Download Figure 1 Aggregate Supply and Demand

Macro2 Manual
Purpose of Program
This module is designed to allow you to get experience with the way the national
economy fluctuates on its own, and the ways it responds to government decisions. You
control all the major tools the government uses to control the economy. You face some
of the difficulties the government has in figuring out what to do with those tools, and you,
like a government, have to decide what you are trying to accomplish.
Unlike the Macro1 module, this one allows you to control three policy tools at the same
time, as real policy makers can. This makes it possible for you to confuse yourself more
easily than in Macro1, since by changing all three tools at the same time you can make it
very hard to figure out what any one of them does. Of course, unlike real policy makers,
you can try out each tool individually without changing the others to avoid this
confusion. Also unlike Macro1, in this module you control the real money supply, rather
than the real rate of interest (real policy makers can choose which of these they prefer to
work on).
Finally, in this module you can stage a “running fight” (over eight years) against the evils
of inflation and unemployment. In other words, each year you can institute new policies,
but the results you get in one year depend on what happened the previous two years
because the previous two years inflation affect the expected rate of inflation in the current
year. This dependence of the current economy on past events adds another note of
realism to the module. It may also add to your understanding of the problems that real
policy makers face over a period of years, as they try to get the macroeconomy where
they want it to be.
The Nature of the Problem
In this module, as in Macro1, you face the problems of inflation and unemployment.
However, in Macro1 there was a fixed tradeoff between the inflation and unemployment
rates, a “Phillips curve.” In this module the inflation rate you get does depend on the
unemployment rate (or equivalently, on the level of real GDP) but it also depends on the
past history of inflation in the economy. As a result, a particular unemployment rate may
appear in a given year with virtually any inflation rate. A further consequence of this is
that the initial (1st year) effect of a policy change on all of the macroeconomic variables is
not the same as its impact in year 2, or year 3, and so on. This makes the problem of
hitting a target (an inflation rate, an unemployment rate, or some combination of the two)
is far harder—and even if you hit it in one year, that does not mean the same policies will
let you hit that target again in the following year.
The problem in this module is learning to control an economy that is far more dynamic
than the one in Macro1, one in which behavior changes even when you have done
nothing to change it. That should make it more interesting, more realistic, and more
difficult to work with.
1
The Model
The overall measure of the level of economic activity in the country is real GDP. Real
GDP is the measure of total production and how much is received by all sectors of the
economy combined. The sectors that get the product are: (1) Households
-Consumption Spending, (2) Business -- Investment Spending (3) Government -Government Spending. Other measures of interest to people are: the unemployment rate,
inflation rate, nominal interest rates, and real interest rates.
Unemployment Rate
This is the number of people unemployed (no jobs, looking for work) divided by the
number of people in the labor force (the unemployed plus those working). Example:
There are 100 people with no jobs, who are actively trying to get jobs, and 900 people
working, so the unemployment rate is 100 / (100 + 900) = 0.10, or 10%. The
unemployment rate indicates the amount of unused resources, and measures (crudely) the
cost to society of having fewer goods and services than it could have had.
Inflation Rate
This is the rate of increase in the price level. Example: The price index at the beginning
of the year is 120 (prices are higher than in the “base year” when the price index was
100). If the price level at the end of the year is 140, the change in the level is 140 - 120 =
20. The rate of inflation is the change in the price level (20) divided by the beginning
price level (120), so the rate of inflation is .167, or almost 17%. The higher the inflation
rate, the more adjustment costs society has, and the more redistribution of income there
may be. (Whether income is redistributed depends partly on whether the inflation was
expected.)
Consumption
This is the amount of (real) spending by households on goods and services. It increases
as real GDP rises, but falls as the real rate of interest rises. (See below for an explanation
of the real rate of interest.) In the real world other variables may affect consumption, for
example: expected future income (and therefore “consumer confidence”), the current
value of the nation’s marketable wealth (i.e. the stock market), and the distribution of
income.
Investment
This is the (real) amount spent by businesses on goods and services that they do not resell to households, government, or foreign buyers by the end of the year. It includes
buildings, machinery, etc. that firms will use for a long time. It also includes stockpiles
of raw materials, semi-finished goods, and finished goods not sold by the end of the year,
inventory. Investment goes down if the real rate of interest goes up. (In reality
2
investment may also go up as real GDP goes up.) Investment in this context does not
include buying stocks, bonds, or other pieces of paper (i.e. financial assets).
