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?
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- Is this a homework question?
– Giskard Jun 03 '15 at 05:15 -
- 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?
– Giskard Jun 03 '15 at 05:16 -
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. – Jamzy Jun 03 '15 at 05:35
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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. – Metta World Peace Jun 03 '15 at 07:11
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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 – economist Jun 03 '15 at 07:29
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Hi and welcome to economics.SE! I edited your question and removed the utility functions, as you don't need them to answer your question (as denesp already pointed out). @denesp doesn't look like a homework question to me. – The Almighty Bob Jun 03 '15 at 07:33
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@Jamzy I am pretty certain that this does not count as a math econ question. – The Almighty Bob Jun 03 '15 at 07:34
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@TheAlmightyBob OP says it is an assignment. – Giskard Jun 03 '15 at 07:52
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@denesp So I guess I was wrong ;-) To the topic: I can't answer the drawing part of the question (Mathematica can do it so I would check Wolfram Alpha, but I never tried), so this is just a comment: An "Edgeworth box" for one good is a projection from $\mathbb{R}^2$ (what player 1 and player 2 has) onto $\mathbb{R}$, for two goods it is from $\mathbb{R}^4$ to $\mathbb{R}^2$ and for three from $\mathbb{R}^6$ to $\mathbb{R}^3$, so your guess is correct. – The Almighty Bob Jun 03 '15 at 15:28
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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 $n = 3$.
NickJ
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6Drawing a $n$ dimensional Edgeworth box by hand might be pretty hard ;-) – The Almighty Bob Jun 03 '15 at 15:28
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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)
Anders
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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:
Manually draw it on paper although this will not help the visualization a lot.
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.
ExtremelySeriousChicken
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