Economic sciences / Mathematical methods in economy
Kerimkulov
Seit Esilbaevich
Lev
N. Gumilyev Eurasian National University, Kazakhstan
Elasticity
of trading balance and a condition
of trade in relation to a rate of exchange
The
macromodel of open economy is closely connected to models of behaviour of the
countries within the framework of process of world trade, and also with
opportunities of import of technological achievements available at the country,
to borrow or lend money (financial shifts) from other countries of the world
during economic growth.
Let's
consider models of elasticity of trading balance and a condition of trade in
relation to a rate of exchange [1].
The conditions of equilibrium:
, (1)
in the export market,
, (2)
in the import market, where
– equilibrium mains of export in indexes of physical mains;
– equilibrium mains of import indexes of physical mains;
– the
equilibrium price of export in national currency;
– the
equilibrium price of import national currency;
– the
equilibrium price of export in a foreign currency;
– the
equilibrium price of import a foreign currency;
–
equilibrium rate of exchange (or the price of a foreign currency, for example,
in tenge / dollars USA);
–
conditions of trade as the relation export and import prices;
–
the supply of a foreign currency by the current calculations, or cost of export
in standard units;
–
demand for a foreign currency by the current calculations, or cost of import
standard units;
–
trading balance of a foreign currency;
–
function of the supply of a foreign currency in the export market;
–
function of demand for a foreign currency in the export market;
–
function of the supply of a foreign currency in the import market;
–
function of demand for a foreign currency in the import market;
–
elasticity of the supply of export at the price of export to a foreign
currency;
–
elasticity of demand for export at the price of export to a foreign currency;
–
elasticity of the supply of import at the price of import a foreign currency;
–
elasticity of demand for import at the price of import a foreign currency;
–
elasticity of the supply of a foreign currency (or cost of export) in relation
to a rate of exchange;
–
elasticity of demand for a foreign currency (or cost of import) in relation to
a rate of exchange;
–
elasticity of trading balance in relation to a rate of exchange;
– elasticity of
conditions of trade in relation to a rate of exchange;
,
.
To differentiated (1) - (2):
(3)
(4)
Having divided (3) on 
, (4) on 
and (3) – (4) on 
, receive:
, (5)
, (6)
From definition of elasticity we
have:
(7)
(8)
(9)
(10)
(11)
(12)
(13)
Having substituted (7) - (8) in (5)
and (9) - (10) in (6), we have:
, (14)
(15)
From (14) - (15) we shall receive:
(16)
(17)
, (18)
. (19)
Note, that
, (20)
, (21)
. (22)
Thus, from (20) - (21), we shall
receive mathematical model of elasticity of trading balance in relation to a
rate of exchange:
, (23)
and from (16) - (17), we
shall receive computing model of elasticity of conditions of trade in relation
to a rate of exchange:
. (24)
For application
of calculated model condition of trade under the relation a rate of exchange on
mineral resources of Kazakhstan the information database the current accounts
and a rate of exchange of dollars has been created. The user materials [2] we
take results in the table 1.
Table 1
Dynamics of foreign
trade on mineral resources RK in 2000.
|
Months |
The
price of export |
The
price of import |
The
price of export |
The
price of import |
Mains
of export |
Mains
import |
Rate of dollars. the
USA in tg. |
|
|
in % by previous period of last month |
in million dollars.
