DEMAPP10¶
Monopolist's Effective Supply Function¶
In [1]:
from demos.setup import np, plt, demo
from compecon import BasisChebyshev, NLP, nodeunif
%matplotlib inline
Residual Function¶
In [2]:
def resid(c):
Q.c = c
q = Q(p)
return p + q / (-3.5 * p **(-4.5)) - np.sqrt(q) - q ** 2
Approximation structure¶
In [3]:
n, a, b = 21, 0.5, 2.5
Q = BasisChebyshev(n, a, b)
c0 = np.zeros(n)
c0[0] = 2
p = Q.nodes
Solve for effective supply function¶
In [4]:
monopoly = NLP(resid)
Q.c = monopoly.broyden(c0)
Setup plot¶
In [5]:
nplot = 1000
p = nodeunif(nplot, a, b)
rplot = resid(Q.c)
Plot effective supply¶
In [6]:
demo.figure("Monopolist's Effective Supply Curve", 'Quantity', 'Price')
plt.plot(Q(p), p)
plt.show()
Plot residual¶
In [7]:
demo.figure('Functional Equation Residual', 'Price', 'Residual')
plt.hlines(0, a, b, 'k', '--')
plt.plot(p, rplot)
plt.show()