The value used in the module is Gross investment which means we are not subtracting off
any depreciation (allowance for wear and tear on existing capital). That means that the
value of investment cannot be negative in the module.
Nominal Interest Rate
A measure of the nominal interest rate is the amount of interest paid on an asset (i.e. a
bond or a bank) account divided by the current value of that asset. Example: A bond is
currently worth $1,000, and its owner gets $15 per year for owning it. The nominal rate
of interest on this bond is 15%. [If an asset has no finite expiration date this is the
general measure of the return on that asset. For assets with expiration dates, there are
other return measures, such as the “return to maturity.] “The” nominal rate of interest is
an overall measure, or index, of interest rates. In common usage, the nominal interest
rate is usually just called the interest rate.
Real Interest Rate
The real interest rate measures the change in real ability to buy that a nominal interest
rate is expected to offer. If the nominal rate is 15% per year, but George expects the
price level to rise 20% per year, by the end of the year, George expects to wind up with
about 5% less ability to buy if he lends money at that rate of interest.
Example: Hannah asks George for a one year $1,000 loan at 15% (nominal) interest. If
George makes the loan, expecting 20% inflation, he gives up $1,000 worth of goods and
services at today’s prices. He will get $1,150 at the end of the year, but expects each
dollar to be worth 20% less. If he makes the loan he expects at the end of the year to be
able to buy goods and services worth about $950 in today’s prices. The expected loss in
purchasing power for George is about $50, a real rate of about negative five percent. In
symbolic form, if the real rate is R, the nominal rate is IN, and expected inflation is EDP:
R = IN – EDP (This is an approximation useful if there is not too much inflation.)
The tools available to control the economy are divided into fiscal policy and monetary
policy. Fiscal policy is divided into two categories: government spending and taxes
Government Spending
If Congress and the President want to raise real GDP, they can raise real government
spending. If everything else (taxes and the real rate of interest) is held constant, the
increase in government buying raises total demand for goods and services. This raises
production (real GDP) and income. The rise in income causes a rise in household
demand for goods and services, and further increases in production and income. This
(government) spending multiplier means the eventual rise in income can be larger than
the initial rise in government spending.
3
Example: Suppose the government spends an extra $100, and the population spends an
extra $0.90 for every extra dollar in income they get. There will be a chain of increases in
income and spending whose first few terms will look like this: change in government
spending = 100  change in consumer spending = 90  change in income = 90 
change in consumer spending = 81  change in income = 81  change in consumer
spending = 72.90 ….. The result of this chain can be calculated using the formula: change
in income = change in spending * (1/(1-MPC)) where MPC is the marginal propensity to
consume, 0.9.
Taxes
If the government wants to raise real GDP it can cut real taxes (holding real interest rates
and government spending constant). If taxes are cut, people have more income available
to spend, and they spend more. This increases consumer demand, which causes
production (real GDP) to rise, and therefore further increases in spending. (Again,
sectors other than households are being ignored.) The eventual rise in real GDP can be
greater than the initial tax cut. The example under Government Spending can be used to
show how this works, but to get the same increase in GDP you must assume that the
initial cut in taxes was just enough to give households the right increase in “after tax”
income, so they will spend another 100. (Using the same behavior as before, the required
tax cut is 100/0.9 = 111.11….). In other words the initial increase in spending will the
MPC times the initial cut in taxes, so the tax multiplier is MPC/(1-MPC).
Monetary Policy
If the government (the Federal Reserve Board) wants real GDP to rise it can cause an
increase in the real money supply. It buys Treasury bonds from banks, so they have more
“reserves” and can offer more loans. As the loan supply increases, the price of loans (the
interest rate) falls. If the real interest rate falls, consumer and business spending rises.
As this demand rises, production and income rise. (The Fed has other methods of
affecting the money supply and interest rates (i.e. discount rate, reserve requirements),
but one is sufficient here.)
If government spending rises, with taxes constant and the money supply constant, interest
rates will not remain constant. If income starts to increase, due to the rise in government
spending, there is more demand for money by consumers and businesses, since they are
making more transactions. This also causes the price of money (still the interest rate) to
go up. As interest rates go up, this has a negative effect on investment and consumer
spending. The same analysis applies to the effects of a cut in taxes.
