Carbon Taxes and Renewable Energy Subsidies: A Discussion About . . .
121
where the left-hand side of Eq. (13) is the labor productivity in the renewable sector
and the right-hand side is the productivity in the consumption good production.
The Design of Climate Policies
Learning the features of the best outcome is essential for the design of optimal policies. It describes the efficient use of alternative energy sources and reveals whether
there should be a transition to renewables. Perhaps, a mixture of different energy
sources is desirable.
The optimal design of climate policies emerges from comparing the market
outcome—that we observe in the real economy—with the best outcome.
The Market Outcome
This section lays out an economic environment equivalent to the environment
described in Section “The Best Outcome”, but from the perspective of a market
economy. In a market economy, oil reserves belong to private companies. There are
oil firms and renewable energy firms. Private firms make decisions to maximize their
profits. This profit obviously depends on the market price.
If there is a carbon tax, the profit will be net of the tax paid. For renewable energy
firms, the profit will depend on the price of renewable energy. Similarly, if there is a
subsidy, then the profit will include the subsidy.
Formally, we can think of a market economy where there are three production units
or “sectors” indexed by j = 0, 1, 2. Sector 0 corresponds to the final consumption
good sector, and the remaining two are the energy producers.
A representative firm operates the technology (6) that produces the final consumption good. The firm hires labor at a wage w t , rents capital from households at
rate r t and buys energy inputs from the energy sectors at relative prices p jt . The
problem of the firm is to choose the path of capital, employment and energy use,
{K t , N 0t , E 1t , E 2t }
∞
t=0 , to maximize discounted profits given by
0 =
∞
t=0
q
0
t [F ( S t , A 0t , N 0t , K 0t , E 0t ) − r t K t − w t N 0t −
2
j=1
p jt E jt ]
(14)
where q
0
t is the price of one unit of consumption in period t in terms of consumption
in period zero, and E t is defined in (2).
A representative firm in the oil sector ( j = 1) owns the oil stock and faces a perunit τ 1t on oil extraction. R 0 is the initial stock of oil. The problem of the firm is to
choose a path of oil extraction {R t }
∞
t=0 to maximize discounted profits given by
121
where the left-hand side of Eq. (13) is the labor productivity in the renewable sector
and the right-hand side is the productivity in the consumption good production.
The Design of Climate Policies
Learning the features of the best outcome is essential for the design of optimal policies. It describes the efficient use of alternative energy sources and reveals whether
there should be a transition to renewables. Perhaps, a mixture of different energy
sources is desirable.
The optimal design of climate policies emerges from comparing the market
outcome—that we observe in the real economy—with the best outcome.
The Market Outcome
This section lays out an economic environment equivalent to the environment
described in Section “The Best Outcome”, but from the perspective of a market
economy. In a market economy, oil reserves belong to private companies. There are
oil firms and renewable energy firms. Private firms make decisions to maximize their
profits. This profit obviously depends on the market price.
If there is a carbon tax, the profit will be net of the tax paid. For renewable energy
firms, the profit will depend on the price of renewable energy. Similarly, if there is a
subsidy, then the profit will include the subsidy.
Formally, we can think of a market economy where there are three production units
or “sectors” indexed by j = 0, 1, 2. Sector 0 corresponds to the final consumption
good sector, and the remaining two are the energy producers.
A representative firm operates the technology (6) that produces the final consumption good. The firm hires labor at a wage w t , rents capital from households at
rate r t and buys energy inputs from the energy sectors at relative prices p jt . The
problem of the firm is to choose the path of capital, employment and energy use,
{K t , N 0t , E 1t , E 2t }
∞
t=0 , to maximize discounted profits given by
0 =
∞
t=0
q
0
t [F ( S t , A 0t , N 0t , K 0t , E 0t ) − r t K t − w t N 0t −
2
j=1
p jt E jt ]
(14)
where q
0
t is the price of one unit of consumption in period t in terms of consumption
in period zero, and E t is defined in (2).
A representative firm in the oil sector ( j = 1) owns the oil stock and faces a perunit τ 1t on oil extraction. R 0 is the initial stock of oil. The problem of the firm is to
choose a path of oil extraction {R t }
∞
t=0 to maximize discounted profits given by