How Can the Leontief Model Help Solve This Problem?

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SUMMARY

The discussion centers on the application of the Leontief model, specifically the equation \textbf{x} = C \textbf{x} + \textbf{d}, where d represents external demand and C is the inter-sector internal demand matrix. Participants are tasked with determining whether it is permissible for diagonal elements cii to exceed 1 and are required to provide both mathematical and real-world justifications for their conclusions. The consensus suggests that while theoretical understanding exists, practical implications of having cii > 1 remain unclear.

PREREQUISITES
  • Understanding of the Leontief model
  • Familiarity with matrix algebra
  • Knowledge of economic demand concepts
  • Ability to interpret mathematical models in real-world contexts
NEXT STEPS
  • Research the implications of diagonal dominance in matrices
  • Study the economic interpretations of the Leontief model
  • Examine case studies where cii > 1 occurs
  • Learn about alternative input-output models in economics
USEFUL FOR

Students of economics, researchers in input-output analysis, and professionals involved in economic modeling will benefit from this discussion.

charlies1902
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I attached the problem.

I honestly have no idea how to even go about solving this problem. If someone can give me a hint, that'd be great.
 

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charlies1902 said:
I attached the problem.

I honestly have no idea how to even go about solving this problem. If someone can give me a hint, that'd be great.

Start by understanding what the problem is saying. You have a Leontief model of the form
[tex]\textbf{x} = C \textbf{x} + \textbf{d},[/tex]
where d is external demand and C is the inter-sector internal demand matrix. The question is asking if it is OK to have cii > 1 for some i, and if not, why not.
It asks for both mathematical and real-world reasons.

RGV
 
Last edited:
I have read about the Leontief model but I still don't know how to answer the question. I think you should be able to have numbers greater than one along the diagnol
 

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