\begin{frame}{Oil and Gas Production }
	\begin{block}{Well Profitablity Before Bitcoin Mining}
		\begin{equation}
			\pi_{w}=\int_{t=0}^{\infty}\left[e^{-rt}\left(P_{o,t}\cdot q_{o,t}+\theta_{GL}\cdot P_{g,t}\cdot q_{g,t}-C(t)\right)\right]dt
	\end{equation}
\end{block}
Where \(P{t} \) is price of the oil (o) or gas (g) at time t,  \(q_{t}\) is the volume of the product produced, C(t) is the cost function, and \(\theta_{GL}\) is a dummy that is one if a gas hookup line attached to the well.
	\begin{block}{Well Profitablity Post Bitcoin Mining}
		\begin{equation}
			\pi_{w}=\int_{t=0}^{\infty}\left[e^{-rt}\left(P_{o,t}\cdot q_{o,t}+(\theta_{GL}\cdot P_{g,t}+\bm{\right|\theta_{GL}-1\left|\cdot P_{g,btc}})\cdot q_{g,t}-C(t)\right)\right]dt
	\end{equation}
\end{block}

Allowing a Bitcoin miner to purchase gas is equivalent to subsidy to oil production. 
The size of the subsidy depends on the path of the GOR, the discount rate, decline rate of the well , and the max willingness to pay for gas of Bitcoin miners.
\end{frame}
