Consider the two-period life-cycle model and suppose that individuals receive labor income in the first and second periods, Y1 and Y2. Denote by r the interest rate and assume that r = 0.1 (10%). There are two individuals in this economy, agent A and agent B. They both have the same labor income, Y₁ = 100, Y₂ = 50. Thus, there is total equality in the labor income distribution. The utility function of agenti, i = A, B, is U₁ (C1, C₂) = In(c₁) + B In(c₂), where c₁ is consumption in the first period, and c₂ consumption in the second period (price of c₁ and c₂ equal to one). Agents differ in the value of & and BA = 0.7 and 3g = 0.6. A) Find the value of the wealth, W;, of each individual in the second period (i.e. their savings before the return they get on it). Is the distribution of wealth more or less equal than the distribution of income? Select one: O a. The distribution of wealth is more unequal because WA-14.4385 and WB-9.09091. Agent B only has 62.963% of the wealth of A, i.e., 9.09091/14.4385 =0.62963 b. The distribution of wealth is more unequal because WA-14.69985 and WB-9.41319. Agent B only has 64.036% of the wealth of A, i.e., 9.41319/14.69985 =0.64036 O c. The distribution of wealth is more unequal because W₁-13.05585 and Wę-8.10319. Agent B only has 62.0656% of the wealth of A, i.e., 8.10319/13.05585 -0.620656 d. The distribution of wealth is more unequal because WA-13.95585 and WB-8.503191. Agent B only has 60.9292% of the wealth of A, i.e., 8.503191/13.95585 =0.609292
Consider the two-period life-cycle model and suppose that individuals receive labor income in the first and second periods, Y1 and Y2. Denote by r the interest rate and assume that r = 0.1 (10%). There are two individuals in this economy, agent A and agent B. They both have the same labor income, Y₁ = 100, Y₂ = 50. Thus, there is total equality in the labor income distribution. The utility function of agenti, i = A, B, is U₁ (C1, C₂) = In(c₁) + B In(c₂), where c₁ is consumption in the first period, and c₂ consumption in the second period (price of c₁ and c₂ equal to one). Agents differ in the value of & and BA = 0.7 and 3g = 0.6. A) Find the value of the wealth, W;, of each individual in the second period (i.e. their savings before the return they get on it). Is the distribution of wealth more or less equal than the distribution of income? Select one: O a. The distribution of wealth is more unequal because WA-14.4385 and WB-9.09091. Agent B only has 62.963% of the wealth of A, i.e., 9.09091/14.4385 =0.62963 b. The distribution of wealth is more unequal because WA-14.69985 and WB-9.41319. Agent B only has 64.036% of the wealth of A, i.e., 9.41319/14.69985 =0.64036 O c. The distribution of wealth is more unequal because W₁-13.05585 and Wę-8.10319. Agent B only has 62.0656% of the wealth of A, i.e., 8.10319/13.05585 -0.620656 d. The distribution of wealth is more unequal because WA-13.95585 and WB-8.503191. Agent B only has 60.9292% of the wealth of A, i.e., 8.503191/13.95585 =0.609292
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.1P
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Transcribed Image Text:Consider the two-period life-cycle model and suppose that individuals receive labor income in
the first and second periods, Y1 and Y2. Denote by r the interest rate and assume that r = 0.1
(10%). There are two individuals in this economy, agent A and agent B. They both have the
same labor income, Y₁ = 100, Y₂ = 50. Thus, there is total equality in the labor income
distribution. The utility function of agenti, i = A, B, is U₁(C₁, C2) = In (C₁)+ B; In(c₂), where c₁ is
consumption in the first period, and c₂ consumption in the second period (price of c₁ and c₂
equal to one). Agents differ in the value of B and BA = 0.7 and Bs = 0.6. A) Find the value of the
wealth, W₁, of each individual in the second period (i.e. their savings before the return they get
on it). Is the distribution of wealth more or less equal than the distribution of income?
Select one:
a. The distribution of wealth is more unequal because WA-14.4385 and WB-9.09091. Agent B only has
62.963% of the wealth of A, i.e., 9.09091/14.4385 =0.62963
b. The distribution of wealth is more unequal because WA-14.69985 and WB-9.41319. Agent B only has
64.036% of the wealth of A, i.e., 9.41319/14.69985 =0.64036
C. The distribution of wealth is more unequal because WA=13.05585 and WB-8.10319. Agent B only has
62.0656% of the wealth of A, i.e., 8.10319/13.05585 =0.620656
d. The distribution of wealth is more unequal because WA-13.95585 and WB-8.503191. Agent B only has
60.9292% of the wealth of A, i.e., 8.503191/13.95585 =0.609292
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