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ECON1110LectureNotes6.docECON 1110 Lecture Notes 6
ECON 1110 Intermediate Macroeconomics
James R. Maloy
Spring 2020
Lecture Notes for Topic 6: Keynesian Macroeconomics (II)
Readings: Froyen Ch. 6 (8th Ed. Ch. 7)
I. Interest Rates and Aggregate Demand
Recall that in the Classical system interest rates were determined by the interaction of the supply of and demand for loanable funds. Interest rates were seen to be the mechanism that ensures the stability of aggregate demand. The Classical economists theorised that a change in one component of aggregate demand would generate a change in the interest rate, and that the change in the interest rate would generate a change in other components of aggregate demand that would cancel out the initial change, thus keeping aggregate demand at the original level. Money, since it did not bear interest, was not a factor in determining interest rates, nor did money affect the real level of income or output (neutrality of money).
Keynes had a different way of looking at the situation. He argued that changes in the interest rate would indeed cause a change in aggregate demand, since the classical theory ignored factors such as a direct link between consumption and the interest rate. He also derived the interest rate not as a function of demand and supply of bonds, but rather demand and supply of money. This is Keynes’ attack on the classical system—changes in money yield changes in the interest rate, which in turns yield changes in aggregate demand. Recalling that in the Keynesian system output and income was demand-determined, we see that changes in the demand and supply of money will generate changes in income.
We have already discussed how aggregate demand affects income in the last chapter. We now must see how interest rates affect aggregate demand, and how money affects the interest rate, to have a full picture of the Keynesian model.
Keynes, like the classical economists, saw a negative relationship between investment and the interest rate. However, he also saw that a decrease in the interest rate could have a positive impact on consumption as well. Many consumer durable goods, such as cars, are purchased on credit. A decrease in interest rates will reduce financing costs and will boost consumption. Likewise, the lower mortgage costs will boost demand for homes, which will increase new housing starts, a component of investment. Keynesians also argue that lower interest rates might boost government expenditures that require financing, especially for local governments with lower funds. Therefore, the forces causing increases in aggregate demand from a decline in the interest rate outweigh the forces causing decreases in aggregate demand—and thus self-correction does not occur.
I. The Keynesian Theory of the Interest Rate
To develop the Keynesian interest rate, some assumptions will be used. First, assume that all financial assets are classified as either money or bonds. Money consists of currency and demand deposit accounts. Money is assumed to not bear interest (if we adjust the model to allow interest on money accounts, we get a similar result as money earns less interest than other assets). Bonds are homogenous perpetuities, which pay a fixed amount at fixed intervals with no repayment on the principle.
Keynes hypothesised that wealth (Wh) could be divided into holdings of bonds (B) and money (M).
Wh = B + M
The equilibrium interest rate is the rate where the demand and supply of bonds are equal. This implies that the bond market is in equilibrium—since the person is satisfied with how much he is holding in bonds at the current rate of interest, there is no excess supply of or demand for bonds. However, if a person is satisfied with the percentage of wealth held as bonds, he must also be satisfied with the percentage held as money. Using the same logic, it is evident that money supply and demand are at equilibrium too. If the person is happy with their bond-money combination, so there can be no excess demand or supply of money. This can be proven by contradiction: suppose that the bond market is in equilibrium but there is excess demand for money. This means people want to hold more money than they currently hold, which means that they want to sell bonds, so there is excess supply of bonds at the current interest rate—which implies that the bond market could not be in equilibrium! When one market is in equilibrium, so is the other. Keynes wanted to emphasise the role of money in the system, so he uses the money market rather than the bond market for determining interest rates.
II. The Keynesian Theory of Money Demand
Since bonds bear interest and money does not, there is obviously an opportunity cost of holding money. So why would someone want to hold any money at all when interest-bearing bonds are available? What factors determine how much of the non-interest bearing asset, money, a person chooses to hold?
Keynes listed three motives for money demand: transactions, precautionary, and speculative demand for money. The transactions motive is essentially the same as in the classical model. Money is a liquid asset and can be easily converted into other goods. Changing back and forth from bonds to money has associated transaction costs, and it makes little sense to incur them for short-run interest gains if the wealth is going to be spent soon anyway. Like the classical economists, Keynes expected the transactions demand for money to increase as income increases.
Keynes’ second motive, precautionary demand, is similar to transactions motive. Keynes felt people would keep some wealth as money in case of unexpected events, such as unemployment or injury. Again, Keynes expected precautionary demand to be directly related to income. One can think of precautionary demand as simply the demand for unexpected transactions.
