Chapter 9: The Demand for Money and the LM CurveInstructor’s Manual
Chapter 9: The Demand for Money and the LM Curve
Problem 1
As real balances rise, the marginal utility of money falls. As a result, interest rates must fall in order to encourage the holding of larger levels of real balances, which generates a downward sloping money demand curve.
Problem 2
YMAX is the maximum possible income of a household if it chooses to hold all of its wealth in interest-bearing corporate bonds:
,
where W/P is the household’s real wealth, w/P is the real wage rate, and L is the amount of labor supplied during a typical week.
The price of a bond, PB, enters the variable YMAX through wealth, W, since
W = M + PBB.
Therefore, an increase in the price of bonds will increase the household's wealth, everything else remaining the same, and hence increase YMAX. The household's wealth increases because an increase in price of bonds increases the value of corporate bonds that the household already owns. Therefore, the bond price increase will shift the budget line to the right, in a parallel fashion.
Problem 3
The velocity of circulation is the number of times a year that the average dollar bill circulates in the economy and is measured in fractions of 1/years. The propensity to hold money is the fraction of a year’s nominal income held as money and is measured in fractions of a year. For example, if k=1/5 of a year's income, then v=5, which means that the average bill changes 5 times a year.
Problem 4
See Box 9.2 in the text. In the data there is a close positive relationship between the nominal interest rate and velocity, just like the utility theory of money demand predicts. This compares favorably to the predictions of the quantity theory, which assumed that velocity was constant and that there should be no relationship between interest rates and velocity.
Problem 5
In the utility theory of money demand, it is the nominal interest rate that determines the level of money demand. The nominal interest rate is the opportunity cost of holding real balances because the nominal interest rate incorporates not just the lost real return of holding money as opposed to holding bonds but also incorporates inflation that decreases the real value of money holdings.
Problem 6
In the classical model, the real interest rate is determined in the capital market, where saving supply and investment demand determine the equilibrium real interest rate. In the new-Keynesian model, it is the nominal interest rate that is matters. The nominal interest rate is the opportunity cost, or price, of holding money and is determined by equating money supply with money demand.
Problem 7
In response to an increase in the money supply, nominal interest rates in the money market will fall. This is consistent with the real world behavior of interest rates in response to Federal Reserve policy, which will be discussed more fully in Chapter 10.
Problem 8
In the classical model, changes in the money supply have no real effects because of money neutrality. Changes in the money supply only lead to changes in the price level. As a result of an increase in the money supply, the real interest rate remains unchanged but the nominal interest rate should increase as inflation increases. This is not consistent with what happens in the real world, where increases in the money supply lead to decreases in nominal interest rates. This is a big problem with the classical model’s explanation of interest rates.
Problem 9
Usually money demand increases during the Christmas season because of the large increase in purchases. This increase in money demand will put upward pressure on nominal interest rates. To offset this, the monetary authority should increase the money supply to keep interest rates at their current level.
Problem 10
The LM curve is upward sloping because an increase in output increases money demand, which in turn increases the equilibrium interest rate. See Figure 9.4 in the text.
Problem 11
According to the classical model, money neutrality holds and there is no relationship between the level of nominal variables and the level of real variables. As a result, the nominal interest rate has no effect on real output and the LM curve is a vertical line. In the utility theory of money demand, nominal interest rates do have an effect on the real demand for money balances and as a result money neutrality does not hold and the LM curve is upward sloping.
Problem 12
A decrease in the price level increases the real supply of money. This increase in the real money supply reduces nominal interest rates. The LM curve shifts to the right towards lower nominal interest rates for a given level of output. See Figure 9.5 in the text.
Problem 13
A proportional increase in both the price level and the money supply leaves the real money supply unchanged. As a result, there is no change in the money market, no change in nominal interest rates, and no change in the LM curve.
Problem 14
Setting Md/P = MS/P, the LM curve is Y = 500 + 200i. Notice that there is a positive relationship between interest rates and output in the money market.
Problem 15
To derive the LM curve, first let us find the demand for money. Instead of obtaining the first-order conditions from the utility maximization exercise, we will make things simpler by setting the slope of the indifference curve (the MRS between M/P and Y) equal to the slope of the budget line.
Having obtained the money demand function above, set money demand equal to money supply, and fix the price: . Simplify the equation by expressing i as a function of Y, the (constant) money supply and the (constant) price level:
This is the equation of the LM curve. Note that it slopes upward, as it should.
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