Suppose Jack lives for two periods. Period one is his working life, during which he earns income $50,000; period two is his retirement, during which he earns nothing. During retirement he consumes from the savings during his working life. The rate of interest on his savings is 10%. His consumption during his working life is Cw, and his consumption during his retirement life is Cr. Assume that Jack's utility function is a standard utility function exhibiting diminishing marginal rate of substitution between Cw and Cr. His current consumption during the working life is 75% of his earned income. a. Using the intertemporal choice model, draw a well labeled graph that details all the information discussed above. Notably, indicate the slope of the budget constraint, the intercepts of the budget constraint on both axes, the value of current and future consumptions, and the current savings. Keep in mind that no tax has been imposed on the saver, yet. b. Now the government taxes interest income, such that it affects the after-tax return to savings. Suppose this tax is 25%. Using this new information, depict the changes in the graph in part a. And again, indicate the new slope of the budget constraint, and the new intercepts of the budget constraint on both axes. c. Describe in general (in words) the intuition of the income and the substitution effect of this tax on returns to savings. d. If the income effect of the lower after-tax income is greater than the substitution effect, how would that affect the savings in the current period, and consequently the retirement consumption? Depict the information in a well labeled graph. Do not reuse the graph from parts a and b. Draw a new one.
Suppose Jack lives for two periods. Period one is his working life, during which he earns income $50,000; period two is his retirement, during which he earns nothing. During retirement he consumes from the savings during his working life. The rate of interest on his savings is 10%. His consumption during his working life is Cw, and his consumption during his retirement life is Cr. Assume that Jack's utility function is a standard utility function exhibiting diminishing marginal rate of substitution between Cw and Cr. His current consumption during the working life is 75% of his earned income. a. Using the intertemporal choice model, draw a well labeled graph that details all the information discussed above. Notably, indicate the slope of the budget constraint, the intercepts of the budget constraint on both axes, the value of current and future consumptions, and the current savings. Keep in mind that no tax has been imposed on the saver, yet. b. Now the government taxes interest income, such that it affects the after-tax return to savings. Suppose this tax is 25%. Using this new information, depict the changes in the graph in part a. And again, indicate the new slope of the budget constraint, and the new intercepts of the budget constraint on both axes. c. Describe in general (in words) the intuition of the income and the substitution effect of this tax on returns to savings. d. If the income effect of the lower after-tax income is greater than the substitution effect, how would that affect the savings in the current period, and consequently the retirement consumption? Depict the information in a well labeled graph. Do not reuse the graph from parts a and b. Draw a new one.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Suppose Jack lives for two periods. Period one is his working life, during which he earns
income $50,000; period two is his retirement, during which he earns nothing. During
retirement he consumes from the savings during his working life. The rate of interest
on his savings is 10%. His consumption during his working life is Cw, and his
consumption during his retirement life is Cr. Assume that Jack's utility function is a
standard utility function exhibiting diminishing marginal rate of substitution
between Cw and Cr. His current consumption during the working life is 75% of his
earned income.
a. Using the intertemporal choice model, draw a well labeled graph that details all
the information discussed above. Notably, indicate the slope of the budget
constraint, the intercepts of the budget constraint on both axes, the value of
current and future consumptions, and the current savings. Keep in mind that
no tax has been imposed on the saver, yet.
b. Now the government taxes interest income, such that it affects the after-tax
return to savings. Suppose this tax is 25%. Using this new information, depict
the changes in the graph in part a. And again, indicate the new slope of the
budget constraint, and the new intercepts of the budget constraint on both axes.
c. Describe in general (in words) the intuition of the income and the substitution
effect of this tax on returns to savings.
d. If the income effect of the lower after-tax income is greater than the
substitution effect, how would that affect the savings in the current period, and
consequently the retirement consumption? Depict the information in a well
labeled graph. Do not reuse the graph from parts a and b. Draw a new one.
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