The third motive, speculative, is more original. Bonds command a price on the open market, and it is a fact of finance that the price of bonds is inversely related to the interest rate (this relationship can be proven rather easily but it is not particularly relevant to the course so it will not be taken up further). Therefore, when interest rates increase, the value of the bond declines, which is a capital loss for the bondholder (and vice versa). Keynes theorised that people formed some judgment as to what was the “normal” rate of interest. If interest rates are above this level, they are expected to fall and the value of the bonds is expected to increase, thus generating both interest and a capital gain for the bondholder. If interest rates are below this level, they are expected to rise, generating a capital loss. Since the net return on a bond is the interest payment plus the capital gain or loss, there is some critical value below the normal rate of interest such that for any point below the critical value, the capital loss outweighs the interest gain and the net return on the bond is negative. Above the normal rate, the expected return is positive since there is a capital gain as well as the interest payment. Between the normal and critical value, the interest payment outweighs the expected capital loss, and the net return is positive. Therefore, speculative demand for money is zero above the critical value, since there is a positive return from bondholding. (Money, remember, bears no interest.) The only money that will be held will be for transactions or precautionary purposes. Below the critical value, people will hold only money and no bonds, since the expected return on bonds is negative.
The aggregate speculative demand for money is the compilation of the individual curves. It is downward sloping since at low interest rates people expect rates to start increasing and will hold more money to prevent a capital loss. The curve is smooth since each person has their own idea of a “normal” interest rate.
Total Money Demand in the Keynesian System
Therefore, we have three motives for money demand. Keynes’ first two (transactions and precautionary) give money demand as a function of income, while speculative demand is assumed to be a function of the interest rate and income. These concepts were later revised by other economists. William Baumol demonstrated that transactions demand is also inversely related to the interest rate, while James Tobin improved Keynes’ speculative demand theory.
Using all of these ideas, we can now express the Keynesian demand for money as
Md = L (Y, r)
Money demand for transactions is positively related to income and negatively related to interest rates. The money demand curve, when plotted against the interest rate, is a downward sloping function.
A typical linear version of this function is:
Md = c0 + c1Y – c2r c1 > 0, c2 > 0
The parameter c1 is the sensitivity of money demand to changes in income, and c2 is the sensitivity of money demand to changes in the interest rate.
Money Supply and Equilibrium: The Liquidity Preference Model
Again, we are assuming that the money supply is fixed by the central bank and is independent of the interest rate; i.e. a vertical line at the fixed money supply (this assumption is actually not correct, and is the topic of a later lecture on the money supply process). Equilibrium in the money market and the equilibrium interest rate are determined by the intersection of money demand and supply. Note that income (Y) is held constant when deriving the demand curve; an increase (decrease) in Y will lead to an increase (decrease) in money demand; the curve will shift right (left) and interest rates will increase (decrease). Interest rates are thus procyclical: they move with the business cycle. Note also that monetary policy (changes in the money supply) will shift the curve; a monetary expansion leads to lower interest rates while a monetary contraction leads to higher rates.
However, what is the relationship between the money market and the goods market (for output)? How do changes in the money market affect the goods market, and vice versa? The IS/LM model shows these ideas by combining the simple Keynesian model with the Keynesian liquidity preference model. Note: The IS/LM model is a demand-side model; both the simple Keynesian model and liquidity preference model are AD-side concepts. The IS/LM model thus assumes that firms automatically supply whatever level of output is demanded at a fixed price (essentially, a horizontal AS curve whereby AD determines Y*). This will be discussed in more detail in a later topic.
III. Money Market Equilibrium: The LM Curve
We have said that money demand is a function of the interest rate and income:
Md = L(Y, r)
or in linear form:
Md = c0 + c1Y – c2r c1 > 0, c2 > 0
The signs indicate that money demand increases as income increases (due to the transactions/precautionary motives) and is negatively related to the interest rate. We have seen that the money demand schedule is downward sloping when plotted against the interest rate. A change in income causes a shift in the money demand schedule (not the money demand function). Why? As income increases, you are demanding more money for transactions at any given interest rate. An increase in the quantity of money demanded for a fixed money supply will naturally cause a rise in the equilibrium interest rate (think of the interest rate as the price of money). Therefore, we note that there is a positive relationship between interest rates and income. This positive relationship is called the LM curve. The LM curve shows all combinations of the interest rate and income that generate equilibrium in the money market, i.e. money supply equals money demand.
The LM curve can be derived graphically by calculating the interest rate for different levels of income (and thus money demand) and plotting this relationship.
The LM curve can also be derived algebraically. The LM curve shows money market equilibrium where money supply and demand are equal. This can be calculated by setting money demand and supply equal and solving for r (alternatively, you can solve for Y but solving for the interest rate is the more common method).
Ms = Md = c0 + c1Y – c2r
r = c0/ c2 – Ms/ c2 + (c1/c2)Y
IV. The Slope of the LM Curve
The slope of the LM curve can be calculated by calculating the change in interest rates from a change in income. This partial derivative is:
∂r/∂Y = c1/c2
Therefore, two things influence the slope of the LM curve. c1 measures the increase in money demand from an increase in income. The higher the value of c1, the steeper the curve. c2 measures the interest elasticity of money demand. The higher the interest elasticity of money demand, the flatter the money demand curve. There is little disagreement about the value of c1 but there is considerable argument about the value of c2.
V. Factors That Shift the LM Schedule
There are two factors that cause a shift in the LM curve. The first is a change in money supply. An increase in money supply will shift the LM curve to the right. The second is a change in the money demand function itself, i.e. a change in the c0 parameter. Basically, this change in anything that affects money demand other than changes in income or interest rates. A shift in the variables of money demand—income and interest rates—does not shift in the LM curve—it causes a movement along the curve, but a change in anything else that affects money demand does shift the LM curve. (Remember your rules of graphing—r and Y are endogenous changes.) An increase in money demand for a given interest rate and income will shift the LM curve to the left, and vice versa.
