Open Economy: the Disequilibrium Macromodel of Exchange Rates and Its Stability
Wang Qifan Chen Zhanqiang Zhou Minghai
School of Management,Fudan University,Shanghai,200433,China
Economists have paid their great attentions to the macroeconomics study under open economy. In this paper, from viewpoints of Systems
thinking, we considered such variables as aggregate supply of products, money supply and wage endogenous. Based on Dornbusch Model,
we established the disequilibrium model including exchange rates, price of products, foreign assets and wage. Finally, we gave the stablity
conditions for the model.
|. The History
With the rapid development of economy and science & technology ,the world economy is becoming more and more
globalized,and the good way to develop the national economy is to expand the scale of its openess to the outside
world.Accordingly, world economists have attached great importance to macroeconomics under open economy.
In macroeconomics under open economy, much original research work has been done by many economists such as
Robert Mundell, Marcus Fleming and Rudiger Dornbusch in the1960s.The Mundell-Fleming Theory [1,2] enlarged the IS-LM
model to open economy. The M-F model considered a small country economy where the monetary system is under
floating exchange rates, the price is fixed, the capital movement is incomplete and the expectation of exchange rates
is static. The emphasis of the model was on the different conditions which determined the balance of capital account
and net inflow of capital. The M-F theory was very popular in the1960s, but the main defect of M-F is the assumption
of the fixed price and static expectation of exchange rates which are impractical for a long-term economic activity.
For this, Dornbusch,the world-famous economist in MIT put forward his famous Dornbusch Model [3] to revise M-F
model in 1976.Based on M-F model, Prof. Dornbusch put into his model the adjustment of price of
products,complete capital movement and complete expectation of exchange rates to make it more practical in real
world.
2. The Problem in the models
The socio-economic system is a complicated system,where many variables are relative and interactive. Capable as
Dornbusch model is in describing and explaining the real world , it merely explores the relationship between
exchange rates and price, and regards many important variables such as aggregate supply of products, money
supply as exogenous. In fact, these variables are heavily interactive with price and exchange rates. Based on
Dornbusch model and from the viewpoints of Systems thinking, we made the following variables as endogenous.
They are aggregate supply of products,money supply, and wage. Moreover, we establish the disequilibrium model
including exchange rates, price, foreign assets and wage. Here, we consider the open economy situation in a small
country where the monetary system is under floating exchange rates, the capital movement and expectation of
exchange rates are complete. As a small country, its economic activities have little impact on the world economy, but
the world
economy greatly affects the country.
3. The Model
This model described the case in which the aggregate supply curve is in the middle area(not in keynes area or
classical area).
In money market,the real demand of money can be written as
(1) m= ay-a!
where y is GNP,ji is domestic interest rate.and the real demand of money equates to supply when the money market
gets to an equilibrium,i.e.
where mis nominal supply of money. For the supply of basic money H,we have H=% F+D,where F is foreign asset
in center bank, D is domestic credit(regarded as a constant here), 7 is the nominal exchange rate. Setting Xo as
money multiplier,we can write the nominal supply of money as
(3) mz *0 (7 F4D)
In product market,the aggregate demand of products is given by
(4) Ye = AGP) thy by +E
where g is the government demand of purchase. In product market,the aggregate supply is determined by the
function of production y=y(N,K), here we didnt consider the change of technology and capital, so the function of
production is stable and the capital K is fixed.Here the supply of labour force N becomes the determining factor to
products y, but the supply of labour force N is determined by the real wage. And finally, the aggregate demand of
products is determined by the real wage. So we have
(5) ¥ = 60 +ei(w—P)
where W is nominal wage.Setting was the long-term expected wage,the adjustment of nominal wage is
6) w=d,(w-w)
We described the process of price adjustment as below
(7) P= We -¥)
where £ is the speed of price adjustment.
The change of foreign assets should be the sum of net exporting value, interest of foreign assets and net inflow of
capital. The capital account includes long-term capital and short-term capital. But the short-term capital has a great
mobility,and has become the main factor which results in volatility of exchange rates in the international finance
market. With the great progress of world economy and information technology, the amount of short-term capital
investment is becoming larger and larger,and the mobility more complete.In our model,we just considered the net
inflow of short-term capital,which is mainly determined by domestic market interest rate.Setting tas foreign interest
rate,we obtained
F=X(O+i*F+e tei
P
a id
where X(” ) is net exporting value, ” is real exchange rate. Here we also took the assumptions that the capital
movement and expectation of exchange rates are complete,
and by UIRP theory [4],we had
(9) @=i-i"
by (1),(2) and (3),we got
substituting (10),(5) into (9),we got
l-a,c. ac, & ac, k +
ga 2 ye Uy
(11) cc a5 a m4
substituting (4),(5) and (10) into (7),we got
C;
bya
rare,
p=[#,(1-2) + — ey |p +[ 2 (b, — 1) +> pot hye
a, a;
&.
Pike oF + xy (by -1)- Pa 4 Sep
(12) % a a
substituting (5),(10) into (8),we got
%. . 2) — a0, ace, Kye, AyCoe, Kye
Fo X(5 +i F+ tp ps - ar Se ete,
P a, a, 4, a4
(13)
For the sake of convenience, we denote the right of equation (11),(12),(13) and (6) as F1(# ,p,F,w),F2(# ,p,F,w),F3(
1 1p,F,w) and F4( ,p,F,w) respectively. From above,we obtained the Disequilibrium Macro-model including
variables 7 ,p,F and w, i-e., the differential equations as below
n= Fi(n,p,F,w)
p= F2(x,p, Fw)
B= FHx,p,F,»)
(14) be= FaCz.p, Fw)
4. The Equilibrium Point and Stability of Model
Here we discussed a general form of system (14),and F1,F2,F3 ,F4 is a general function respectively.In autonomous
system (14), given F1,F2,F3 ,F4 as zero,we reached the equilibrium point of system (14) (7 P.#¥) . General
speaking, the equilibrium points of system (14) are not unique , so here we just only considered the case when the
equilibrium points of system are unique.
To discuss the stability of system (14) near the equilibrium point of system (14) ("PF ow) .we derivated the
functions F1,F2,F3 ,F4 in system (14) with respect to variables 7 ,p,F,w,and obtained
| F1 1 #1 #1
A(7p,F.w)=—
Near the equilibrium point of system (14) (Pw) ,if the eigenvalues of matix A( ,p,F,w) As (i=1,2,3,4), have
negative real part, i.e., Re*# <0, the equilibrium point (*-?-"-”) is a stable point.
References
[1] Robert A-Mudell(1963)Capital mobility and Stabilization Policy under fixed and flexible exchnaeg
rates",Canadian Journal of Economics and Political Science 78,475-485.
[2] Marcus Fleming(1962)Domestic financial under fixed and under floating exchange rates", /MF staff papers 3,369-
380.
[3] Rudiger Dornbusch(1976)Expectations and exchange rate dynamics" Journal of Political Economy 84,1161-
1176.
[4] Laurence S.Copeland(1989) Exchange Rate and International Finance, Addison-Wesley Publishing Company.
ISDC'97 CD Sponsor Bagel beet
