%------------------------------------------------
\begin{frame}{Bitcoin Mining}
    \begin{columns}[t] % The "c" option specifies centered vertical alignment while the "t" option is used for top vertical alignment
        \column{.45\textwidth} % Left column and width
        \textbf{Rewards and Fees}
        \begin{enumerate}
	\item{Awarded by ``lottery''}
	\item{Lottery completes \(\approx \) every 10 minutes}
	\item{Risk pools smooth returns}
        \end{enumerate}

        \column{.5\textwidth} % Right column and width
        \textbf{Costs}
        \begin{enumerate}
	\item{Fixed cost: Specialized computers }
	\item{Marginal cost: Electricity}
        \end{enumerate}
    \end{columns}
    \mbox{}
    \newline
    \newline
    \textbf{Model of Single Period Returns}
    \newline
    \(Revenue=\text{Total Reward}\cdot \frac{\text{Tickets Owned}}{\text{All Tickets}}\)
    \newline
    \(Costs=\text{Electricity Used}\cdot\text{Price of Electricity}\)
    \newline
    \(\text{Tickets Owned}=f(\text{Computer Output},\text{Electricity Used})\)
    \newline
    \(\text{Total Reward}=\text{Mining Reward} + \text{User Fees}\)

    
\end{frame}

