Question
2). An economy has three industries, farming, building and clothing. For every GH 1
of food produced, the farmer uses GH 0.20 , the builder uses GH 0.15 and the tailor
uses GH 0.5 . For every GH 1 worth of building, the builder uses GH 0.25 , the farmer
uses GH 0.20 and the tailor GH 0.10 . For every GH 1 worth of clothing, the tailor
uses GH 0.10 , the builder uses GH 0.20 and the farmer uses GH 0.15 . If the external
demand for food is GH 100 million, for building GH 200 million and for clothing GH
300 million. Find the total production for each industry using the Input-Output model.
of food produced, the farmer uses GH 0.20 , the builder uses GH 0.15 and the tailor
uses GH 0.5 . For every GH 1 worth of building, the builder uses GH 0.25 , the farmer
uses GH 0.20 and the tailor GH 0.10 . For every GH 1 worth of clothing, the tailor
uses GH 0.10 , the builder uses GH 0.20 and the farmer uses GH 0.15 . If the external
demand for food is GH 100 million, for building GH 200 million and for clothing GH
300 million. Find the total production for each industry using the Input-Output model.
Ask by Watkins George. in Ghana
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The total production for each industry is as follows:
- Building: approximately GH 483.87 million
- Clothing: approximately GH 532.26 million
- Food: approximately GH 548.39 million
Solution
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Mind Expander
To tackle this problem using the Input-Output model, we first need to establish the input-output table based on the information given.
Let’s denote the industries as follows:
- Farming:
- Building:
- Clothing:
We can summarize the input needs for each industry in the following matrix format where each entry shows the amount of one industry’s output consumed by the others:
Now, the external demand vector for the three industries is:
Next, we can express the total production vector as
Using the Input-Output model formula
Where
- Calculate the matrix
. - Solve for
.
Let’s conduct this step-by-step.
- The matrix
is taken from the input needs, hence:
So, we calculate
Thus,
- We now need to solve the matrix equation:
- This can be solved using various methods (e.g., substitution, elimination, matrix inversion).
After solving, you will find the production values for each industry (F, B, C).
To make this task easier, you could also use computational tools or a calculator designed for matrix equations!
