# 1) Consider an economy in which the marg

1) Consider an economy in which the marginal product of labor MPN isMPN = 309 ? 2N, where N is the amount of labor used. The amount of labor supplied, NS, is given by NS = 22 + 12w + 2T, where w is the real wage and T is a lump-sum tax levied on individuals. With T = 35, the government passes minimum-wage legislation that requires firms to pay a real wage greater than or equal to 7. What are the resulting values of employment and the real wage? Compare to 7b from Homework 2.2) Consider an economy with 500 people in the labor force. At the beginning of every month, 5 people lose their jobs and remain unemployed for exactly one month. One month later, they find new jobs and become employed. On January 1 and July 1 of each year, an additional 20 people lose their jobs and remain unemployed for six months before finding new jobs.a) What is the unemployment rate in this economy in a typical month?b) What fraction of unemployment spells lasts for one month? What fraction lasts for six months?c) What is the average duration of an unemployment spell?d) On any particular date, what fraction of the unemployed are suffering a long spell of more than 1 month of unemployment?3) Using a diagram, show that, if a consumer prefers more to less then his indifference curves cannot cross.4) 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 consumers 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 where1 + 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?5) 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?6) A consumers 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 consumers lifetime wealth.b) Suppose that current and future consumption are perfect complements for the consumer and that he or she always wants to have equal consumption in the current and future periods. Draw the consumers indifference curves.c) Determine what the consumers optimal first- and second-period consumption are, and what optimal saving is, and show this in a diagram with the consumers budget constraint and indifference curves. Is the consumer a lender or a borrower?d) Now suppose that instead of y = 110, the consumer has y = 150. Again, determine optimal consumption in the first and second periods and optimal saving, and show this in a diagram. Is the consumer a lender or a borrower?e) Explain the differences in your results between parts (c) and (d).7) Redo Problem 5 assuming the household has preferences U = c3/5(cf)2/5. (You do not need to draw graphs of the budget constraint and indifference curves.

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