homework3
Homework 3
Due 2/24/14
1) Using a diagram, show that, if a consumer prefers more to less then his indifference curves cannot cross.
2) Suppose that current and future consumption are perfect substitutes. The indifference curves will consist of parallel lines with the negative slope m, where m > 0.
a) How does the marginal rate of substitution between current and future consumption relate to the geometry (i.e. the slope and the intercept) of the consumer’s indifference curves?
b) Given perfect substitutes, is more preferred to less? Do these preferences satisfy the diminishing marginal rate of substitution property?
c) Determine the optimal consumption bundle for a situation where the gross interest rate 1 + r is greater than the marginal rate of substitution, for a situation where
1 + r is less than the marginal rate of substitution, and for a situation where 1 + r equals the marginal rate of substitution.
d) Do you think it likely that any consumer would view current and future consumption as perfect substitutes?
3) An employer offers his or her employee the option of shifting x units of income from next year to this year. That is, the option is to reduce income next year by x units and increase income this year by x units.
a) Would the employee take this option (use a diagram)?
b) Determine, using a diagram, how this shift in income will affect consumption this year and next year, and saving this year. Explain your results.
c) What do you infer from this about whether it is a good thing to get a refund on your income taxes?
4) A consumer’s income in the current period is y = 110, and income in the future period is yf = 120. He or she pays lump-sum taxes t = 30 in the current period and tf = 10 in the future period. The real interest rate is 0.1, or 10% per period.
a) Determine the consumer’s lifetime wealth.
b) Suppose that current and future consumption are perfect complements for the consumer and that he or she always wants to have
Due 2/24/14
1) Using a diagram, show that, if a consumer prefers more to less then his indifference curves cannot cross.
2) Suppose that current and future consumption are perfect substitutes. The indifference curves will consist of parallel lines with the negative slope m, where m > 0.
a) How does the marginal rate of substitution between current and future consumption relate to the geometry (i.e. the slope and the intercept) of the consumer’s indifference curves?
b) Given perfect substitutes, is more preferred to less? Do these preferences satisfy the diminishing marginal rate of substitution property?
c) Determine the optimal consumption bundle for a situation where the gross interest rate 1 + r is greater than the marginal rate of substitution, for a situation where
1 + r is less than the marginal rate of substitution, and for a situation where 1 + r equals the marginal rate of substitution.
d) Do you think it likely that any consumer would view current and future consumption as perfect substitutes?
3) An employer offers his or her employee the option of shifting x units of income from next year to this year. That is, the option is to reduce income next year by x units and increase income this year by x units.
a) Would the employee take this option (use a diagram)?
b) Determine, using a diagram, how this shift in income will affect consumption this year and next year, and saving this year. Explain your results.
c) What do you infer from this about whether it is a good thing to get a refund on your income taxes?
4) A consumer’s income in the current period is y = 110, and income in the future period is yf = 120. He or she pays lump-sum taxes t = 30 in the current period and tf = 10 in the future period. The real interest rate is 0.1, or 10% per period.
a) Determine the consumer’s lifetime wealth.
b) Suppose that current and future consumption are perfect complements for the consumer and that he or she always wants to have