Edgeworth Box

[VictorFavela]

Where is this model used

Economics

What is this model

The edgeworth box is use in economics as a way to represent how distributions of resources can be better for certain parties. The graph is a box that represents the amount of resources available and then two parties are represented along their split of the two resources. By plotting their Indifference curves (curves that show where the trade off between both resources is negligible) for both parties finding where they converge points to the optimal distribution of resources.

How could this be applied to oil

The situation of having a set of resources which need to be divided seems common enough. Perhaps this could relate to how two nearby wells can share both frac fluid and land, or how given two wells expected production frac stages and length are distributed between the two. The most important aspect of this would be determining a resource that is shared among two wells.

Notes

Finding indifference curve will likely be the most complicated aspect of this method, in particular the two resources analyzed must have some quantifiable trade off between the two

[VictorFavela]

Edgeworth Box Notes

• An Edgeworth Box is a way of representing the distribution of two or more resources. The axis of the graph represent the entire space of resource distribution with the amount of resources given to both agents at any point is equal to (X,Y) and (X_max - X, Y_max - Y).
• Indifference Curves are then created for both agents, with one of them being rotated to match the axis.
• The Initial Endowment is the point at which the two agents begin before any trade.
• For any point on the graph it is either an Inefficient Exchange or an Efficient Exchange, also known as a Pareto Optimality. An Inefficient Exchange is any point where the slope of the Indifference Curve for both agents is not equal (in other words the Marginal Rate of Substitution (MRS) is not equal), meaning that there are still actions that can be taken to improve the utility of one agent while either improving or not affecting the utility of the other agent. These movement are called Pareto Improvements and will continue to exist until you reach a Pareto Optimality
• An Efficient Exchange (or Pareto Optimality) is a point where the slope of the two indifference curves is equal, meaning there are no possible Pareto Moves that can be made to increase either agents utility while not harming the others. The line of all Efficient Exchanges is called the Contract line.

Indifference Curves Notes

• An indifference curve is a line that can be drawn on a resource consumption graph that represents all points that are of equivalent utility to the current point. For any point on the graph there exist a curve of different combinations of X and Y resource that to the agent are equivalent and therefore there is no preference between them. Each indifference has a utility and the agent wants to maximize this by moving across indifference curves.
• The slope of a given indifference curve is called the Marginal Rate of Substitution (MRS)

[VictorFavela]

55

The initial testing for the edgeworth model is relatively complete. What I was able to do is both create indifference curves and an edgeworth diagram for the completion type of a well. This assumes that there are a limited number of stages of each completion type (Sleeve and P&P to be specific). The main correlation is found by creating an estimation function, I opted to fit an exponential function to the completion type for reasons stated in the notebook. The error has not been fully calculated for this section. I then was able to reverse this function to create a P&P function given a specific Sleeve count, this also has some error which is quantified in the notebook. Finally I created the graph using dummy data, in the future if this seems promising perhaps a feature should be implemented that allows for initial endowment to be added as well as a limited set of possibilities.

[SsanyaS14]

Review 1 By Sanya Srivastava, 1:30 pm, 06/09/2020

Overview Looking over the Edgeworth Box, I believe it is an excellent model; however, I noticed that some of the errors were a bit high, but compared to other models, it is the best model error we have. This gives more opportunity to better the model and thus have a lower error. Reading over some of the markdowns for the model, the extra testing, and the plan of attack on the hypotheses, I agree in terms of how the model is being structured and coded. However, looking through the notebook, I am not exactly sure how correlation was measured, I was getting a basic idea. Maybe having a longer explanation over the relationship of the graph directly would be beneficial.

Future Work The Extra testing that is set up could be helpful in as stated, specializing in one completion type to yield optimal results. However, I do wonder how it would be possible not to have a concern of one completion type and to mix the stages for the optimal. Additionally, for error, I like the mistake that was on the notebook but looked into the other python libraries for failure as MAE and RMSE, which could be helpful to a specific model.

Rankings Clear Definition - A Shown Correlation - B Shown Error - B Potential - A Excitement - A