General equilibrium in a closed economy (autharky)
and in an open economy
Sanna Randaccio: Lectures 9-10
GENERAL EQUILIBRIUM IN CLOSED ECONOMY
•The closed economy model (autarky)
•Equilibrium conditions for the good X (Y) market in a closed economy
•Walras’ law in a closed economy
•General equilibrium described with the TR and the SIC
Vedi MMKM (1995), p. 53
Closed Economy
1) Producer optimization :
p x / p y  MRT
2) Consumer optimization : p x / p y  MRS
i
3) Market clearing condition
Equilibrium conditions for the goods markets
Xc  X p
Ex  X c  X p  0
Yc  Y p
E y  Yc  Yp  0
TOTAL INCOME : HOW WE MEASURE IT?
•Perfect competition w / p y  MPLy
r / p y  MPK y
•Euler’s theorem: Under conditions of constant returns to scale, if
each factor is paid the amount of its marginal product, the total product
will be exactly exhausted by the distributive shares for all the input
factors (the pure economic profits=0)
Yp  Ly
Y
Y
 Ky
L
K
thus
Yp  Ly
w
r
 Ky
py
py
wL y  rK y  p yY p
•Full employment:
L  Lx  Ly
K  Kx  K y
Total factor rewards = production value
Community Budget Constraint
Total expenditure of the community  Total income of the community
px X c  p yYc
?
In each sector:
Total factor rewards = production value
rK x  wLx  px X p
rK y  wLy  p yYp
Total income of all individuals in the economy
r ( K x  K y )  w( Lx  Ly )  px X p  p yYp
Community budget constraint
px X c  p yYc  px X p  p yYp
Walras’s law in a closed ecomy
Community budget constraint (satisfied as equality due to nonsatiation)
px X c  p yYc  px X p  p yYp
From which
px ( X c  X p )  p y (Yc  Yp )  0
px Ex  p y E y  0
Since the two markets are linked by a budget constraint, if at a given
px
one market is in equilibrium also the other market will be in equilibrium
py
 px 
p   
 py 
a
a
Determined by the characteristics of production (TC) and demand (SICs)
It is influenced by:
•Factor endowments
•Technology (factor productivity)
•Community tastes
The equilibrium at point A is optimal .
community can reach.
U a is the highest SIC which the
The production point and the consumption point coincide.
GENERAL EQUILIBRIUM IN AN OPEN ECONOMY (2x2x2)
--The model for the open economy
--Equilibrium condition for the market of good X (Y) in open economy
--Budget constraint for country H (from which the trade balance condition)
--Meaning of the trade balance condition
--Meaning of isoincome (national budget line)
--The excess demand curves for the two countries
--Composition and volume of international trade
--Determination of world prices and an international general equilibrium
--General equilibrium in open economies and Walras’ law
OPEN ECONOMY
We assume the absence of natural (e.g. transport costs) and artificial
barriers (e.g. tariffs)
In the post-trade situation, prices in the domestic market are the
same as prices in the international market
EQUILIBRIUM CONDITIONS FOR GOOD MARKETS IN THE
OPEN ECONOMY
Goods markets have an international dimension
Global demand = Global supply
X c  X c*  X p  X *p
Yc  Yc*  Y p  Y p*
From which
E x  E x*  0
E y  E *y  0
Observe the difference with the closed economy case.
Budget constraint for country H evaluated at post-trade prices
p Tx X c  p Ty Yc  p Tx X p  p Ty Y p
where national income is given by the value of production at posttrade prices pT
We obtain the trade balance condition
p Tx ( X c  X p )  p Ty (Yc  Y p )  0
Which implies that:
--A country is not bound to consume the same quantity of X (Y) that is
producing internally.
--if X c  X p  0 (import X)
Yc  Y p  0
(export Y)
--The value at post-trade price of goods imported and exported is the same.
Trade balance is always in equilibrium. Exchanges takes the form of barter.
General equilibrium in an open economy
T
 px 
   pa
p 
 y
A
N
T
Markusen et al. (1995) p. 55
Compostion and volume of international trade
If
pT  p a
Ex  0
( E y  0)
T
p T  p1T
If
that is
 px 
   pa
p 
 y
The relative price of good X in free-trade decreases
•The eq. production point is
Xp 
Q1
(firms shift resources from X to Y )
Yp 
•The eq. consumption point is C1. Consumers substitute Y with X
Xc 
Y  ( if the substitution effect prevail on the income effect)
c
Excess demand for good X is positive (for good Y is negative if the income
effect is moderate).
Thus if
H:
p T  p1T  p a
Ex  X c  X p  0
import X
export Y
T
T
a
Se p  p2  p
H: export X
import Y
Ex  X c  X p  0
The excess demand function
T
T
T
T
T
Markusen et al. (1995) p. 55
The equilibrium world price ratio
a*
a
T
T
If p  p the international equilibrium price ratio p ( p2 ) is
obtained when
X c*  X *p  ( X c  X p )
Quantity of X which F is
willing to import
Quantity of X which H is
willing to export
The condition for equilibrium in market X with open economies then
holds, since:
E x  E x*  0
We can show that if at given p the market for X is in equilibrium also
the market for Y will be in equilibrium
T
EQUILIBRIUM RELATIVE PRICE RATIO WITH TRADE
T
T
Markusen et al. (1995) p. 58
WALRAS’ LAW EXTENDED TO OPEN ECONOMIES
In each country the value of community consumption is equal to the
value of total income (=value of total production)
p Tx X c  p Ty Yc  p Tx X p  p Ty Y p
from which
p Tx X c*  p Ty Yc*  p Tx X *p  p Ty Y p*
p Tx ( X c  X c* )  p Ty (Yc  Yc* )  p Tx ( X p  X *p )  p Ty (Y p  Y p* )
p Tx [( X c  X c* )  ( X p  X *p )]  p Ty [(Yc  Yc* )  (Y p  Y p* )]  0
 px 
Then the   for which the market for good X is in equilibrium will lead to
 py 
equilibrium also the other market (Y)