Download Money Supply

Macro3 Manual
Purpose of the Module
This module expands on the material covered in the first two macro modules. This
module differs from those in three ways. First, it incorporates “net exports” in GDP and
the exchange rates that were ignored previously. Second, changes in prices and wages
matter for aggregate demand and supply. This means you get to see reactions to policy
changes in a more complex way, including how changes in prices and wages cause long
run adjustment toward “full employment” real GDP. This module also incorporates
supply and demand shocks, which can cause problems in addressing the ones in the initial
conditions. Finally, you will be able to see how long run adjustment of prices and wages
eventually lead to a full employment equilibrium, even without changes in policies.
Nature of the Problem
The basic macroeconomic problems of inflation and unemployment are no different in
this module than in previous ones. However, in this module you will see that what
effects your attempts to cope with those problems have on net exports and on the
exchange rate (the price of the dollar in terms of the Euro). Further, you will only be
able to control the nominal value of one of the policy tools, the money supply (just like
the actual Federal Reserve System). This will make controlling short run fluctuations of
unemployment and inflation more difficult.
The Model
This module is based on the Aggregate Supply-Aggregate Demand model. On the
demand side, the determination of demand is discussed in terms of the four sectors of the
economy, consumers, business, government, and net exports. In other words, if AD is
aggregate demand, C is consumer demand, I is (business) investment demand, G is
government demand for goods and services, and NX is (net) demand by foreigners:
AD = C + I + G + NX
To determine AD it is necessary to look at each of its components. Of course, in this
module G is whatever you decide it should be.
Consumption
Consumer demand is affected by after tax income (real GDP minus taxes) and by the real
rate of interest:
C = a1 + a2 * (GDP – T) + a3 * Rate
Where T is the total amount of taxes collected, Rate is the real rate of interest, a1, a2, and
a3 are parameters. The underlying theory requires that a1 be non-negative (> 0) and in
this module it is set at a1 = 10. Theory also requires that the response of consumption to
variations in after tax in income be positive, but less that one (1 > a2 > 0) and in this
module its value is set at 0.9 that is the “marginal propensity to consume”. In principle
the relationship between the real rate of interest and consumer spending could be either
positive or negative (or even zero), however decades of empirical research have led
economists to conclude that the relationship is in fact negative. In this module the value
of a3 is set at –25.
Investment
In reality many things affect investment behavior, but in this module the only influence is
the real rate of interest. Investment demand in this module is:
I = b1 + b2 * Rate
Certainly b1 must be positive, and in the module b1 is set at 870.
negatively related to the real rate of interest, and b2 is set at –75.
Investment is
Net Exports
The determination of net exports involves determination of both exports and imports. In
this module it is the price level that determines the level of export demand for this nations
products. What is being implicitly assumed is that an increase in the nation’s price level
implies a reduction in the ability of this country’s ability to compete in international
markets. [If the exchange rates between this country’s currency and the currencies of its
trading partners was strictly set according the model called “purchasing power parity”
(PPP) a rise in the price level would always be offset by an equal drop in the exchange
rate. However, in reality the PPP model does not fully explain the relationship between
price levels and exchange rates, so price level changes do affect exports.] In this module
imports are determined by the level of domestic GDP, the higher domestic income, the
more imported goods are bought. The ratio between the change in imports and the change
in income is often called the “marginal propensity to import.” With the domestic price
level called “p,” in the module net exports are:
NX = (c1 / p) – c2 * GDP
Since c1 represents nominal exports, so c1 must be a positive number. However, real
exports are c1 / p, so the higher the price level goes, the less this country will export. In
the module the value of c1 is set at 10. Since the second term represents the nation’s
imports, c2 is positive (higher GDP means more imports) and in the module the value of
c2 is set at 0.01, so the “marginal propensity to import” is one percent.
The Money Market
The foregoing relationships would allow you to construct an aggregate demand curve, but
one which depends only a little on the price level (just exports) and which does depend
on the real rate of interest -- with no way to determine what that real rate was. In a
previous module the real rate was set by the user as one of the policy tools. That is one
way of viewing monetary policy. In this module the monetary policy tool is control over
the nominal money supply (total number of dollars). However, the demand for money is
a demand for purchasing power, so to find where the demand for money equals the
supply of money, money supply has to be described in terms of purchasing power as
well. If M is the nominal money supply, set by the user, the real money supply is M / p.
