Macroeconomic Implications
of the Exchange Rate Theory
Based on Productivity
Marcin Jędrzejczyk
http://www.rigel.pl/ina
http://swed.ae.krakow.pl
mailto:jedrzejm@ae.krakow.pl
“Purchasing Power Standard (PPS)
shall mean the artificial common reference currency
unit used in the European Union to express the
volume of economic aggregates for the purpose of
spatial comparisons in such a way that price level
differences between countries are eliminated.
Economic volume aggregates in PPS are obtained by
dividing their original value in national currency units
by the respective PPP. One PPS thus buys the same
given volume of goods and services in all countries,
whereas different amounts of national currency units
are needed to buy this same volume of goods and
services in individual countries, depending on the
price level”.
Comparative analysis of the 1,5 kW engines
manufactured in Poland and the USA
TAMEL
Power 1,5 kW
Sg 90 L-4
B3
380 V
50 Hz
Insulation class F
1200 rpm
BALDOR ELECTRIC
Power 1,5 kW
4 Pole
B3 Mounting
380 V
50 Hz
Insulation class F
1160 rpm
SELLING PRICE:
312,32 zł
$ 380
AFTER TRANSLATION (CONVERSION):
$ 78
1520 zł
PURCHASING POWER STANDARD
312 zl
PPS 
 0,82 zl / $
380$
Macroeconomic Implications of the
Exchange Rate Theory Based on
Productivity
In case of production of the economic system, the
problem seems to be quite different than in
consolidated balance sheet. Let us take the real GDP
(GDPR) which represents the nominal GDP
expressed in the last years’ prices for Poland and for
the USA. We consider GDPR as a product of wage
(cost of labour) W and real productivity coefficient
(RWP). The subscript P denotes Polish and subscript
A the American wage and real productivity.
GDPRP  WP  RWPP
GDPRA  WA  RWPA
Macroeconomic Implications of the
Exchange Rate Theory Based on
Productivity
Let us divide the equations:
GDPRP WP RWPP


GDPRA WA RWPA
Then reformulating we obtain:
WP RWPP
GDPRP [ zl ] 

 GDPRA [$]
W A RWPA
Macroeconomic Implications of the
Exchange Rate Theory Based on
Productivity
The above formula shows some applications of
the exchange rate. Therefore we write
subsequent formula where f(ER) denotes some
function of exchange rate.
GDPRp [ zl ]  f ( ER)  GDPRA [$]
Macroeconomic Implications of the
Exchange Rate Theory Based on
Productivity
Dividing labour cost W by number of employees
we obtain formula where AP means average pay
and L number of employees of the given
countries:
APP LP RWPP
GDPRP [ zl ] 
 
 GDPRA [$]
APA LA RWPA
where GDPRE – GDPR per one employee.
Macroeconomic Implications of the
Exchange Rate Theory Based on
Productivity
Factor of the above equation including average pays
and wage productivity is according to our research the
exchange rate formula. Thus only GDP per one
employee can be reasonably multiplied by the
exchange rate. Therefore the fundamental formula is:
$
GDPRE P [ zl ]  ER
zl
 GDPRE A [$]
Macroeconomic Implications of the
Exchange Rate Theory Based on
Productivity
To achieve comparability of GDP per capita following
procedure should be applied:
GDPRP [$]  LP  GDPRE P [ zl ]  ER zl
$
where LP means the overall number of employees in
Poland.
Macroeconomic Implications of the
Exchange Rate Theory Based on
Productivity
To convert the GDP per employee to GDP per capita
(GDPRC) we have to include the relation between
the number of employees (LP) and the number of
inhabitants (LM) of the considered country:
LP
GDPRC P [$] 
 GDPRE P [ zl ]  ER zl
$
LM
Macroeconomic Implications of the
Exchange Rate Theory Based on
Productivity
We can come up to the conclusion that exchange
rate does not apply directly to wages, prices of
goods and conversion of GDP to dollars. According
to the introduced formula one can estimate GDP in
dollars starting with GDPR per one employee as
has been shown in this paper. To conduct the
calculations it is only necessary to have the data
from both countries such as number of employees,
number of inhabitants, average pays dependent on
the productivity.
CONCLUSIONS
 Exchange rate is not applicable in converting
the value of manufactured goods ,
 Exchange rate is applicable only to real GDP
per one employee,
 Exchange rate is not applicable to GDP per
capita,
 To convert value of assets, PPS ratio is
applicable.