the-consumption-matrix-c-for-the-us-economy-in-1972-has-the-property-that-every-entry-in-the-matrix-

Name: the consumption matrix c for the us economy in 1972 has the property that every entry in the matrix
Uploaded: 2019-08-10
Duration: 4 min 18 s
Channel: Numerade
Description: The consumption matrix $C$ for the U.S. economy in 1972 has the property that every entry in the matrix $(I-C)^{-1}$ is nonzero (and positive). What does that say about the effect of raising the demand for the output of just one sector of the economy?

Question

The consumption matrix $C$ for the U.S. economy in 1972 has the property that every entry in the matrix $(I-C)^{-1}$ is nonzero (and positive). What does that say about the effect of raising the demand for the output of just one sector of the economy?

Gideon Idumah · Accepted Answer

not answer this question. Let&#x27;s go back to question. It&#x27;s B So we see that from it&#x27;s B. We saw that the first column off I might not see in verse gifts the Ramones, each sexo most produce to satisfy on increase in Yeah, your needs in the final demand from sick toe I no, from sector one, actually from sector One. Now look at this one that is here. Look at this first column. So that implies that&#x27;s this implies. That day I come on a J entry. Oh, I mindless See in verse gifts the Amman&#x27;s. I&#x27;m just writing these each sexo. It&#x27;s sick toe. I writes each of the sector I because the eyes in the rule, it said. So I must produce so satisfy on increase in one units in the final demand for all its foods from sector G. All right, so just going from question, it&#x27;s B. We can assert cities now. This implies that since so we&#x27;re giving that the entries. Since entries off, I mind a seat universe on non zero on deposits in use. This would imply that&#x27;s on increase in the final demand for the out sports off just one sec so off the economy well costs the production off all the other sectors to increase right because it&#x27;s positive. So when one increases every nothing also asked to increase said. Therefore, we can conclude those on increase in the demand four and this sector. So this is not answer to the question for any sector. We lied so on. Increase in the demands for all sectors, not statement, sir.

Michael Jacobsen · Answer

In this example, we are dealing with an economy that has the following consumption matrix C divide defined here as well as the demand vector d as here. What we like to do is to find out the production level which will call X given this matrix and this demand vector well, the first step is to four mount the model for this type of situation which is of the form X. The production level equals the intermediate demand, which is C Times X plus the final demand, which is deep Now if we rearrange this equation by subtracting, see extra bull sides, we have the equation I minus C times a vector X equals the demand vector d And then we know by our theorem in this section that this matrix is in vertebral. Since the column sums are both less than one. This then tells us that the solution will be X equals I minus C in verse times d. So let&#x27;s start off then in our solution by finding I minus c inverse here. So we&#x27;ll have I minus c is going to be first. I consist of just ones on the main diagonal, So we&#x27;re going to subtract one minus zero from the main Dagnall of sea to produce a one here and will have a negative 0.5 here, a negative 0.6. Then take one minus the point to, and we have a 0.8 altogether. But what we need here is its inverse. So let&#x27;s take the determinant of I minus C. It&#x27;s going to be the product of the main diagonal. So 0.8 subtract the product of the off diagonal, which is negative 0.6 times 0.5, resulting in a point 30 And we get all together that the determinant of this matrix is 300.5, which also tells us it is in vertical as we predicted. So let&#x27;s calculate its inverse Next I minus see in verse is going to be first take the main diagonal which is in purple and alternate it so point it goes here and 0.0.1 goes here. We&#x27;re going to then negates the off diagonal these entries here So we have a positive 0.6 a positive 0.5. Then divide by the determinant which is one over 10.5 Well, one over 10.5 results in two, so the inverse becomes 1.61 1.2 and there was an issue right here. This should have been a positive one or a point not 10.0.1, but just one itself multiplied by two and we get a two here. So this is our inverse matrix. This now tells us that the production level required to meet this demand vector will be X equals First, the inverse matrix of I minus C, which is 1.6 1.212 Multiply by the demand vector D, which says take 50 from the first sector, 30 from the second sector as the demand and multiply we see then that will require ah 110 units from the first sector of the economy and 120 units from the second sector and the solves our problem here.

Michael Jacobsen · Answer

in this example, we have a consumption matric see which provide is provided here and this is a seven by seven matrix of the United States economy as it was in 1958. So what we have here next is a particular demand factor. This vector D is given to be first 74,000 then 56,000. For the third sector of the economy, we have 10,500 for the fourth sector, we have 25,000. The next sector is 17,500. Next we have 196 100,000 and the final is 5000 from the seventh sector. So the units here are in millions of dollars. And the long Tom Fif model for this particular situation is of the form, see or rather, I minus c times the production Vector X, which is are unknown, which is equal to the demand vector d. So we consult this, but what we would need to do is form a new matrix, which is going to be C minus. I augmented with the demand vector d. This takes quite a while to compute such a matrix. Even if it&#x27;s just working out to this portion. Hope and it should be I minus c here. Not a C minus I, but putting this into a computer algebra system. We see that this is equal to this rather large matrix that we see here. So informing that matrix I took, I dont matrix that we see here we went to the main diagonal. It took one minus all of these entries. So, for example, in this entry, one mice 10.12 gives us the 0.9988 then the remainder entries in the and the consumption matrix C We just took the opposites. That&#x27;s why you see all these negative signs and that gives us I minus c. Then here we have a augmented with the vector d. What we need to do next is ro reduce this entire seven by eight matrix, but this is not something that should be done by humans. So let&#x27;s put this back into the computer algebra system and roll reduce. So, in my computer algebra system, I found that this matrix is row equivalent to this monstrosity we see below. But don&#x27;t forget that we have augmented. Oh, dear. That was a wrong matrix. It&#x27;s Rocca linked to this matrix we see displayed here. We have ones on the main Dagnall going this way, which tells us that our consumption matrix see when we for my my a c we did get a convertible matrix. Now this column here tells us that the production level X that&#x27;s required is X equals 99,575 0.7 and these are in units of millions of dollars from the first sector of the economy. Then it&#x27;s 97,000 703. 51,230 0.5 from the third sector, then 131,570 49,000 488 0.5, then 329,000 554. And lastly, 13,000 835.4 from the last sector of the economy. So this vector X is the production vector required, given the consumption matrix and the demand vector