The demand for money is affected by real income (GDP) and by the nominal rate of
interest (Nrate). In this module, equilibrium in the market for money is found when:
M /p = d1 + d2 * GDP + d3 * Nrate
Parameter d1 is assumed to be positive (people would hold some money even if income
and the nominal interest rate were zero) and in the module it is set at 15. As income rises
the demand for money would also rise, since having more income means people will
want to spend more (buy more) and that means -- somewhere along the line -- having
the money to pay for what they buy. The module assumes that the money market is
always in equilibrium, adjusting far more quickly than the markets for goods and services
or the market for labor and other resources.
[Warning: the demand for money is not a demand for income, economists generally
assume people want unlimited incomes, but can’t get them. This is the demand for
holding, at a moment in time, some of that income in the form of money -- cash, checking
account balances, etc.]
The relationship between income and the demand for money is described by d2, assumed
to be equal to 0.025. In other words, every time income rises by $10, people want to hold
another twenty-five cents in “money.” The relationship between the nominal rate of
interest and the demand for money is negative. Think of the nominal rate of interest as
the “opportunity cost” of holding money, instead of holding bonds or stocks or other
assets that pay returns to their owners (cash obviously doesn’t pay interest, and neither do
most checking accounts). The greater the opportunity cost of holding money (higher
interest rates) the less money people want to hold. In the module this involves parameter
d2, which is set at -0.95.
Combining information from the money market with the information from the demand
for goods and services, it is possible to describe aggregate demand as depending on the
parameters, on government spending and taxes (fiscal policy), on the money supply
(monetary policy), on the price level, and on expected inflation. Expected inflation gets
into the picture because the demand for money depends on the nominal interest rate, not
just the real interest rate.
Real and Nominal Interest Rates
The real interest rate is the increase in purchasing power you’d expect if you gave
someone a loan, or the real cost to you, in terms of purchasing power, of paying back a
loan if you borrowed from someone else. If you borrowed at 10% interest, so that for
every $100 you borrowed you have to pay back $110 at the end of the year, your real
interest rate depends on how much you expect prices to change over the year -- how
much would you be able to buy with that $110 if you didn’t have to pay off the loan. If
you expected prices to go up 10%, then the purchasing power of $110 at the end of the
year is the same as the purchasing power of the $100 you borrowed at the start of the year
-- and the real interest rate to you is 0, no cost at all. In other words the real rate is the
nominal interest rate minus the expected inflation rate (0 = 10% - 10% in the example):
Rate = Nominal Rate – Expected Inflation
This is actually only an approximation; useful when real interest rates and expected
inflation rates are relatively low. There is a more complex formula used when one or the
other or both of these are high, but that more complex formula is not used in this module.
Aggregate Supply
Output is supplied by firms whose interests are in profits. If the prices for the goods
firms sell rise compared to their costs, it will be profitable for firms to increase
production. If the costs of resources rises relative to the prices of goods firms would
have an incentive to reduce production. In this module the aggregate supply of goods and
services is:
AS = e1 – e2 * (wages / p)
Wages are used in this relationship to describe the level of all resource costs (not a bad
thing, since about 70% of all costs are labor costs in the US). As the price level rises
toward infinity (relative to wages), the amount of goods supplied rises toward e1, which is
2500 in this module. If GDP is above the “full employment level” the value of e2 is set at
150.012, so if the wage and the price levels are equal to each other aggregate GDP
supplied is e1 – e2, which is the “full employment long run equilibrium” in this module.
If GDP is below the full employment level e1 and e2 have different values, so that the
slope of the aggregate supply curve is much flatter for low output levels than for high
output levels.
The Tools
Government Spending
Government spending is set in real terms so the amount of goods the government gets
does not depend on what happens to the price level. Since in this module the real rate of
interest is not constant when you change government spending (holding taxes and the
money supply constant), do not expect to see the full Keynesian multiplier effect of the
spending change. There will be “crowding out” effects on investment and consumer
spending.
Taxes
Taxes are also set in real terms, a change in the price level has no effect on the amount of
purchasing power households and firms have to turn over to the government. Again, do
not expect to see the full multiplier effects since real interest rates are not constant when
you change taxes (holding government spending and the money supply constant).
