def compute_optimal_quantities(c, tau):
"""
Compute the reservation wage, job finding rate and value functions of the
workers given c and tau.
"""
mcm = McCallModel(
alpha=alpha_q,
beta=beta,
gamma=gamma,
c=c - tau, # post tax compensation
sigma=sigma,
w_vec=w_vec - tau, # post tax wages
p_vec=p_vec)
w_bar, V, U = compute_reservation_wage(mcm, return_values=True)
lmda = gamma * np.sum(p_vec[w_vec - tau > w_bar])
return w_bar, lmda, V, U
"""
Plots reservation wage against the discount factor
"""
import numpy as np
import matplotlib.pyplot as plt
from mccall_bellman_iteration import McCallModel, solve_mccall_model
from compute_reservation_wage import compute_reservation_wage
grid_size = 25
beta_vals = np.linspace(0.8, 0.99, grid_size)
w_bar_vals = np.empty_like(beta_vals)
mcm = McCallModel()
fig, ax = plt.subplots()
for i, beta in enumerate(beta_vals):
mcm.beta = beta
w_bar = compute_reservation_wage(mcm)
w_bar_vals[i] = w_bar
ax.set_xlabel('discount factor')
ax.set_ylabel('reservation wage')
ax.set_xlim(beta_vals.min(), beta_vals.max())
txt = r'$\bar w$ as a function of $\beta$'
ax.plot(beta_vals, w_bar_vals, 'b-', lw=2, alpha=0.7, label=txt)
ax.legend(loc='upper left')
ax.grid()
