Appendix

Algebraic model summary

Two classes of conditions characterize the competitive equilibrium: zero profit
conditions and market clearance conditions. The former class determines activity levels and
the latter determine price levels. In our algebraic exposition, the notation ∏^z_i is used to
denote the profit function of sector i where z is the name assigned to the associated production
activity. Differentiating the profit function with respect to input and output prices provides
compensated demand and supply coefficients (Shephard’s lemma), which appear
subsequently in the market clearance conditions. Table A1 explains the notations for variables
and parameters. Table A2 gives an overview of key elasticities and parameter specifications
For the sake of transparency, we do not write down the explicit functional forms but instead
use the acronyms CET (constant elasticity of transformation), CES (constant elasticity of
substitution), CD (Cobb-Douglas) and LT (Leontief) to indicate the class of functional form
in place.

Zero profit conditions

Aggregate output: ∏ Y = Pi -CES[PR,,LT(PAYj,I,PK,,PL)]=0 Vi e F

∏Y = P, -LT[PAY_j,N,PACru,,CES(PL,CES(PK,,PEi))] =0 Vi∈ V          (A1)

Energy aggregate: ∏ C = PEi- CES PACLE, CES ( PACOL, CES ( PAC_as , PAOIL )) = 0 V i ∈ V (A2)

Armington aggregate: ∏d_i = PAd - CES (Pi, PMi ) - P^co2aCO² = 0                      (A3)

Aggregate imports:       ∏M^,r = PMi - CES(PC,PFX) = 0                        (A4)

Investment:                 ∏ ^inv = PINV - LT ( PAC_ie1 )                             (A5)

Public demand:      ∏Z - PZ - CD (PA_βn , CES (PA^zZ_eβC )) - 0                     (A6)

Final demand:     ∏C = PC - CES(CD (PAC_ee ), CD (PAC_neN )) = 0                  (A7)

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