In the real world the Federal Reserve directly controls the nominal money supply -- the
dollar value not corrected for changes in the price level. That means a surprise change in
the price level could make the FED miss a target expressed in terms of the real money
supply (nominal money supply divided by the price index). In this module your job is
simplified because you directly control the real money supply.
4
Aggregate Supply and Aggregate Demand
The aggregate supply curve describes the levels of production that firms will offer at
given price levels for final goods and services, holding constant prices of resources used
in production. The higher the prices of final goods and services are, relative to resource
prices, the larger the level of output and visa versa.
Aggregate demand is the combined demand for final goods and services from
government, consumers, and business (investment). The determination of demand is
discussed in terms of the three sectors of the economy: consumers, business, and
government. In other words, if AD is aggregate demand, C is consumer demand, I is
(business) investment demand, and G is government demand.
AD = C + I + G
In equilibrium aggregate demand is equal to real GDP, but that level of GDP may or may
not be at full employment. The full employment real GDP (GDPFE) is the long run
equilibrium level of output. It corresponds to a level of unemployment where there is
zero cyclical unemployment, and workers are not being fooled about the purchasing
power of their wages. In the module, the new price level is equal to the old price level
plus the change in the price level from the previous year.
Information concerning monetary and fiscal policy, and the behavior of investors and
consumers is summarized in the Aggregate Demand (AD) curve in Figure 1. The
behavior of firms, which determines the goods and services supplied, is summarized in
the Aggregate Supply (AS) curve.
Figure 1 Aggregate Supply and Demand
P
AS
P1
P0
AD1
AD0
GDP0
GDP
GDP1
GDPFE
5
In Figure 1 the aggregate demand line AD0 could represent an original level of demand
in a recession, and AD1 the impact of expansionary monetary and/or fiscal policies.
Performance Over Time
This graph allows you to see how the unemployment (red in the module, dotted in the
figure below) and inflation rates (blue in the module, dashed in the figure below) changed
over your time in office, compared to the values they had at the end of your predecessor’s
regime. Each (inflation and unemployment) is measured compared to the original value.
In other words, if the inflation rate was 5% before, and is 5% now, the line for inflation
will be at zero (5% - 5%). If Unemployment was 6% before and is 8% now, the
unemployment line will be at 2% (8% - 6%). For example, if Figure 2 below, over the
user’s first three years in office the unemployment rate (starting at a base figure of
3.81%) was 3%, 5%, and 7%, while the inflation rate, starting at 3.26%, varied from 6%,
5%, and 2% the results look like this:
Figure 2 Performance Over Time
%
Unemployment Rate
6
3
Inflation Rate
1
2
3
Time
(In the module the inflation rate is measured on the left vertical axis, as usual, but the
unemployment rate is measured on a right side vertical axis. The two are measured on
different scales.)
Running the Program
When you start running the program, you must choose whether to begin in a recession or
in an inflationary situation. The first year you have to take the policy decisions made by
the previous administration - and get the “initial conditions” results you’ve already seen.
After that, by clicking on “New Year” you get a chance to enter policies of your own. If
you keep running the economy and keep using the same values for your policies you will
notice that your results keep changing. This is due to the fact that you do not control the
6
rate of inflation that people in this economy expect. The inflation rate they expect is a
weighted average of the actual inflation experienced in the past two years (65% of the
weight on the most recent year). If the actual inflation rate is changing they keep
changing their expectations. If nominal interest rates stayed the same, the real interest
rate would fall. A reduction in the real rate of interest would encourage more investment
and consumption spending, and that means higher real GDP, lower unemployment, and
more inflation.
In spite of this, the first time you run the program it might be a good idea to run it for a
while with the same policy numbers, just to see what happens. If you do, you may
discovery that there are some patterns to the results. In any case, doing this will give you
a basis for comparison - if you are trying to change your policies every year to get better
results, how do you know they are better? If you could change your policies to get less
inflation, or less unemployment, or best of all, less unemployment and inflation that you
get if you just keep the same policy numbers, then you’re helping.
Math Model
One of the ways the model used in this module differs from many elementary textbook
models is the direct incorporation of the expected rate of inflation. In this module the
expected inflation rate for the current year (EDP) is a weighted average of the actual
inflation rate in the previous year and the actual inflation rate of two years back. The
more recent experience carries more weight.
