Natural resource economics under the rule of Hotelling

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Substitution between biofuels and fossil fuels: is there a green paradox? (2012, background): “Proof: Using Lemma 1 and our speci cation of demand and supply as in (16) and (17), condition (13) is satis ed if and only if Z”
Hotelling under Pressure (2018, background): “rate, as in Switzer and Salant (1986). In our model, the constraint decays over time, shifting relentlessly toward zero whenever production occurs due to declining reservoir pressure.”