\begin{frame}{Oil and Gas Production }
	\begin{block}{Well Profitability 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 is attached to the well.
	\begin{block}{Well Profitability 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 a subsidy for oil production. 
The size of the subsidy depends on the path of the GOR, the discount rate, decline rate of the well, and the maximum willingness to pay for gas of Bitcoin miners.
\end{frame}
