# aps5 - Economics 102 Introductory Macroeconomics Spring...

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Economics 102 Introductory Macroeconomics - Spring 2006, Professor J. Wissink Problem Set 5 – ANSWERS 1. Consider the super simple linear frugal governed open economy with the marginal propensity to consume being the only non-zero marginal propensity. Ralph understands why the multiplier for G’ is opposite in sign of the multiplier for T’, but he can’t seem to intuitively figure out why its value would be smaller. That is, why would a change in G’ work “better” or be “stronger” than an equivalent and opposite change in T’? Help Ralph out. Changes in government spending (∆G) directly boost the economy. By the full amount in the first period, by c ∆G in the second period (assuming the super simple model), etc. (To get the total change in output at the end of the day, just sum the infinite series.) On the other hand, changes in taxation (∆T) boost economy indirectly and less. The reason is that households save part of their tax rebate. Thus, in the first period, (assuming the super simple model) output changes by c∆T, in the second period by c 2 ∆T, etc. (To get the total change in output at the end of the day, just sum the inifinite series.) 2. The Merriam-Webster Online Dictionary defines a spendthrift as, “a person who spends improvidently or wastefully.” Suppose this actually means a person who never saves. Suppose we had a linear spendthrift UNgoverned closed economy with no investment. What is the value of the aggregate desired expenditure multiplier in this world? The multiplier would be infinite. Initial change in autonomous consumption will increase output by the whole amount in each period. There will be no “equilibrium” level of output, it will grow till infinity. 3. In a governed model, if taxes are not lump-sum, but depend on income, what happens to the size of the government spending multiplier, and why? The easiest answer is to derive the multiplier. Denoting by C an autonomous consumption and by t a marginal tax rate, let us write: ' * * * ' * * ' (1 ) ( ) (1 ) 1 (C +I+G) 1 (1 ) d d AE C I G C c t Y I G Y AE Y Y C c t Y I G Y c t = + + = + - + + = = + - + + = - -

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1 1 As long as 0< t < 1, . 1 1 (1 ) c c t - - - If taxes are not lump-sum, the multiplier is smaller. The reason is that the effect of a change in government expenditures on equilibrium output is dampened by taxation. (So, the initial ∆G will change output by ∆G in the first period, but only by c(1-t)∆G in the second period, etc. Sum the series to get the total change in output
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