Borrowing\ Rate, i

Current\ Consumption

Future\ Consumption

No\ borrowing,\ no \ lending\ point\ (Endowment)

Optimal \ consumption\ point

Utility\ Curve

Budget\ Constraint

Note:Point\ A \ serves\ as \ the \ endowment\point,\ which\ could\ be\ moved.

The Permanant Income Theory

i = 0 (slider from 0 to 0.5, step 0.05)
A = (4.009265424942057, 0.9942133839041618)
B = Point(yAxis)
C = Intersect(xAxis, yAxis)
D = Point(xAxis)
a = Segment(C, B)
b = Segment(C, D)
f = If(0 ≤ x ≤ 10, -(1 + i) * x + y(A) + (1 + i) * x(A))
E = Point(f)
c = Line(E, A)
F = Intersect(c, a)
G = Intersect(c, b)
d = Segment(F, G)
H: (0.3 * (y(A) + (1 + i) * x(A)) / (1 + i), (1 - 0.3) * (y(A) + (1 + i) * x(A)))
k: x(H)^(0.3) * y(H)^(0.7)
g = If(0.3 < x < 4.5, (k / x^(0.3))^(1 / 0.7))
I = Point(g)