CompEcon Toolbox:
DemApp10
Monopolist's Effective Supply Function
Randall Romero Aguilar, PhD

This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.

Last updated: 2020-Sep-09

In [ ]:
if 'google.colab' in str(get_ipython()):
print("This notebook is running on Google Colab. Installing the compecon package.")
!pip install compecon

In [ ]:
import numpy as np
import matplotlib.pyplot as plt
from compecon import BasisChebyshev, NLP, demo


### Residual Function¶

In [ ]:
def resid(c):
Q.c = c
q = Q(p)
marginal_income = p + q / (-3.5 * p **(-4.5))
marginal_cost = np.sqrt(q) + q ** 2
return  marginal_income - marginal_cost


### Approximation structure¶

In [ ]:
n, a, b = 21, 0.5, 2.5
Q = BasisChebyshev(n, a, b)
c0 = np.zeros(n)
c0 = 2
p = Q.nodes


### Solve for effective supply function¶

In [ ]:
monopoly = NLP(resid)
Q.c = monopoly.broyden(c0)


### Plot effective supply¶

In [ ]:
nplot = 1000
p = np.linspace(a, b, nplot)
rplot = resid(Q.c)

In [ ]:
fig1, ax = plt.subplots()
ax.set(title="Monopolist's Effective Supply Curve",
xlabel='Quantity',
ylabel='Price')
ax.plot(Q(p), p);


### Plot residual¶

In [ ]:
fig2, ax = plt.subplots()
ax.set(title='Functional Equation Residual',
xlabel='Price',
ylabel='Residual')
ax.hlines(0, a, b, 'k', '--')
ax.plot(p, rplot);


### Save all figures to disc¶

In [ ]:
#demo.savefig([fig1, fig2], name='demapp10')