The keneysian model states 
that the goods market is at 
equilibrium when Y (income =
GDP) = Yd (Aggregate demand)

 Y = C(Y-T) + I(Y+i) + G + 
  BT (ø)

Aggregate demand (yd) 
is composed of :

consumption (C)
Investment (I) 
Government spendings (G)
Trade balance BT (X-M)

To analyze equilibrium of the
goods market and impact on 
BT, we need to turn the 
equation Y = yd to two 
equations (income) and
(spending)

We consider that planned 
leakages = planned injections

We consider that x| is 
exogenous and fixed 

x = x| and m = my 
(marginal propensity to 
import) is constant 

so BT(x-m) turn into

YBT = (1/my)*x|

The final equation is :
y = (1/sy + Cyty + my) * 
(C0 + I + G + x|)

sy = marginal propensity
to save
Cy = marginal propensity to
consume

sy + Cyty + my = planned
leakages (income equation)

C0 + I + G + x| = planned
injection (spending equation)


Graph :
  
Equilibrium in goods market
is meet at point E0 where
planned leakages = planned
injections

vertical axis :
  
 x| (level of
exports) below imports curve

planned leakages equation

angle (corner of the graph) :

planned injection curve (up
curve)

my curve just above x|

in horizontal axis 
(numerotation) :
  
horizontal axis represents 
Y (income)
  
point where x| and my crossed
each other = YBT (income of
BT : output)

point where planned leakages
= planned injection = Y0



Analysis :
We see that my is higher
than x|, leading to 
a detrioration of BT

To solve that, we need to
increase x| so planned
leakages will increase too
leading to a higher Y
(income at the end) at Y1
and on the graph point B
(new equilibrium)

and for BT : x| > my, so
there will be a higher 
YBT, (equilibrium) called
YBT' in the graph,

there will be an improve
of BT (trade balance)