Problem Set 2 - Answers.pdf

Problem Set 2 - Answers.pdf - York University Department of...

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York University Department of Economics ECON 3140N Monetary Economics Professor Tasso Adamopoulos Answers to Problem Set 2 February 21, 2006 1. Answers to Exercises 3.1, 3.2, 3.3, 3.4, 3.6 from Champ and Freeman (Ch.3, pp.70-72- 29), are at the end. 2. The statement is partly true. If the source of inflation is the issuing of new money at a constant rate z > 1 then the monetary equilibrium cannot be efficient, i.e., it cannot maximize the utility of future generations. This is true regardless if the receipts from printing money are used to provide transfers to individuals or to undertake wasteful government purchases. The reason is that inflation alters the slope of the budget constraint of individuals and distorts their behavior (see next question too). Since the budget line and the resource constraint do not coincide, the consumption bundle that an individual will choose in a stationary monetary equilibrium will not be the one that a central planner would choose (see Ch.3). If inflation is caused by a declining population but the supply of money if fixed, i.e., n < 1 and z = 1, then the lifetime budget constraint of the individual and the economy’s resource constraint are identical and the welfare of future generations is maximized in the stationary monetary equilibrium (see Ch.1). 3. The statement is false. Even though printing money at a constant rate has a low resource cost (the administrative cost of printing notes) it introduces a distortion on the activity of holding money. It causes inflation which erodes the real value of fiat money (inflation tax). The inflation tax induces people to change their behavior: they economize on their money holdings, and thus end up holding less real money balances than is optimal for them (and less than they would hold in a world without inflation). 1
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Furthermore, the inflation tax is a proportional tax: the more money an individual holds, the more severe the loss in real value he will experience. A lump-sum tax, by definition takes away a fixed amount of goods from an individual, in a way that does not depend on any actions that the particular individual undertakes. Thus the lump- sum tax does not induce people to alter their behavior. Under a lump-sum tax the welfare of future generations is maximized. Consequently the lump-sum tax is superior to seigniorage from an efficiency point of view. 4. (a) The resource constraint that a central planner would face would be to allocate the total amount of goods available in the economy at every point in time between the young and the old. In this case the resource constraint is: N t · c 1 ,t + N t - 1 · c 2 ,t +1 N t · y t + N t - 1 · ψ · y t - 1 (1) Since y t = γy t - 1 we can re-write the resource constraint as: N t · c 1 ,t + N t - 1 · c 2 ,t +1 ( γ · N t + ψ · N t - 1 ) · y t - 1 (2) (b) The budget constraints for the individual when young and when old are: c 1 ,t + v t · m t y t (3) c 2 ,t +1 v t +1 · m t + ψ · y t + a t +1 (4) Combining (3) and (4) in the standard way we can derive the individual’s lifetime budget constraint: c 1 ,t + v t v t +1 · c 2 ,t +1 y t · [1 +
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