Gideon Idumah · Answer

we have that g changes to D plus doubt the D No Wanna sure that&#x27;s our new production level Will be equal to X plus daughter bex No record of originally we have that&#x27;s X equal to see X plus d All right, so that implies dots. Our ex new should be recalled to see more supplied by ex New plus de new which is just see times X knew Plus, our Dinu is D close dots and deep So this is ex new When you bring this together you off I minus c turns ex new equal to deep plus dat&#x27;s de So that implies that X knew equal to ay minus c inverse So you multiply beside by the inverse You have to remember to put in brackets d plus delts and d So this is when you multiply each one of them off I&#x27;m minus See in verse More supply by D plus I minus c universe More supply by Delta D Now what is I might not see Eve us more sublime. I d recall. That&#x27;s from here. This is the symptom. Nas eggs According to I Oh, minus c inverse multiplied by D So this is just X writes Mrs X from here them plus I might not see ive us don&#x27;t d which I can write us eggs loss don&#x27;ts of X So this implies that&#x27;s what I mean is that Sam is the ex new equal to X Plus, don&#x27;t x Were those eggs he called Sue, I might know. See, each of us times don&#x27;t d So that&#x27;s him. Blood shows. That&#x27;s we&#x27;ve unsaid. Ah, question number E Now, for the question would be we told ads. We&#x27;re told that, um, let&#x27;s don&#x27;t debate the vessel with warm in its forced entry. So let&#x27;s suppose dosa dy oz Juan in forced entry on zero everywhere else else with. So that means my daughter d looks like something like this. I want to make an explanation for this. That&#x27;s not like 100 Everything else zero, right? Something like this. Now, recall that&#x27;s from here. Having my daughter eggs, he called to eye minus c invest darts a d that is from here. So that implies, nal. It&#x27;s our supposed that I mean is don&#x27;t us. I&#x27;m gonna see even something like Star Star. I&#x27;m just putting in a random figures here random figures, random fandom figures. And then I knew that my doubts are decent. Like 100 Any time you multiply these all you get is just the first because one who wants applied these zero multiplied. This column zero multiplied this column. So that implies that we have dads, says Dummies, the daughter ex. It would just be the first column off I minus sea divers forced colon off. I might not see universe by the virtue off the composition of Dr D.

Liuxi Sun · Answer

a negative of a matrix given Matrix is a matrix with the negative numbers of the of numbers that are opposite of the ones that are given. So if we, for example, ever given a matrix 1234 and we want to find a negative of The Matrix, we just take opposite of each value. Or actually, let&#x27;s do negative to example. So opposite of that one is negative. One opposite of negative two is positive to obstinately. Three of three is negatory. Opposite a positive four is Nick before? So if you look at these two, Major sees, you see that if you add them together, you get one plus negative one, which is zero negative two plus two, which is 03 plus number three here again and for plus negative for just zero. So night of of a Matrix, when added to the original matrix, is zero should give you a zero matrix

Ankit Gupta · Answer

the Matrix. A given to us is equal to zero minus 110 while the Matrix B, which represents the graphic alphabet A is given. US. 033 110 001155 So therefore, we need to calculate the product a being which will be equal toe zero minus one van zero multiplied with 0331 van zero on 001155 Which will be equal toe Zito zero minus one minus one minus five minus five zero 33 110 So, therefore, they changed Johns for mated graph for l will be having the coordinate 00 03 minus 13 minus 11 minus 51 on minus 50 So let&#x27;s see how the new L will look like since the given solution was for part A. So for part B from the given diagram off L on the graph, we can conclude that the product matrix a being rotates the original l anti clockwise throw 90 degrees

Problem

The Leontief production equation, $\mathbf{x}=C \…

Problem 10 Medium Difficulty

The consumption matrix $C$ for the U.S. economy in 1972 has the property that every entry in the matrix $(I-C)^{-1}$ is nonzero (and positive). What does that say about the effect of raising the demand for the output of just one sector of the economy?

Answer

if the demand in any sector increases, then the production in every sector will also increase.

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Grace H.

Catherine R.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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if the demand in any sector increases, then the production in every sector will also increase.

Linear Algebra and Its Applications

Grace H.

Catherine R.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Grace H.

Catherine R.

Kristen K.

Michael J.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications