import numpy as np

from pyx import *

alpha, s, a = 0.5, 0.25, 7

kstar = ((s*a)**(1/(1 - alpha)))

def h(k):

return s * a * (k**alpha)

def plotcurve(X, Y, canv):

for i in range(len(X)-1):

canv.stroke(path.line(X[i], Y[i], X[i+1], Y[i+1]), [style.linewidth.Thick])

c = canvas.canvas()

upper = 6

# axes

c.stroke(path.line(0, 0, upper, 0), [deco.earrow(size=0.3)])

c.stroke(path.line(0, 0, 0, upper), [deco.earrow(size=0.3)])

# 45 degrees

c.stroke(path.line(0, 0, upper, upper), [style.linestyle.dashed])

# function curve

X = np.linspace(0, upper, 100)

Y = [h(x) for x in X]

plotcurve(X, Y, c)

# arrows

k = 0.5

for i in range(4):

c.stroke(path.line(k, k, k, h(k)),

[deco.earrow(size=0.15), style.linewidth.Thin])

c.stroke(path.line(k, h(k), h(k), h(k)),

[deco.earrow(size=0.15), style.linewidth.Thin])

c.stroke(path.line(k, 0, h(k), 0),

[deco.earrow(size=0.15), style.linewidth.THIN])

k = h(k)

k = 5.8

for i in range(3):

c.stroke(path.line(k, k, k, h(k)),

[deco.earrow(size=0.15), style.linewidth.Thin])

c.stroke(path.line(k, h(k), h(k), h(k)),

[deco.earrow(size=0.15), style.linewidth.Thin])

c.stroke(path.line(k, 0, h(k), 0),

[deco.earrow(size=0.15), style.linewidth.THIN])

k = h(k)

c.stroke(path.line(kstar, 0, kstar, kstar), [style.linestyle.dotted])

c.text(kstar, -0.5, r"k^*", [text.mathmode, text.size.normal])

c.text(upper*1.06, -0.5, r"k_t", [text.mathmode, text.size.normal])

c.text(-0.5, upper*1.06, r"k_{t+1}", [text.mathmode, text.size.normal])

c.writePDFfile("stable45deg")