def supply(self):
"""
>>> sp.var('p q', positive=True)
(p, q)
>>> f = Firm(q, p, q**2/1000., SFC=1000)
>>> f.supply()
Piecewise((0, p < 1000.0), (500.0*p, And(0 <= p, p >= 1000.0)))
>>> f = Firm(q, p, 10*q, SFC=0, FC=0)
>>> f.supply()
p - 10 == 0
"""
min_atc, min_atc_cond = self.min_atc_sfc()
supply, supply_cond = tools.maximize(self.earnings(), over=self.q)
if supply is None:
return sp.Eq(sp.diff(self.earnings(), self.q), 0)
return sp.Piecewise((0, sp.Lt(self.p, min_atc)),
(supply, sp.And(sp.Ge(self.p, min_atc),
supply_cond,
min_atc_cond)))
def supply(self):
"""
>>> sp.var('p q', positive=True)
(p, q)
>>> f = Firm(q, p, q**2/1000., SFC=1000)
>>> f.supply()
Piecewise((0, p < 1000.0), (500.0*p, And(0 <= p, p >= 1000.0)))
>>> f = Firm(q, p, 10*q, SFC=0, FC=0)
>>> f.supply()
p - 10 == 0
"""
min_atc, min_atc_cond = self.min_atc_sfc()
supply, supply_cond = tools.maximize(self.earnings(), over=self.q)
if supply is None:
return sp.Eq(sp.diff(self.earnings(), self.q), 0)
return sp.Piecewise(
(0, sp.Lt(self.p, min_atc)),
(supply, sp.And(sp.Ge(self.p, min_atc), supply_cond,
min_atc_cond)))
def demand(self, rational=True):
"""Compute the demand as the maximization of the utility function.
>>> sp.var('x p')
(x, p)
>>> cu = Consumer(x, p, benefit=tools.benefit_from_demand(x, p, 9/p - 1))
>>> sp.simplify(cu.benefit() - 9*sp.log(x + 1))
0
>>> cu.demand()
Piecewise((0, p < 0), ((-p + 9)/p, True))
>>> tau = sp.Symbol('tau')
>>> cu_rat = Consumer(x, p, benefit=2*sp.sqrt(x))
>>> cu_del = Consumer(x, p, benefit=2*sp.sqrt(x),
... decision_benefit=20*sp.sqrt(x),
... other=-(1+tau)*p*x)
>>> sp.solve(cu_del.demand(rational=False)-cu_rat.demand(), tau)
[-11, 9]
"""
maxima, condition = tools.maximize(self.utility(rational), over=self.x)
if maxima is None:
maxima = 0
return sp.Piecewise((0, sp.Lt(self.p, 0)), (maxima, condition),
(0, True))
def demand(self, rational=True):
"""Compute the demand as the maximization of the utility function.
>>> sp.var('x p')
(x, p)
>>> cu = Consumer(x, p, benefit=tools.benefit_from_demand(x, p, 9/p - 1))
>>> sp.simplify(cu.benefit() - 9*sp.log(x + 1))
0
>>> cu.demand()
Piecewise((0, p < 0), ((-p + 9)/p, True))
>>> tau = sp.Symbol('tau')
>>> cu_rat = Consumer(x, p, benefit=2*sp.sqrt(x))
>>> cu_del = Consumer(x, p, benefit=2*sp.sqrt(x),
... decision_benefit=20*sp.sqrt(x),
... other=-(1+tau)*p*x)
>>> sp.solve(cu_del.demand(rational=False)-cu_rat.demand(), tau)
[-11, 9]
"""
maxima, condition = tools.maximize(self.utility(rational), over=self.x)
if maxima is None:
maxima = 0
return sp.Piecewise((0, sp.Lt(self.p, 0)),
(maxima, condition),
(0, True))
