Download The Product Market Equation

THE PRODUCT MARKET EQUATION:
• is: x = p + q
• addresses the questions:
o What are the effects of changes of spending? or What happens if spending changes?
o What happens if technology changes?
o What happens if costs of production change?
• says: Any percent change of spending must be accompanied by changes of inflation and real
growth that add up to the percent change of spending.
• can be used to describe how the product market responds to changes of spending, technology
and costs.
Derivation:
X = dollars of spending = (nominal) GDP
P = the price level
Q = the quantity of output = real GDP
x = %∆X = growth rate of nominal GDP
p = %∆P = inflation rate
q = %∆Q = growth rate of real GDP
The Product Market Equation states the fact that the dollar amount spent (X) is equal to the price
(P) times the number of units bought (Q). That is: X = P·Q. In its rate of change form, this
equation becomes x = p + q.
A. CALCULATING the numbers in the Product Market Equation -- x = p + q
The percentage change between any two numbers, over a year’s time, is calculated by -Value in sec ond year

Value in sec ond year − Value in first year
OR 
x100%
− 1 x100%
Value in first year
 Value in first year

•
x = nominal GDP growth -- the percent change of spending between two years
This is the “easiest” number to get. Roughly speaking, we ask every store in the country (by
way of tax records, for example) how many dollars worth of goods they sold in each year.
We compute the percentage difference between any two years.
•
p = inflation rate -- the percent change of the price level1 between two years
To get this number we select a representative (“average”) selection of goods (a “basket”). We
buy this same basket in consecutive years and measure the percent change of the price of this
basket. We find out what percent more it costs in the second year than in the first. This is the
inflation rate.
This measurement has lots of problems:
o It’s unclear what “average” means. Different people buy very different combinations of
goods.
o It’s impossible to keep the contents of the basket typical of real consumption, without
changing its contents occasionally, but this defeats the concept of buying the same goods so
as to compare only price changes. We problem can be stated as whether you want the
“basket” to be “current” or to be “constant.”
1
. The price level can be thought of as “the cost of living.”
Section D. The Product Market Equation. page 1
Macroeconomics, Kvaran
o This process does not work well when the quality of the goods in the basket changes. The
cars we drive, the computers we use and the medical care we get are all quite different than
they were not long ago. So even if we keep a computer in the basket, it is hard to account for
the fact that this year’s computer is different from last year’s.
•
q = real growth rate -- the growth rate of real GDP.
This is intended to measure how much more real “stuff” we have than we did a year ago.
This is computed by using the Product Market Equation in the form q = x - p. Once we have
x and p we can calculate q. For example, if we spent 7% more than we did last year (x = 7)
and if 3% percent of that went to pay higher prices (p = 3%), then we must have bought 4%
more “stuff” than we did the year before.
Notice a problem. If we are unsure about how well we measured inflation (p), then we have
to be equally uncertain about the number for real growth (q), which we got by using p. (We
can measure x about as well as we can measure anything in macroeconomics).
A recession is typically declared if we have two consecutive quarters of negative real growth.
Problems In The Calculations. It has been reported than Federal Reserve worries that we have
overestimated inflation and consequently underestimated real growth (q).
For example, suppose x = 7% for some year, that we measure inflation as p = 3, and from that we
calculate real growth as q = 4. But imagine that actually inflation is only 2%: then real growth is
actually 5%.
It seems quite likely that as the quality of a good improves, the “real” price of the good will be
overestimated. As an example, suppose this year’s computer computes 25% faster than last
year’s computer and sells for the same price. This actually means that the price of buying
computing has fallen -- the same amount of money can buy more of it. But all we see are two
machines of the same price. We say that computers got no cheaper this year, even though
computing did get cheaper. We have yet to find a way to measure that difference. Increasingly
more of our modern economy involves producing goods of ever-improving quality and we have
yet to find away to satisfactorily capture that truth in our numbers.
Section D. The Product Market Equation. page 2
Macroeconomics, Kvaran
B. THE EFFECTS OF SPENDING CHANGES. (Changes of demand in the product
market) What happens when Demand changes. What is the effect of a change of spending?
An increase in nominal spending (x) will produce some combination of real growth (q) and
inflation (p) that add up to the percent change of spending.
If spending rises by 10% in a given year, then some of the possible outcomes are given in the
table.
A 10% increase of spending could cause -inflation real
of:
growth of:
1%
9%
a little inflation, a
lot of real growth.
9%
1%
a lot of inflation, a
little real growth
… or any number of other possibilities.
