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325_PracticePS9_Soln - Department of Economics University...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Practice Problem Set 9 Suggested Solutions Professor Sanjay Chugh Spring 2011 1. Consolidated Government Budget Constraint. Suppose that at the beginning of period t , M t -1 = 100 and the government has to repay 10 nominal units in government bonds (our usual one-period, FV = 1 bonds). In period t , the fiscal authority (Congress) decides to spend 190 nominal units in government spending, collect 180 nominal units in taxes, and instructs the Treasury to raise 20 nominal units by issuing new (one-period, FV = 1) bonds (that is, the Treasury is ordered to raise 20 nominal units by selling bond, not ordered to sell 20 bonds). a. Under this scenario, can the monetary authority decide to expand the money supply (i.e., can it choose M t > M t -1 )? Briefly explain why or why not, or, if it is not possible to determine, explain why it cannot be determined. Solution: Simply use the consolidated period- t GBC, 1 1 b t t t t t t t t Pg B T P B M M ± ± ² ² ² ± along with the given values: M t -1 = 100, B t- 1 = 10 (i.e., the bond repayment the government must make in period t ), P t g t = 190 (the nominal spending of the government in period t ), T t = 180 (the nominal tax collections of the government in period t ), and 20 b t t P B (the amount of nominal revenue the Treasury is instructed to raise on the bond markets for Congress). The only remaining unknown is M t , which clearly must = 100 in order for the consolidated GBC to be satisfied. Thus, no, the monetary authority cannot expand the money supply because it would violate the consolidated GBC. b. Under this scenario, is the monetary authority active or passive? Briefly explain. Solution: Based on the arguments above, it is clear the monetary authority is passive because it is reacting to the decisions of the fiscal authority. The monetary authority’s hands are tied (i.e., it is forced to set M t = 100) by the choices made by the fiscal authority. Thus, if the monetary authority did for some reason want to expand the money supply (to help stimulate GDP in the economy, for example), it cannot. 2. Unpleasant Monetarist Arithmetic 1 . Consider a finite period economy, the final period of which is period T (so that there is no period 1 T ² ) – every agent in the economy knows that period T is the final period of the economy. In this economy, the government conducts both 1 This problem is based on a classic work in macroeconomic theory by Thomas Sargent and Neil Wallace (“Some Unpleasant Monetarist Arithmetic,” Federal Reserve Bank of Minneapolis Quarterly Review, Vol. 5, 1981).
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2 fiscal policy (engaging in government spending and collecting taxes) and monetary policy (expanding or contracting the money supply). The timing of fiscal policy and monetary policy will be described further below. The economy has now arrived at the very beginning of period T , and the period- T consolidated government budget constraint is 1 1 1 (1 ) T T T T T T T T T M M B P t i B P g ± ± ± ± ² ² ² ² ,
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