# Talk:Input–output model

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## Untitled, Marked 2008-07-03

aaa I want to insert the equation $$X = \left[ {\matrix  {x_1 } \\ {x_2 } \\ {x_3 } \\ {x_4 } \\  \endmatrix } \right]\quad C = \left[ {\matrix {c_1 } \\ {c_2 } \\ {c_3 } \\ {c_4 } \\  \endmatrix } \right]\quad I = \left[ {\matrix 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\  \endmatrix } \right]\;A = \left[ {\matrix {a_{11} } & {} & {} & {a_{14} } \\ {} & {} & {} & {} \\ {} & {} & {} & {} \\ {a_{41} } & {} & {} & {a_{44} } \\  \endmatrix } \right] $$

but the software can't parse. dml 13:38, 9 Oct 2004 (UTC)

Yes they should be merged, but I suspect that in time both shall be supplanted with deeper more thorough entries.

MikelahrMike Lahr

Support merge JQ 23:06, 6 May 2006 (UTC)

## Table of Regional Flows

A) why is it empty, B) where is it referred to? Lycurgus (talk) 16:17, 3 July 2008 (UTC)

## title should be changed

title should be:

Input-output model (economics)

## Grave error in explanation of concept?

I was reading the following paragraph to try to get a grasp of the concept: Each row of the input-output matrix reports the monetary value of an industry's inputs and each column represents the value of an industry's outputs. Suppose there are three industries. Row 1 reports the value of inputs to Industry 1 from Industries 1, 2, and 3. Rows 2 and 3 do the same for those industries. Column 1 reports the value of outputs from Industry 1 to Industries 1, 2, and 3. Columns 2 and 3 do the same for the other industries.

Comparing that to my other source (a 10 page copy from a book with a chapter called "Foundations of Input-Output analysis", i don't know what the book is called but it looks like it's quite credible) the whole paragraph above seems to be opposite of what is correct.

Here is one example from the book:
X      1         2
1    0.15    0.25
2    0.20    0.05

And the text says: "To produce one dollar worth of goods from sector 2 one needs as interindustry ingredients 25cents worth of good 1 and 5cents worth of good 2."
I would translate that to: Column 2 reports the value of inputs to Industry 2 from Industries 1 and 2.
Opposite of what the paragraph in the wikipedia article says.

Can someone correct me or verify this? I'm new to this whole concept.

Mariux 17:50, 14 May 2007 (UTC)Marius

I agree regarding "Grave error"

Funny that we should stumble upon this at about the same time. I agree that the text in the first section is reversed. The proposed correction is: Row 1 reports the output from Industry 1 used as inputs in Industries 1, 2, and 3; that is, Row 1 describes the use of output from Industry 1 as an input in other industries. Column 1 reports the value of inputs to Industry 1 that were produced in Industries 1, 2, and 3; that is, Column 1 describes the use as inputs to Industry 1 of outputs from other industries.

I don't feel confident enough to make the change myself, but I hope that someone else will. (It's obviously pretty easy to get tripped up here.)

The table in the section Key Ideas is correct. Note that Labor, an input, has its own row and Final Demand an output, has its own column.

Michaelaoash 09:08, 23 May 2007 (UTC)

Is there a way we atleast could mark the passage with 'disputed' or something?
Mariux 17:56, 26 May 2007 (UTC)

not quite a "grave error", it is just definitional, what is a row and what is a column, what I think you are questioning, is arbitrary, and different expositions use different customs. Just as putting price on the Y-axis and quantity and the X-axis in economics is customary, but sometimes reversed. However the article should be internally consistent, so I reversed row and column in introduction as suggested. dml 18:03, 6 July 2007 (UTC)

## Style issues

1. The crucial concept of the Leontief coefficient aij is not explained. Is it the amount of input i needed for a unit of output j, or the other way round?

2. It is pretentious to refer to the Nobel Prize for Economics by its full legal title, which is given in the relevant Wikipedia page.

--JamesWim 17:18, 6 October 2007 (UTC)

The lower part (especially from Further_research) doesn't really read like an encyclopedia.

The part with additional vectors in Measuring input–output tables) is confusing; showing it in a table like above would make it clearer.

A remarkable single sentence (in Example): "... it might be challenging to actually compute the inverse matrix, given that some input–output tables are in excess of hundreds of sectors." Is this just very outdated (My cheap desktop computer can invert a 10,000x10,000 matrix in less than two minutes) or should that be "many thousands" instead of "hundreds"?

(I have read this page to get information and with few prior knowledge, so I can't fix it myself, sorry.) --149.148.63.51 (talk) 16:32, 29 July 2013 (UTC)

## Example mistake?

Perhaps I overlooked something in the text that could explain this, but the "example" problem for the article, contained in the Basic Derivation has the matrix of coefficients, A, an the vector of final demand, D. Yet, the output vector supposedly solved for in the example leads to absurdly low numbers of 1.9 for good A and 2.2 for good B. Even at face-value this is absurd as the outputs should be at least as large as the final demands, since you are taking the sum of required input for that commodity plus the final demand for it! Checking with the formula (I-A)X = D confirms that it must have been written wrong in the article.

The correct answers I got, inverting the (I-A) matrix and multiplying it by the demand vector would have the output vector at approx. (19.189 , 12.97) rather than the current (1.9 , 2.2).

If I am wrong please let me know but if I am not it would be good to see this changed. Thank you. 76.199.149.227 (talk) 01:36, 16 January 2013 (UTC)