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, Y, = 100, Y½ = 50. Thus, there is total equality in the labor income distribution. The utility function of agenti, i = A, B, is U,(C1, c2) = In(c:)+ ß In(c2), where ci is consumption in the first period, and c2 consumption in the second period (price of c, and c2 equal to one). Agents differ in the value of B and Ba = 0.7 and ße = 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? Continue with the same economy as in the previous question. If the government establishes a tax rate of 25% on the capital income ( and the government does not return that revenue to the agents), what happens with the distribution of wealth ? Select one: O a. The distribution of wealth becomes more unequal than before because now WA=13.98103 and Wg=8.22021. Agent B only has 58.7955% of the wealth of A, i.e., 8.22021/13.98103 =0.587955 O b. The distribution of wealth becomes more unequal than before because now WA=14.88150 and We=9.01023. Agent B only has 60.5465% of the wealth of A, i.e., 9.01023/14.88150 =0.605465 O c. The distribution of wealth does not change because the agents have preferences such that savings do not depend on the tax rate on capital income. O d. The distribution of wealth becomes more unequal than before because now WA=13.8167 and W838.43023. Agent B only has 61.0149% of the wealth of A, i.e., 8.43023/13.8167 0.610149
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, Y, = 100, Y½ = 50. Thus, there is total equality in the labor income distribution. The utility function of agenti, i = A, B, is U,(C1, c2) = In(c:)+ ß In(c2), where ci is consumption in the first period, and c2 consumption in the second period (price of c, and c2 equal to one). Agents differ in the value of B and Ba = 0.7 and ße = 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? Continue with the same economy as in the previous question. If the government establishes a tax rate of 25% on the capital income ( and the government does not return that revenue to the agents), what happens with the distribution of wealth ? Select one: O a. The distribution of wealth becomes more unequal than before because now WA=13.98103 and Wg=8.22021. Agent B only has 58.7955% of the wealth of A, i.e., 8.22021/13.98103 =0.587955 O b. The distribution of wealth becomes more unequal than before because now WA=14.88150 and We=9.01023. Agent B only has 60.5465% of the wealth of A, i.e., 9.01023/14.88150 =0.605465 O c. The distribution of wealth does not change because the agents have preferences such that savings do not depend on the tax rate on capital income. O d. The distribution of wealth becomes more unequal than before because now WA=13.8167 and W838.43023. Agent B only has 61.0149% of the wealth of A, i.e., 8.43023/13.8167 0.610149
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:hello! can you solve question B. thanks
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, Y = 100, Y2 = 50. Thus, there is total equality in the labor income
distribution. The utility function of agenti, = A, B, is U;(c1, c2) = In(c;)+ ß In(c2), where cz is
consumption in the first period, and c2 consumption in the second period (price of c, and c2
equal to one). Agents differ in the value of ß and Ba = 0.7 and fe = 0.6. A) Find the value of the
wealth, Wi, 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?
B) Continue with the same economy as in the previous question. If the government establishes a
tax rate of 25% on the capital income ( and the government does not return that revenue to the
agents), what happens with the distribution of wealth?
Select one:
O a. The distribution of wealth becomes more unequal than before because now WA=13.98103 and Wg=8.22021.
Agent B only has 58.7955% of the wealth of A, i.e., 8.22021/13.98103 =0.587955
O b. The distribution of wealth becomes more unequal than before because now WA=14.88150 and Wg=9.01023.
Agent B only has 60.5465% of the wealth of A, i.e., 9.01023/14.88150 0.605465
c. The distribution of wealth does not change because the agents have preferences such that savings do not
depend on the tax rate on capital income.
O d. The distribution of wealth becomes more unequal than before because now WA=13.8167 and WB=8.43023.
Agent B only has 61.0149% of the wealth of A, i.e., 8.43023/13.8167 0.610149
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