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Exercises 1–4 refer to an economy that is divided into three sectors—manufacturing, agriculture, and services. For each unit of output, manufacturing requires .10 unit from other companies in that sector, .30 unit from agriculture, and .30 unit from services. For each unit of output, agriculture uses .20 unit of its own output, .60 unit from manufacturing, and .10 unit from services. For each unit of output, the services sector consumes .10 unit from services, .60 unit from manufacturing, but no agricultural products.Construct the consumption matrix for this economy, and determine what intermediate demands are created if agriculture plans to produce 100 units.

$\left[\begin{array}{c}{60} \\ {20} \\ {10}\end{array}\right]$

Algebra

Chapter 2

Matrix Algebra

Section 6

The Leontief Input–Output Model

Introduction to Matrices

Yohannis H.

March 5, 2021

The income vector of the economy referred in table above is given by the transpose vector [???????? ???????????? ????????????????] = [40 10 50] . Calculate the direct and indirect employment impact of (a) A unit change in agriculture (AGR) sector final de

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In this example, we have an economy that's been broken down into three different sectors. Manufacturing, agriculture and services. What we want to do then, is given the inputs purchased from these different sectors, determined the following. We want to determine what the construct consumption matrix will be in this situation, so call this a consumption matrix. It's equal to upper Casey. See is found by inserting columns C one, C two and C three, where each one of these columns are determined from this table we see here. So this column corresponds to see one then C two and C three, respectively. So the consumption matrix is going to be 0.10 point 30 0.30 from the four. The first column. The second column is 0.60 point 20 and 200.10 and the last column is 0.60 0.0 and then 0.10 So this is our consumption matrix coming from this table here. Next, let's determine the intermediate demands if agriculture plans to produce 100 units. So the idea here is we can take that matrix or column, whichever we prefer that corresponds to see to or the entire consumption matrix and multiply by either the right scaler or the right victor. If you decide to use, say, this column vector here, then the intermediate demands are going to be equal to 100 times C two, which is then 100 times 1000.6 so points to oh, and then 0.10 so this will result in intermediate demand vector 60 20 and 10. And this means we need 60 units for manufacturing, 20 units from agriculture and 10 units from services. If we're going to produce 100 units in agriculture, another method that you might prefer is to do the following. You can take here to find the intermediate demand. If we plan to produce 100 units, take the consumption matrix C and multiply it by the vector or replace a zero, then 100 in the second entry to correspond to agriculture on the second row and then zero. Multiplying in this way produces this, which gives us the same vector

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