Real aggregate
expenditure, AE

Real GDP, Y

C

C + I

C + I + G

C + I + G + NX = AE

Y=AE

Consumption

Planned
investment

Government
 purchases

Net exports

Equilibrium
real GDP

Macroeconomic Equilibrium: Decomposition of AE

Macroeconomic equilibrium occurs 
where the AE line crosses the 45° 
line. Slide each of the slider below 
to see how the equilibrium point 
change when MPC and the quantities 
of C, I, G, NX changes.

The quantities of planned investment, government purchases, 
and net exports are constant because we assumed that the 
variables they depend on are constant.

u = Vector((0, 0), (14, 0))
v = Vector((0, 0), (0, 12))
f(x) = If[0 ≤ x ≤ 12, x]
MPC = 0.4 (slider from 0.1 to 0.9, step 0.01)
C = 5.8 (slider from 0 to 10, step 0.1)
I = 1.8 (slider from 0 to 3, step 0.1)
G = 1.1 (slider from 0 to 3, step 0.1)
NX = 0.9 (slider from 0 to 3, step 0.1)
p(x) = If[0 ≤ x ≤ 14, ((-(x(y - C - I - G = (MPC * (x - 10))) / y(y - C - I - G = (MPC * (x - 10))))) * x) - z(y - C - I - G = (MPC * (x - 10))) / y(y - C - I - G = (MPC * (x - 10)))]
q(x) = If[0 ≤ x ≤ 14, ((-(x(y - C - I - G - NX = (MPC * (x - 10))) / y(y - C - I - G - NX = (MPC * (x - 10))))) * x) - z(y - C - I - G - NX = (MPC * (x - 10))) / y(y - C - I - G - NX = (MPC * (x - 10)))]
h(x) = If[0 ≤ x ≤ 14, ((-(x(y - C - I = (MPC * (x - 10))) / y(y - C - I = (MPC * (x - 10))))) * x) - z(y - C - I = (MPC * (x - 10))) / y(y - C - I = (MPC * (x - 10)))]
r(x) = If[0 ≤ x ≤ 14, ((-(x(y - C = (MPC * (x - 10))) / y(y - C = (MPC * (x - 10))))) * x) - z(y - C = (MPC * (x - 10))) / y(y - C = (MPC * (x - 10)))]
N_0 = Point(r)
N_1 = Point(h)
N_2 = Point(p)
N_3 = Point(q)
E = Intersect(f, q, (9.333333333333332, 9.333333333333332))
N_{12}: (x(E), 0)
a_1 = Segment(E, N_{12})
N_{11} = Point(q)
C_3: (x(E), 1)