def test_liquidity_constraint(self):
KinkyExample = KinkedRconsumerType()
KinkyExample.cycles = 0
# The consumer cannot borrow more than 0.4
# times their permanent income
KinkyExample.BoroCnstArt = -0.4
# Solve the consumer's problem
KinkyExample.solve()
self.assertAlmostEqual(
KinkyExample.solution[0].cFunc(1).tolist(), 0.9623337593984276
)
self.assertAlmostEqual(
KinkyExample.solution[0].cFunc(4).tolist(), 1.343766303734248
)
KinkyExample.BoroCnstArt = -0.2
KinkyExample.solve()
self.assertAlmostEqual(
KinkyExample.solution[0].cFunc(1).tolist(), 0.9346895908550565
)
self.assertAlmostEqual(
KinkyExample.solution[0].cFunc(4).tolist(), 1.3401428646781697
)
#
# (This example builds on the ConsIndShockModel notebook; digest that before proceeding)
#
# The $\texttt{KinkedRconsumerType}$ class solves the problem of a consumer for whom the interest rate on borrowing is higher than the rate that the consumer will receive on any positive saving they do. The default calibration is meant to capture a case where the borrowing occurs at an interest rate typical of credit cards.
#
# (Fuller discussion of the issues here can be found in [A Theory of the Consumption Function, With or Without Liquidity Constraints](http://econ.jhu.edu/people/ccarroll/ATheoryv3JEP.pdf))
# +
# Create an instance of the type of consumer we are interested in
KinkyExample = KinkedRconsumerType(**Params.init_kinked_R)
# Make the example infinite horizon (not a life cycle model)
KinkyExample.cycles = 0
# The consumer cannot borrow more than 0.4 times their permanent income
KinkyExample.BoroCnstArt = -0.4
# Solve the consumer's problem
KinkyExample.solve()
# Plot the results
plt.ylabel('Consumption c')
plt.xlabel('Market Resources m')
plotFuncs([KinkyExample.solution[0].cFunc], KinkyExample.solution[0].mNrmMin,
5)
# -
# 'Market Resources' $M$ is the total amount of money (assets plus current income) available to the consumer when the consumption decision is made. Lower case $m = M/P$ is the ratio of $M$ to permanent income. Likewise, $c = C/P$ is the ratio of consumption to permanent income.
#
# The line segment near $m=1$ captures the interval over which the consumer spends all of their market resources, because it's not worth it to borrow at the high credit card interest rate, but also not worth it to save at the low bank account interest rate.
#