the USA |
in individual physical
mains |
||||||
|
1 |
January |
-1,0 |
-0,5 |
0,990 |
0,995 |
460,0 |
18,1 |
139,03 |
|
2 |
February |
13,2 |
6,5 |
1,121 |
1,060 |
459,9 |
20,2 |
139,79 |
|
3 |
March |
-0,9 |
1,6 |
1,111 |
1,077 |
475,9 |
12,8 |
141,27 |
|
4 |
April |
8,4 |
0,1 |
1,204 |
1,078 |
526,0 |
10,9 |
142,17 |
|
5 |
May |
3,8 |
-4,5 |
1,250 |
1,029 |
439,0 |
12,1 |
142,29 |
|
6 |
June |
4,2 |
-5,3 |
1,302 |
0,975 |
416,1 |
9,9 |
142,49 |
|
7 |
July |
3,3 |
5,9 |
1,345 |
1,032 |
481,0 |
11,6 |
142,69 |
|
8 |
August |
-3,7 |
2,2 |
1,295 |
1,055 |
431,0 |
12,1 |
142,66 |
|
9 |
September |
4,6 |
2,5 |
1,355 |
1,081 |
439,9 |
13,1 |
142,72 |
|
10 |
October |
7,7 |
1,8 |
1,459 |
1,101 |
423,2 |
12,7 |
142,64 |
|
11 |
November |
-7,7 |
4,4 |
1,347 |
1,149 |
528,4 |
10,5 |
143,51 |
Trend of the price of export on mineral resources RK
in 2000 (million dollars USA)
Figure 1
Trend of the price of
import mineral resources
RK in 2000 (million dollars
USA)
Figure 2
From figure 4 we
notice, that as change of conditions of trade on mineral resources time,
despite of tactical changes as the prices of export (figure 1), and the prices
of import (figure 2) it is necessary to react by change of balance of the
current operations. In other words, improvement of conditions of trade should
conduct to formation active, and deterioration - passive balance, that it, as a
rule, is realized with the help of a rate of exchange as devaluation national
currencies.
Trend a condition of
trade on mineral resources RÊ in 2000y.
Figure 3
Elasticity a condition of
trade under the relation a rate of exchange
of dollars USA on mineral resources RK in 2000y.
Figure 4
The
offered mathematical model of elasticity of conditions of trade in relation to
a rate of exchange (24) is expressed through concepts of elasticity, but the
information base set as table 1 does not allow direct application for a
necessary condition of calculations of elasticity is existence of a derivative
that demands to proceed(pass) to their trends (figure 1-4). The last is
realized in a package of applied programs Excel MS environment, through the Main menu /
the Master of diagrams / To add a line of a trend.
It is known
[3-4], that Kazakhstan it is integrated into system world economic connections as the
country with small open economy. Therefore export and import
Table 2
Factor of elasticity condition of trade under the
relation a rate
of exchange of dollars USA on mineral resources RK in 2000y.
|
N |
Months |
Elasticity |
|
1 |
January |
-1,1777 |
|
2 |
February |
-1,0477 |
|
3 |
March |
-1,1036 |
|
4 |
April |
-1,0993 |
|
5 |
May |
-1,1287 |
|
6 |
June |
-1,2944 |
|
7 |
July |
-1,1034 |
|
8 |
August |
-2,9879 |
|
9 |
September |
-0,9417 |
|
10 |
October |
-2,5508 |
|
11 |
November |
-1,0550 |
prices are established in foreign currencies in an environment, in
particular in the world markets. From figure 4 it is visible, that devaluation,
or depreciation of national currency, conditions trade in mineral resources of
Kazakhstan definitely improves, that in turn affects and the currency market.
For example, devaluation for one tenge stabilizes conditions of trade on the
average on 1,4 % (table 2) and forms a basis for a conclusion, that change of a
condition of trade facilitates a task of stabilization of the currency market.
References
[1] Seit E. Kerimkulov, Computing model of elasticity of trading balance by a rate of exchange / Ten years of reforms
on the post Soviet space: expectations, results, prospects: Materials of the
international scientific conference on May, 18-19 2001y.: In five parts. P.3. -
Almaty: University "Turan", 2001.-pp. 203-207, (in Russian).
[2] Kazakhstan Economic Trends - January - March, 2001, Astana, 150 p.
(in Russian).
[3] Seit E. Kerimkulov, Modelling
of macroeconomic processes in Kazakhstan. - Almaty: NIS "Gylym", - 2001. – 240p. (in
Russian).
[4] Seit E. Kerimkulov, Computable
model of the general equilibrium of the macroeconomic markets: the Manual.
- Almaty: NIS "Gylym", - 2002. - 264 p. (in
Russian).