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Unformatted text preview: Economics W3213 Spring 2010 Bruce Preston Problem Set 4 Solutions Short Answer Questions Indicate whether you think the following statements are true, false or uncertain. Support your answer by giving all necessary reasoning and calculations. 1. The government, concerned about weak consumption expenditures, pursues a cut in taxes to stimulate the economy. This policy will be successful, though national saving will decline. Solution: Uncertain A good answer would note the following: (a) Note that the answer depends on whether Ricardian equivalence holds or not. (b) De&ne Ricardian Equivalence: that for a given path of government expenditures G, the timing of taxes does not matter. Only the present discounted value of taxes matter as only changes in life time income should lead to a revision in the optimal level of consumption today. (c) If Ricardian equivalence holds, households save the entirety of the tax cut to pay fu- ture taxes of the same amount in present discounted value. Consumption therefore does not change because life time resources are unchanged. (d) On the other hand, Government saving declines by the amount of the tax cut. There is therefore no change in national saving, only the composition of saving between private agents and the government changes. (e) If households do not correctly anticipate having to pay future taxes to pay for to- days tax cut the life time income may be perceived to have risen. Hence consump- tion will rise by some amount as will saving. However, consumption smoothing implies saving cannot rise by the amount of the tax cut. It follows that national saving must decline as government saving falls by the amount of the tax cut, more than o/setting the increase in private saving. Under this scenario the statement is true: consumption would rise buy national saving would fall. 2. In the Life-cycle model of consumption, if a household cannot borrow against future income, we would expect to observe consumption to be excessively sensitive to income. Solution: True Excess sensitivity implies that consumption in some future period is observed to change when income changes, even though the income change was perfectly predictable prior 1 to the time of the income change. Under the life cycle model of consumption, whenever households learn of a change in life time income, say through a predictable change in future income (such as a pay rise or a tax refund) then the optimal level of consump- tion should change today. This is just the consumption smoothing motive. In the case that a household cannot borrow then the assumptions of the life cycle model are being violated. Suppose you anticipate receiving $200,000 in a years time. According to our model, consumption smoothing would dictate an increase in consumption today. That consumption would be funded by borrowing against the $200,000 to be received in a year. Of course, if a consumer cannot borrow, then she cannot raise consumption un- til the increase in income is actually received in a years time even though the income...
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