# How can I draw an edgeworth box with 3 different goods?

If there are 3 types of goods(x,y,z) and 2 consumers (a,b) how can I draw the Edgeworth box? It must be 3 dimensional, right?

Is there a software or online tool that I can use to draw a 3D Edgeworth box?

• 1. Is this a homework question? Jun 3 '15 at 5:15
• 2. What exactly do you want to draw? Utility functions are not needed to draw the box itself. Do you also need to draw the contract curve? Jun 3 '15 at 5:16
• Is this a mathematical economics question? I know there has been some discussion about it in the meta. I read this question as how to define the space in $R^3$ that satisfies the constraints that all of $x, y, z \geq 0$ and the utility function. An edgeworth box is just a visualisation of that space. Jun 3 '15 at 5:35
• I think a lot of software can plot it, e.g. Maple, and Latex. As to online tools, there're a lot online Latex website you can use for free. Jun 3 '15 at 7:11
• This is an assignmet I'm working on. I need to draw an edgeworth box and find all pareto efficient allocations. A contract curve would help clarify my thought Jun 3 '15 at 7:29

I assume what you're asking based on your comments is: "How can I visualize indifference curves for 3 goods?" I can think of three options:

1) Use a tool like Matlab, or its open-source equivalent, Octave, to plot 3 dimensional indifference curves. Here is a tutorial on how to do that.

2) Make a series of 2-dimensional indifference curves for two of the goods, and fix a different level of the third good for each one, that is, plot a series of cross-sections of the 3 dimensional box.

3) Using paper and pencil, draw a general $n$ dimensional Edgeworth box, then, set $n = 3$.

• Drawing a $n$ dimensional Edgeworth box by hand might be pretty hard ;-) Jun 3 '15 at 15:28

I have had luck making 3-D plots with R and Plotly: https://www.youtube.com/watch?v=SBj-M_WyyoM

Although as others mention, it would be very difficult to visualize 3 goods on a 3-D contour plot (essentially 4 dimensions, 3 goods and utility)

Yea. If you have n number of goods and you would like to visualize it, you should use n-dimension of graph. Therefore, in your case, it is three dimensional. In terms of visualizing it, you can:

1. Manually draw it on paper although this will not help the visualization a lot.

2. If you are looking for software, I think that any software that can help you visualize a graph using certain set function can help you. For me, I personally will go for Matematica, but there are other programs like Matlab, which are also fine. Just look for programs that can get certain mathematics function and project it into a 3D graph.