Which outcome actually occurs will depend on a variety of factors facing producers and sellers,
such as:
• what are the costs of producing additional production.
o are inventories available, or must you produce new output
o do you have idle equipment and workers
o is it easy to find additional supplies and to hire additional workers
• are you expected to increase output for a long time or only a short time.
• how much competition there is.
For a given x, we would expect growth (q) to be large and inflation (p) to be small if:
• the costs of production additional output are high/low
• increased demand will be met with existing inventories/new output
• additional supplies and workers are cheap and easy/difficult and expensive to find
• producers have/do not have idle equipment.
• the economy is in a recession/boom
• the time under consideration is a long/short time.
• there is/is not a lot of competition (foreign competition, for example)
For our purposes, the two most important variables are (a) the length of time involved, and (b)
how the economy is doing when spending changes.
a. the passage of time: the shorter the amount of time involved, the greater the impact on output
(q). As more time passes, it is more likely that we will get more inflation and less real growth.
That is, when faced with an increase in spending (demand) an economy’s first reaction is to
produce more goods. It takes some time for the inflationary effects to assert themselves. An
economy can produce bursts of increased output that may not be sustainable over time.
Section D. The Product Market Equation. page 3
Macroeconomics, Kvaran
more in the short run
x=p+q
more in the long run
b. how full employment is. The further an economy is from full employment, the more likely it
is that spending increases will cause output growth, rather than inflation. Near full employment,
spending is more likely to cause inflation. This is because, as the economy approaches full
employment, the costs of generating additional output tend to rise as it becomes more difficult to
get additional inputs, and production costs get pushed up.
more with high unemployment
x=p+q
more with low unemployment
c. how much competition there is. Competition, domestic or foreign, tends to limit price
increases.
more with a lot of competition
x=p+q
more with little competition
C. THE EFFECTS OF CHANGES OF COST AND TECHNOLOGY.
What happens when Supply changes. We can consider two types of supply changes.
1. changes of technology. This seems to have been an important factor in the growth of the
1990s.
2. changes of costs of production. This seems to describe the effects of the oil price increases of
the 1970s.
1. An improvement of technology can be thought of as an increase of real growth (q). For a given
x, we would expect a decrease of inflation (p).
2. An increase of the cost of production could be seen as an increase of inflation (p). For a given
x this would cause a decrease of real growth.
D. SUMMARY of the Product Market Equation Results.
1. x↑ ⇒ p↑ and q↑. This shows the effect of an increase of demand.
2. Improved technology ⇒ q↑ and p↓.
3. Increased production costs ⇒ q↓ and p↑.
Section D. The Product Market Equation. page 4
Macroeconomics, Kvaran
E. A BIT OF HISTORY by the Decades
Decade
1930s
1940s
1950s
1960s
the Depression
World War II
1970s
early 1980s
later 1980s
1991
1990s
2000
the Democrat era
expansion #2
oil price increases
the Volcker recession
Reagan expansion
expansion #3
Desert Storm recession
tech expansion (?)
expansion #1
Recession
Real Growth
Unemployment
Inflation
really high
really low
low -price controls
high
low
rising
low
low
high
high
high
falling
high
falling
low
high
low
low
low
rising
falling
We would expect real growth and unemployment to be opposites.
9.0
AVERAGES
8.0
q
7.0
p
U
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1960s
1960s
1970s
80 - 83
84 - 89
1990s
2000s
All
1970s
Averages
q
p
U
4.3
2.5 4.8
3.3
6.6 6.2
1.8
6.5 8.5
3.8
3.1 6.9
3.2
2.2 5.8
2.5
2.0 5.2
3.3
3.7 5.9
80 - 83
q
-5.2
-4.8
-8.1
1.0
-3.0
-1.4
-8.1
Min
p
0.4
2.3
2.9
1.0
0.8
1.1
0.4
84 - 89
U
3.4
4.2
6.3
5.2
4.1
3.9
3.4
1990s
2000s
Max
COMMENTS
q
p
U
9.8 5.8 7.0 A walk up the Phillips Curve
15.8 12.4 8.9 Oil Prices rise twice
9.0 11.2 10.7 The Volcker recession ends inflation
7.8 7.8 7.9 The Reagan expansion
7.1 4.8 7.6 Technology triumphs (?)
7.2 3.3 6.1
15.8 12.4 10.7
Section D. The Product Market Equation. page 5
Macroeconomics, Kvaran
F. GRAPHING the product market equation
1. Equilibrium
12
11
10
9
8
7
6
5
4
3
2
1
0
%p
D
%q
D
0
12
11
10
9
8
7
6
5
4
3
2
1
0
The Demand line shows all the combinations
of growth and inflation that add up to 10% -what buyers are willing to spend.
The Supply line then determines which
combination will be offered.
In this case we get:
growth of 4%
inflation of 6%
S
p
1
2
3
4
5
6
7
8
9
10 11
12
2. Demand Changes
p%
Suppose there is an increase of demand. Buyers
are now willing to spend x = 12% instead of
the previous x = 10%. Price and quantity both
increase.
S
In this case we get:
growth rises from 4% to 4.8%
inflation rises from 6% to 7.2%
D2
D1
0
1
2
3
4
5
6
7
8
9
q%
10 11
12
3. Supply Changes
12
11
10
9
8
7
6
5
4
3
2
1
0
%p
S1
S2
Suppose costs of production decrease, perhaps
because of improved technology. This is
shown by an increase of supply. In this case
inflation decreases (6% to 4.8%) and growth
speeds up (from 4% to 5.2%).
D
0
1
2
3
4
5
6
7
8
9
%q
10 11
12
Section D. The Product Market Equation. page 6
Macroeconomics, Kvaran