Consider J symmetric firms operating in two periods with constant over time cost functions C^j (x _j, e _j) = (x_jb_je_j)²/2b_j, +c_jx²_j /2 The output prices are exogenous and given by p₁ and p₂ for the two periods. When relevant, emission caps are denoted by E̅₁and E̅₂ in periods 1 and 2, respectively.

(a) Assume that first period emissions are unconstrained. Consider an allocation scheme for the second period given by:

Determine the firms’ emission and output choices in the two periods, as well as the second period equilibrium permit price.

(b) For part (a), verify that the allocation is efficient if λ^e= E̅₂/E₁ and λx=0

(c) Determine the firms’ choice in period 1 when lx =

(d) Consider now an open trading scheme from the perspective of a particular jurisdiction that takes both output and emission prices as given and uses an allocation scheme

Determine the firms’ emission and output choices in the two periods for the cases when there is no emission cap in the first period and when there is a binding cap in the first period.

Transcribed Image Text:

= 8 ( xX; ) = + Ae + 2;x j = 1 2 = E