Production of good one (energy) uses Cobb-Douglas technology, using capital K_E and labor L_E as inputs X_1=A_E K_E^(_E ) L_E^(1-_E ) (3) A_E is a fixed production function parameter (chosen to make the initial price of energy p=1 ) Labor L_E can be purchased at the market wage w Capital K_E can be purchased at the market price r, set up producer max profit using lagrange