\section{Results}
\subsection{Restoration Cost and Value}
The results from the \ac{NPV} model of the five observed mine operations find an average aquifer restoration costs of 15 million dollars per mine. This is equivalent to \$4.3 dollars per pound of uranium\footnote{When production is discounted bya rate of 10\% per year.}. This can be compared to the expected economic benefits of restoration to determine if the current rules balance costs and benefits of aquifer quality.

Ideally a hedonic model would be estimated that uses the sale price of the land affected by in situ mining. Unfortunately there is not enough data to complete a hedonic model of uranium in situ mines. 

%While hedonic models have been frequently applied in the context of surface water \citep{lansford1995,vasquez2013,poor2007,petrie2007} or groundwater access in agriculture \citep{hornbeck2014,gebben2024,stage2003}, only a few studies have evaluated the economic costs of groundwater water quality \citep{mukherjee2014,guignet2015}. These place estimates of the cost to decreased groundwater quality between 0.3\% of land price for a mild increases in salinity for farms, up to 15\% residents relying on groundwater with nitrogen over the \ac{EPA} drinking water standards
In lieu of a formal hedonic model, the average land value that overlays a identified uranium resource is calculated. The market value as reported by Wyoming county assessors averages \$239 per acre. This value is weighted by total acreage, so a single large ranching plot such as the one containing the Christen Ranch Mine is weighted higher than small home plots. The average leased area of a in situ project is 13,750 acres, making the median expected land value of the leased land 3.29 million dollars\footnote{The leased land is an over estimation of total affected land since much of a lease is used for exploration. For example, the Shirley Basin project has an area under pattern of 283 acres, but a lease area of 3,536 \citep{schiffer2023}}. Since the cost of aquifer restoration is 4.5 times larger than the entire expected land value it is not plausible that the current restoration rules are efficient.

Externalities were also considered. If the groundwater pollution spreads to nearby homes the restoration requirements can reduce social costs. However, the geochemistry of in situ mining, makes this scenario unlikely. The chemical process that bound the uranium to the produced sandstone, continues once the constituents flow from the mine zone. Geologic models of water flow from a in situ mine indicate that the flow occurs at around 1,000 feet over a hundred years, or half a mile in 400 years \citep{roshal2006}. Further with time the aquifer is restored naturally, and total dissolved solids are reduced \citep{borch2012,hu2011}. While casing leaks of uranium wells have occurred no pollution increases farther than a quarter mile away from a uranium mine has been identified by the \ac{NRC} \citep{leftwich2011,wright2013,nuclearregulatorycommission2014}.

Interestingly, two potential negative externalities were identified for the restoration process. After being treated the groundwater can be disposed of by surface irrigation. In one instance, water with elevated levels of selenium moved up the food change, increasing selenium levels in grass, grass hoppers, and finally to toxic levels in birds \citep{ramirez2002}. Second the sweeping of groundwater, lowers the aquifer which affects neighbors using groundwater. One rancher who leased his land to a uranium operation reported a decline of the water table at his nearby well of 100 ft \citep{lustgarten2012}. 

On the other hand uranium mining creates some positive externalities. First the exploration for uranium creates lower costs for other producers \citep{mason2014,mason1989,mason1985}. It can also identify aquifers that contain elevated levels of radon, which causes lung cancer as well as mental health problems in children \citep{taylor2024,chen2017c}. By exploring uranium rich regions, geologist help homeowners avoid and manage radon. 

%\begin{figure}
%\begin{subfigure}{0.4\textwidth}
%	\includegraphics[width=\textwidth]{./Images/Irigary1.png}
%    \caption{}
%    \label{fig:first}
%\end{subfigure}
%\hfill
%\begin{subfigure}{0.4\textwidth}
%	\includegraphics[width=\textwidth]{./Images/Irigary2.png}
%    \caption{Second subfigure.}
%    \label{fig:second}
%\end{subfigure}
%\end{figure}

\subsection{Uranium Supply Elasticity}
%The model predicts the total quantity of uranium concentrate produced in the U.S. each year. Uranium operations make decisions about expanding capacity in stages. First, existing projects respond to prices immediately, by increasing exploration rates and extraction at operating wells. Next, the exploration expenditures lead to new production wells. It takes time for the in situ wells to reach full capacity, so the response in uranium production caused by a uranium price shift is expected to occur over time. Further, operators factor in the available uranium inventories of nuclear power plants when making investment decisions. If uranium stockpiles are large, then powerplants will augment newly produced uranium with these reserves. 
The change in uranium production is estimated as a function of uranium price, using yearly lags in uranium production, a one-year lag of total uranium inventories, and a time trend. The time trend prevents a spurious regression that attributes correlated trends with casual changes to supply \citep{granger1998}. It also incorporates long run trends in mineral depletion due to extraction. Two lags in uranium production are included in the final model\footnote{This selection is based on the \ac{AIC} \citep{akaike1974}. Two lags minimize the \ac{AIC} score.}. One difficulty in estimating uranium supply is the possibility  of endogeneity.

An instrumental variable method is utilized. We apply the West Texas Intermediate price of oil as an instrument, following past literature \citep{kahouli2011,mason1985}. A change in the demand for energy will affect both the price of oil and uranium, but a change in the price of oil does not plausibly change the operating cost of uranium recovery operations. The estimate from these models is provided in \cref{REG}. 

\begin{table}[!htp]
	\centering
\caption{Uranium Supply Estimate}
\label{REG}
\includegraphics[width=0.7\textwidth]{./Images/UR_Supply_Reg_Table.png}
\end{table}

The results from \cref{REG} provide insights into the production decision of Wyoming operations. The effect on production over time matches the dynamics expected from uranium recovery operations. Based on model one, uranium companies can add to production in the same year that prices increase. However, the largest effect occurs two years following the price change, as exploration from the previous year leads to new production wells becoming operational. Finally, after three years existing production declines as resources are extracted. The previous years inventories levels reduce current production as an alternative source of mined uranium. 

Because the response of uranium production to price shocks is dynamic, the cumulative effect over time is provided in \cref{IMPACT}.  The value on the y axis is the percentage of a price increase that translates to production. For example, if a 1\% increase in uranium price expands production by 0.7\% this value is 70\%. 
\begin{table}[!htp]
	\centering
\caption{Dynamic Production Response to a Uranium Price Shocks}
\label{IMPACT}
\includegraphics[width=\textwidth]{./Images/Price_Shock.jpeg}
\end{table}
When an increase in uranium price occurs, uranium producers increase output with a peak extraction rate two years after the price change. A sustained 1\% increase in uranium price translates to a 0.66\% increase over the long term.   

 Recently, uranium prices have surged, going from \$35.65 per pound in 2020, to \$90 in 2024. The model estimates this will lead to a doubling of Wyoming uranium production, if these prices are sustained.
