 5%. Solve for the household's choice of
C1.
(a) 125.12
(b) 126.58
(c) 175.16
(d) 341.88
14. Now a government wants to introduce income tax in both time 1 and time
2 {1, 2} to finance a construction project that costs $50 in time 1 and
another $52.5 in time 2. Which ones of the following are the household
intertemporal budget constraints.
(a) y1 + 1/2 =C1+
1+1
Y2
(b) w+y1 + = C₁ +
1+r
1+r
(c) wy1T1 +
Y2
T2
1+r
Y2
1+r
= €1 + 12
1+r
(d) wy171 + =C1+
1+r
C2 (1+72)
1+r
15. Solve for the household's choice of consumption in time 1 (c₁) if tax in
time 1 (71) is $30.
(a) 100.76
(b) 125.12
(c) 160.97
(d) 175.16
16. Solve for the private saving.
(a) 19.24
(b) -5.76
(c) -40.97
(d) -75.76
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