EDP = (0.65 * inflation last year) + (0.35 * inflation two years ago)
The values for the inflation rates for the two years before you took over are built in to the
two scenarios, but you can figure out the expected inflation rate from looking at the first
year’s results—just subtract the real interest rate from the nominal interest rate.
The structural equations for the sectors are:
Consumption:
C = a1 + a2 (GDP - T) + a3 R
where C = real consumer spending, R = real rate of interest, GDP = real Gross Domestic
Product, T = taxes, a1 through a3 are parameters. In this module the parameter values for
the consumption function are: a1 = 10, a2 = 0.9, a3 = - 25
Investment:
I = b1 + b2 R
Where I is real investment spending, b1 and b2 are parameters. In this module the
parameter values for investment spending are: b1 = 870, b2 = 0.70
7
Government spending is the value set by the user and real GDP is, as usual:
GDP = C + I + G + NX
NX stands for net exports, but this is a closed economy module so net exports are
assumed to always be zero.
The spending multiplier (SM) in the module is (IF real interest rates are kept
constant):
SM = 1 / (1 - a2) = 1 / (1-.9) = 10
The tax multiplier is (IF real interest rates are kept constant):
TM = .9 / (1-.9) = 9
The monetary sector assumes real money supply (determined by the user) equals real
money demand. (MD is real money demand, IN is the nominal rate of interest, d1 d2, and
d3 are parameters)
MD = d1 + d2 IN + d3 GDP
In this module parameter values for the money demand equation are: d1 = 15, d2 = -0.95,
d3 = 0.025
A complicating feature in solving the model is that, for sufficiently high values of the real
interest rate investment spending becomes zero. For even higher values of the real rate
investment spending would be negative if that were possible--which it isn't. When
determining outcomes at such high real rates it is necessary to force investment spending
to zero and determine all outcomes using the structural equations for only two sectors.
The solution for real GDP is (M is the money supply--and demand):
GDP = {(a1+b1)+(G- a2 T) + (a3+b2)(M-d1-d2 EDP) / d2) / (1-a2 + (d3 / d2)(a3 + b2))
Where M (money supply), G (government spending), and T (taxes) are all obtained from
inputs provided by the user.
And
R = IN – EDP = (M – d1 – d3*GDP)/d2 - EDP
However, in cases where the solution for R (using the parameter values shown along the
way) produces a value greater than -b1 / b2, the result is a negative value for investment.
When this happens real GDP and R are recalculated using zero values for b1 and b2
(guaranteeing an investment value of zero).
8
The unemployment rate is determined using a version of Okun's law:
Unemployment = 0.5 - (0.000199 GDP)
The inflation rate is also calculated using the real GDP and expected inflation rate already
obtained. The equation below could be combined with the one for unemployment to
produce a Phillips curve equation.
The real Phillips curve is nonlinear. (Real world estimates are consistent with a non linear
function) It is approximated for this module by a set of linear equations, one for each of
several ranges of real GDP. If dp is the inflation rate then:
If realGNP > 2400
dp = 0.003 * EDP + (0.1152 + (0.0142 * (realGNP - 2400)))
If realGNP <= 2400 and realGNP > 2350
dp = 0.003 * EDP + (0.0748 + (0.00083 * (realGNP - 2350)))
If realGNP <= 2350 and realGNP > 2300
dp = 0.003 * EDP + (0.05 + (0.0005 * (realGNP - 2300)))
If realGNP <= 2300 and realGNP > 2211
dp = 0.003 * EDP + (0.01 + (0.000449 * (realGNP - 2211)))
If realGNP <= 2211 and realGNP > 2200
dp = 0.003 * EDP + ((0.0009009 * (realGNP - 2200)))
If realGNP <= 2200
dp = 0.003 * EDP - 0.0002 + (-0.000022 * (2200 - realGNP))
If dp < -0.02, then dp = -0.02. This last part represents the lower limit on price changes,
due to some downward inflexibility of prices.
Since the expected inflation rate is incorporated into the Phillips curve technically the
above equations represent segments on an inflation-augmented Phillips curve. In the short
run with constant inflationary expectations they represent a short run Phillips curve.
When expectations vary they represent a longer run Phillips curve.
Once all the previous results have been obtained, new values for consumption,
investment, government spending, and the nominal interest rate are calculated.
9