Carbon Taxes and Renewable Energy Subsidies: A Discussion About . . .
119
The damage function x is increasing, concave and twice differentiable with lim S→ ¯
S x
(S) = 0, where ¯
S represents a lower bound on the atmospheric CO 2 concentration.
The amount of labor is exogenously given and can vary over time.
Individuals derive utility from consumption and leisure and discount the future
with the discount factor β ∈ (0, 1). Over time, individuals care about the value
∞
t=0
β
t
[u(C t ) − v(N t )].
(7)
The utility function u is increasing, concave and twice differentiable with lim c→0 u
(c) = ∞. The function v is increasing, convex and twice differentiable with lim N →0 v
(N ) = 0. Individuals consume and work.
The feasibility constraints in this economy are given by
C t + K t+1 = Y t
(8)
for every period t, together with
N t =
2
i=0
N it
(9)
K t =
2
i=0
K it
(10)
for every period t.
The Best Outcome
What is the best path to follow to solve the climate problem? Economics calls it “the
social optimum”. The social optimum is the level of output, consumption, energy
use and carbon dioxide that maximizes society’s welfare. In this model, consumption
increases social well-being, and work effort decreases it. In this sense, there exists a
climate problem because consumption comes from oil extraction, which is polluting.
The best for society is not to cut emissions to zero—it can eventually be if countries
do not implement climate policies soon enough. Instead, the best for society is to
pollute at the optimal level: the level of carbon emissions that maximizes social wellbeing. The restriction is that global consumption cannot exceed global production,
after taking into account the output loss from the climate externality.
Formally, the social optimum is the path {C t , N t , E t , S t }
∞
t=0 that maximizes (7)
subject to conditions (1)–(5) and (8)–(10).
119
The damage function x is increasing, concave and twice differentiable with lim S→ ¯
S x
(S) = 0, where ¯
S represents a lower bound on the atmospheric CO 2 concentration.
The amount of labor is exogenously given and can vary over time.
Individuals derive utility from consumption and leisure and discount the future
with the discount factor β ∈ (0, 1). Over time, individuals care about the value
∞
t=0
β
t
[u(C t ) − v(N t )].
(7)
The utility function u is increasing, concave and twice differentiable with lim c→0 u
(c) = ∞. The function v is increasing, convex and twice differentiable with lim N →0 v
(N ) = 0. Individuals consume and work.
The feasibility constraints in this economy are given by
C t + K t+1 = Y t
(8)
for every period t, together with
N t =
2
i=0
N it
(9)
K t =
2
i=0
K it
(10)
for every period t.
The Best Outcome
What is the best path to follow to solve the climate problem? Economics calls it “the
social optimum”. The social optimum is the level of output, consumption, energy
use and carbon dioxide that maximizes society’s welfare. In this model, consumption
increases social well-being, and work effort decreases it. In this sense, there exists a
climate problem because consumption comes from oil extraction, which is polluting.
The best for society is not to cut emissions to zero—it can eventually be if countries
do not implement climate policies soon enough. Instead, the best for society is to
pollute at the optimal level: the level of carbon emissions that maximizes social wellbeing. The restriction is that global consumption cannot exceed global production,
after taking into account the output loss from the climate externality.
Formally, the social optimum is the path {C t , N t , E t , S t }
∞
t=0 that maximizes (7)
subject to conditions (1)–(5) and (8)–(10).