Money Supply
You control the total nominal money supply, the number of dollars in the hands of the
public. (This module takes no notice of the distinctions among the various types of
money -- currency, checking account funds, etc.) You do not control the real money
supply, which is the nominal money supply divided by the price level, because you do
not control the price level. Your policy decisions do influence the price level, as they
influence all the rest of the economy, but that isn’t the same as being able to simply set
the price level. This distinction is one that faces monetary authorities in the real world as
well, and limits their power.
Aggregate Supply and Demand Graph
The analysis of the model used can be done using a simple graph. Information about
monetary and fiscal policy, and the behavior of consumers, investors, and international
markets is summarized in the aggregate demand curve in Figure 1. The behavior of firms
that produce output is summarized in the aggregate supply curve in that diagram.
Figure 1 Aggregate Supply and Demand (short run)
P
AS
P1
P0
AD1
AD0
GDP0
GDP1
GDPFE
GDP
In Figure 1, AD0 represents original aggregate demand (in a recession), while AD1
represents the impact of expansionary monetary and/or fiscal policy, or the impact of a
non-policy expansionary shock. Both combinations (P0 and GDP0) and (P1 and GDP1)
represent short run equilibrium positions. Any long run equilibrium would have to occur
at the level of GDP labeled GDPFE, the full employment level of real output.
Starting with either AD0 or AD1, in the long run adjustments of the real wage to its long
run equilibrium level will induce shifts in the supply curve so that equilibrium will be
reached at GDPFE, the only difference, in terms of this graph, will be the price level at
long run equilibrium. The process of adjustment in the long run involves the way wages
eventually catch up with prices. If demand increases, in the demand for goods and
services prices rise relative to costs (wages) in the short run, which is why output
increases. However, this increases demand for labor and, while the labor market adjusts
more slowly than the market for goods and services, after awhile the increased demand
for labor means that wages rise (for a given current price level). As a result the profit
maximizing output for firms at the given price level decreases -- a shift to the left in the
short run AS. This is illustrated in Figure 2.
Figure 2 Long Run Equilibrium
P
AS1
P1
AS0
P0
AD1
AD0
GDPFE
In Figure 2, AS0 is the aggregate supply curve that will result if for some reason
aggregate demand is at AD0, while AS1 is the short run supply curve after the full
adjustment to a shift in aggregate demand to AD1. With high aggregate demand (AD1),
in the long run the economy winds up with a high price level P 1 (and high money wages)
but with real output at GDPFE. With “low” aggregate demand (AD0) the economy winds
up in the long run with a low price level P0 (and low money wages) -- and the same real
GDP, GDPFE.
If a disturbance caused a shift in aggregate supply the adjustment process still leads to a
long run equilibrium at GDPFE, as long as the disturbance did not change the economy’s
capacity to produce. Only a change in capacity causes the value of GDPFE to change, and
changes the long run equilibrium in this model. The kinds of disturbances and policies
used in this module cannot affect capacity, and cannot affect GDPFE.
Running the Module
When you begin the module you have to choose whether your economy will start off in
an inflationary period or in a recession. Whichever way you start off, you will be shown
the initial conditions the levels of real GDP, inflation, unemployment, etc. When you
begin to control your society you can leave the values of the three tools at their initial
default values and see the results, but if you do, all you will see is the initial conditions
already presented. Alternatively, you can change one or more of the three tools
(government spending, taxes, and the money supply) to try to fix the existing problem.
Since at first you will not know how much effect each tool will have on each of the
various aspects of the economy, it is best if you change only one tool at a time. For
example, if the economy is in an inflation you could note the initial conditions, then cut
government spending from its default level and see the results. (At this point you need to
click on “No Shock” on the tool bar to get results if the economy has NOT experiences
either a demand shock or a supply shock.) When you get the short run results the
options on the tool bar will have changed and if you wish you can click on “No Shock
Long Run” to see the long run effects of your policies. Then try “new policy” – which
resets everything – and leave government spending at its default value while increasing
taxes.
Finally, try “new policy” again and, leaving government spending and taxes at their
default values, reduce the money supply. To see what the long run equilibrium is like,
click on “long run” and you will get the values the economy will eventually arrive at
without your help. Then you can try to get it to similar values without waiting for the
long run to arrive (the long run does assume the default values for government spending
and taxes, so if you change those you can’t get exactly the same results for all aspects of
the economy).
