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Preface

First, install CFEDemand package if necessary:

!pip install CFEDemands --upgrade

Compensated Policy Experiments

Compare Marshallian (uncompensated) and Hicksian (compensated) demands:

from costs_preface import *

#USE_GOOD = 'Rice'
USE_GOOD = 'Milk'

U0 = r.indirect_utility(x0,p)

plt.plot([r.demands(x0,my_prices(p0,i=USE_GOOD))[USE_GOOD] for p0 in P],P)
plt.plot([r.demands(U0,my_prices(p0,i=USE_GOOD),type="Hicksian")[USE_GOOD] for p0 in P],P)
plt.ylabel('Price')
plt.xlabel(USE_GOOD)
plt.axhline(p.sel(i=USE_GOOD).values)
plt.legend(("Marshallian","Hicksian"))

Define some useful functions for measuring costs:

def compensating_variation(U0,p0,p1):
    x0 = r.expenditure(U0,p0)
    x1 = r.expenditure(U0,p1)

    return x1-x0

def revenue(U0,p0,p1,type='Marshallian'):
    """(Un)Compensated revenue from taxes changing vector of prices from p0 to p1.

    Note that this is only for *demand* side (i.e., if supply perfectly elastic).
    """
    
    dp = p1 - p0 # Change in prices

    return [email protected](U0,p1,type=type)


def deadweight_loss(U0,p0,p1):
    """
    Deadweight loss of tax/subsidy scheme creating wedge in prices from p0 to p1.

    Note that this is only for *demand* side (i.e., if supply perfectly elastic).
    """
    cv = compensating_variation(U0,p0,p1)

    return revenue(U0,p0,p1,type='Hicksian') - cv
    
    
def compensated_nutrient_demand(U,p,z=None):
    c = r.demands(U,p,z=z,type='Hicksian')
    fct0,c0 = fct.align(c,axis=0,join='inner')
    N = fct0.T@c0

    return N

def compensated_nutrient_adequacy_ratio(U,p):
    return compensated_nutrient_demand(U,p)/hh_rda


fig,ax2 = plt.subplots()
ax2.set_ylabel('log NAR')
ax2.plot(P,[np.log(compensated_nutrient_adequacy_ratio(U0,my_prices(p0))[UseNutrients]) for p0 in P])
ax2.legend(UseNutrients)
ax2.axhline(0)
ax2.set_xlabel("Price of %s" % USE_GOOD)

fig, ax1 = plt.subplots()

ax1.plot(P,[compensating_variation(U0,p,my_prices(p0)) for p0 in P])
ax1.set_xlabel("Price of %s" % USE_GOOD)
ax1.set_ylabel("Compensating Variation")

ax1.plot(P,[revenue(U0,p,my_prices(p0)) for p0 in P],'k')
ax1.legend(('Compensating Variation','Revenue'))
ax1.axhline(0)
ax1.axvline(p.loc[USE_GOOD])