Problem set 2 Key

Problem set 2 Key - Solution to Problem 1 a) In the usual...

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Solution to Problem 1 a) In the usual diagram with the interest rate on the vertical axis and the quantity of money at the horizontal axis, the money demand is a downward sloping curve, because it depends negatively on the interest rate. This negative dependence reflects the fact that the interest rate represents the opportunity costs of holding money. The opportunity cost incurred while holding money is the foregone returns of alternative interest-bearing assets that could be purchased with money. The only remaining factor which could shift the money demand curve in this diagram is the second argument of the money demand: the output level. For a given price level in the short run, a change in the output level or the transaction volume can be only generated by an increase in real output. b) In order to generate a reduction of the equilibrium interest rate the central bank can only turn to the variable which it controls: the money supply. Because the central bank knows that the money demand is negatively related to the interest rate (explanation see a)), it has to increase the supply of money therefore raising the quantity of money in circulation. The resulting excess supply of money while force the interest rate downwards in order to restore the balance between the demand for and the supply of money. c) An increase in real income raises the necessary transaction volume due to the assumption of fixed prices. Because for a higher transaction volume c.p. (i.e. ceteris paribus, which means under the assumption that all other exogenous variables remain constant) more money is needed, the demand for money expands and, since the supply of money is unchanged, the resulting excess demand pushes the interest rates upwards in order to restore the equilibrium in the money market. d) As we already saw in a) to c) the demand for money is reduced by an increase in the interest rate, while it is increased by an increase in output .These reactions carry over to both components of the money demand, currency as well as deposits, because both are just constant fractions of overall money demand. Reserves of banks are a constant fraction of deposits and thus react in the same
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manner. The demand for central bank money comprises both reserves and currency, so the demand for central bank money reacts in exactly the same manner. e) The money multiplier is the ratio of the economy’s supply of money to the monetary base supplied by the central bank. Its size is determined by the fraction of money held in the form of currency as well as the fraction of deposits held as reserves by private banks. Both fractions are negative arguments of the multiplier, which implies that any positive variation in these ratios results in a lower money
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Problem set 2 Key - Solution to Problem 1 a) In the usual...

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