Once you have explored these aspects of the module, you can see what happens to your
initial conditions when the economy is further disturbed by a “shock.” A shock is an
unpredicted disturbance that shifts either AD or AS and in this module you can choose to
either cause a shock to demand or to supply. (Click on “Demand Shock” or “Supply
Shock.”) In the real world there are many possible sources of shocks to both sides of the
market, in this module there is one type of shock to each. On the demand side, the shock
is a sudden change in the expected rate of inflation. In the basic model people expect an
inflation rate of 0.01% (in other words, virtually no inflation. If you pick the demand
shock, there will be a significant change in that expectation and you can see what effect
that has by clicking on “results.” After you see the immediate effects of the shock you
may want to click on the new option “Demand Shock Long Run” to see the eventual
effects of the shock and of your policies.
On the supply side the shock changes the parameter e2 (an example of this type of shock
would be a change in the tax code so that employers no longer pay a Social Security tax - though other taxes have to be raised so total tax collections don’t change). Again, to see
the impact of this type of shift in the short term, click on “results.” To see the long run
effects, click on “long run.”
Mathematical Model
Short Run
Most of the underlying equations for this module were shown in the “model” section,
with explanations of the parameters and their meanings. Those equations will just be
repeated here, beginning with the ones related to aggregate demand:
1)
AD = GDP = C + I + G + NX
2)
C = a1 + a2 * (GDP – T) + a3 * Rate
3)
I = b1 + b2 * Rate
4)
NX = (c1 / p) + c2 * GDP
Combining equations (1) through (4), and solving for GDP:
Let:
5)
AA1 = {[(a1 + b1 + (c1/p)] / [1 – a2 – c2]}
AA2 = {[a3 + b2] / [1 – a2 + c2]}
AA3 = {1 / [1 - a2 + c2]}
GDP = AA1 + AA2 * Rate + AA3 * [G – a2 * T]
Since (5) depends on the real interest rate we need to combine it with the money
market information in (6):
6)
M / p = d1 + d2* GDP + d3 * Nrate
Since the nominal rate is the real rate plus expected inflation, (6) can be re-written
(EDP is the expected rate of inflation) as:
a)
M / p = d1 + d2 * GDP + d3 * [Rate + EDP]
Combining (5) and (6a) and solving for the real interest rate:
7)
Rate = aa1 + (aa2 * M / p) + (aa3 * EDP) + (aa4 * (G - (a2 * T))) + (aa5 / p)
Where:
den = (((b2 + a3) / (1 - a2 + c2)) + (d3 / d2))
aa1 = - ((d1 / d2) + ((a1 + b1 + cc1/p) / (1 - a2 + c2))) / den
aa2 = (1 / d2) / den
aa3 = - (d3 / d2) / den
aa4 = (-1 / (1 - a2 + c2)) / den
aa5 = c1 * aa4
Equation (7) does not depend on anything except the parameters of the original
equations, the policy tools you enter, and the price level. Taking the solution for
Rate in (7) and using it to substitute for Rate in (5), then simplifying:
8)
GDP = bb1 + bb2 * M/p + bb3 * EDP + bb4 * (G – a2* T) + bb5 * (1/p)
Where:
bb1 = - ((d1 / d2) + ((d3 / d2) * aa1))
bb2 = (1 / d2) * ((b2 + a3) / (1 - a2 + c2)) / den
bb3 = - (d3 / d2) * ((b2 + a3) / (1 - a2 + c2)) / den
bb4 = (d3 / d2) * (1 / (1 - a2 + c2)) / den
bb5 = - (d3 / d2) * aa5
Equation (8) has GDP (demanded) depending on parameters, the expected
inflation rate, the policy tools you control, and the price level. The aggregate
supply equation in this module is:
9)
AS = GDP = e1 - e2 * (wage / p)
In (9) e1 (at or above full employment) is 2500, e2 is 150.012, so if the real wage
(wage/p) is 1, GDP supplied is about 2350. In this module that is full
employment output. (Having p = 1 and wage = 1 means you are at the original
equilibrium, wage and price values are measured relative to the original
equilibrium values—these are wage and price indices not dollar values.) Note
that because of the minus sign in front of e2, the higher the price level compared
to the wage rate, the higher the level of GDP supplied. As the real wage falls
toward zero, output rises toward 2500 that is its maximum value (not its
equilibrium value—long or short run).