VI. Product Market Equilibrium: The IS Curve
We have stated two equivalent ways to describe product market equilibrium:
Y = C + I + G
or
I + G = S + T
The IS curve can be derived from either of these equations. The second one will be used to derive the IS curve graphically.
First, ignore the government sector, i.e. G and T are zero. Now that we have developed the Keynesian interest rate, we can express investment as a function of the interest rate. Again, this is a negative relationship. Again, saving is a positive function of income.
Now add the government sector. The government is assumed to not be concerned about the interest it has to pay for its borrowing. Therefore, adding government spending to the investment function and taxes to the saving function will be a parallel shift of these functions. Adding government spending will shift the investment function to the right, and the saving function will shift to the left since taxes will decrease the level of disposable income and thus savings. Combining these two functions will give us the IS curve. The IS curve shows all possible combinations of output and the interest rate that generate equilibrium in the product market. It shows an inverse relationship between interest rates and output.
The IS curve can also be derived algebraically, using either of the two conditions for equilibrium. From the first condition,
I + G = S + T
we can express investment as a linear function of the interest rate
r
i
I
I
1
-
=
0
1
>
i
The savings function is again:
)
)(
1
(
T
Y
b
a
s
-
-
+
-
=
Taking government spending and taxes as exogenous, we have
T
T
Y
b
a
G
r
i
I
+
-
-
+
=
+
-
)
)(
1
(
1
Rearranging and solving for Y yields an expression for the IS curve: (Usually, the LM curve is solved for r. The IS curve is solved for Y.)
[
]
b
r
i
bT
G
I
a
b
Y
-
-
-
+
+
-
=
1
1
1
1
We can also find the IS curve by using Y = C + I + G. Substituting our equations for investment and consumption and solving for Y gives an identical expression for equilibrium.
Factors That Determine the Slope of the IS Curve
As for the LM curve, the slope of the IS schedule is calculated by taking the partial derivative of the IS curve equation, ∂r/∂Y. This yields:
∂r/∂Y = - (1-b)/i1
This slope is negative, as previously mentioned. Two factors influence the slope of the IS curve. 1 – b is the marginal propensity to save (MPS), which is the slope of the savings function. The IS curve is steeper the higher the MPS. We will not consider saving in more detail until next term.
The second factor that influences the slope of the IS curve is i1, the slope of the investment function and more commonly called the interest elasticity of investment. The higher the interest elasticity of investment, the flatter the investment function. In this case, there are large changes in investment with small changes in interest rates, and since investment is a component of income, small changes in interest rates therefore yield large changes in income; thus the flatter the IS curve. Conversely, low interest elasticity of investment will yield a steep IS curve.
VII. Factors That Shift the IS Curve
The factors that shift the IS curve are the same factors that cause a shift in the simple Keynesian model from the last chapter. Changes in government spending, taxes, and autonomous investment and consumption will shift the position of the IS curve. The magnitude of this change can again be calculated by using the multiplier, which are again calculated by taking partial derivatives. These multipliers are unchanged from the last section—the multiplier is 1/(1 – b) for changes in G, I, and a; and –b/(1 – b) for changes in T.
We can graphically show the effects of changes in government spending, investment, consumption, and taxes. An increase in autonomous investment or government spending will shift the IS curve to the right.
An increase in autonomous consumption will shift the savings function and thus the IS curve will shift right. An increase in taxes, again, reduces aggregate demand and the IS curve will shift left. Decreases in any of these factors will yield opposite effects. Note that if the interest rate is unchanged, output will change by the full amount of multiplier, as in the simple Keynesian model. If the interest rate changes at all, output will not increase by the full amount.
VIII. The IS and LM Curves Combined
The point of intersection between the IS and LM curves gives the interest rate and output level at which the money market and product market are simultaneously in equilibrium.
Again, the equilibrium values of the interest rate and income can be calculated algebraically. Since in equilibrium Y and r must be the same in both the IS and LM curves, substituting the LM curve into the equation for the IS curve and solving for Y gives equilibrium income:
Substituting this value of Y into the equation of either the IS or LM curve and solving for r yields:
The point of the IS/LM model is to improve the simple Keynesian model by acknowledging the fact that money and interest will affect output levels and vice versa—the goods market and money market are interrelated. For example, suppose that there is an increase in autonomous investment, which shifts the IS curve to the right. The new equilibrium occurs at higher interest rates and higher output levels. We know what causes the higher output—higher investment means higher AD which means higher output, as in the Keynesian cross diagram. However, more output (income) leads to more money demanded for transactions and as a store of wealth—the money demand curve shifts upward and to the right, hence higher interest rates. IS/LM shows both of these effects on a single diagram. A similar thing occurs due to LM shifts. An increase in the money supply lowers interest rates; lower interest rates boost I, and thus AD and output, Y, as shown by IS/LM.
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