The AS equation has GDP (supplied) depending on the parameters, the wage rate,
and the price level. In equilibrium AS must equal AD, so if we equate GDP from
(8) with GDP from (9) we can solve for the (short term) equilibrium price level as
a function of the parameters, the current wage rate, expected inflation, and the
policy tools:
10)
p = [bb2 * M – e2 * wage + bb5] / [(e1 – bb1) – (bb3 * EDP) – (bb4 * (G – a2 *
T)]
In the short run the price level is determined by (10) because the wage rate stays
constant in the short run. Substituting (10) for the price level in (9) gives a
solution for (short run) equilibrium GDP:
11)
GDP = e1 + (e2 * wage) / [bb2 * M – e2 * wage + bb5] / [(e1–bb1) – (bb3 *
EDP) – (bb4 * (G – a2 * T)]
Since (11), (10), and (7) in combination determine everything that goes into the
consumption, investment, and net export values, the components of GDP can be
obtained by using these equilibrium values and substituting into (2), (3) and (4)
respectively.
All that is left for the short run is to determine the unemployment, inflation and
exchange rates. The inflation rate is quite simple to obtain. The price level starts
at 1, of course, the new price level is obtained from (10) and the inflation rate is:
12)
Inflation = (p0 – p1) / p0
Where p0 is the original price level (1) and p1 is the price level obtained in (10).
The unemployment rate is determined by an equation adapted from Okun’s law,
so in this module the unemployment rate is:
13)
Unemployment = 0.05 - (0.001 * (GDP - 2350.37))
If GDP is at its long run equilibrium value (full employment), then the
unemployment rate is at 0.05, or 5%.
The exchange rate is determined by supply and demand for the nations currency.
In other words this is a perfectly flexible exchange rate system, with no direct
government intervention in the exchange market. In this module part of the
market is derived from the balance of trade (Net exports) that depends on the
domestic price level and on domestic GDP. [Purely foreign influences, such as
foreign GDP, are held constant.] The exchange market also depends on
international capital flows, so (other things constant) it depends on the level of
domestic interest rates compared to foreign rates. Strictly, the exchange rate
would depend on the differences between domestic and foreign interest rates and
on the comparison between domestic and foreign price levels. However, only the
domestic values are variable in this module.
14)
Exchange = (0.9 + (0.02 * (Rate - 4.237))) / p
If the domestic interest rate equals the foreign rate (4.237%) and the price level is
at its original value of 1, the exchange rate is 0.9 Euros equals $1.
Long Run
The difference between the long and short run in this model is that in the long run the
wage rate changes if the economy is not at the long run equilibrium. Over time the wage
will adjust in response to price level changes, and if productivity conditions meant that
there was a long run equilibrium with the wage price ratio equal to 1, the new wage price
ratio will return to 1 in the long run. If the price level rose in the short run, encouraging
output supplied at the original wage to rise, in the long run the wage rises by an equal
proportion, returning the ratio to 1. That means long run output is determined by the
supply equation (9). Meanwhile the price level can be determined from (10) with the
added information that the wage level is equal to the price level. The revised long run
price equation is:
15)
p = [bb2 * M + bb5] / [e2 + (e1 – bb1) – (bb3 * EDP) – (bb4 * (G – a2 * T)]
Given the statement about the equality of the wage and price levels in the long run
equilibrium, (15) also determined the wage rate. The real rate of interest (Rate) can be
determined from (7), then the components of GDP can be resolved from their original
equations (2), (3), and (4).
The long run equilibrium in this module is similar to the one predicted by the quantity
equation: p* real GDP = v * M where v is the velocity of money. In the long run real
GDP is at its equilibrium full employment value, if the velocity of money is back to its
original equilibrium value, the price level changes by the same proportion as any change
in the money supply. Indeed, for any given change in the money supply, with
government spending and taxes constant, there is an equi-proportional change in the price
level and the money supply. However, since the demand for money depends on interest
rates, and government spending and taxes can affect interest rates even in the long run,
changes in fiscal variables can affect the price level in the long run. The long run value
of real GDP cannot be affected by these variables because they do not affect aggregate
supply, in the long run the changes in prices are offset by the changes in money wages, so
long run output cannot depend on these aspects of demand.