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csilvia
csilvia
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I have been reading the paper of Acemoglu et al., 2016 [Networks and the macroeconomy : an empirical exploration][1]Networks and the macroeconomy : an empirical exploration, and I have been struggling with a maximization programm in the early pages of the article. Even if I get the following parts, I am a bit frustrated I can't prove one of the first results.

The production function is :

enter image description here

With $x_{ij}$ the products of the firm $j$ treated as input for the output of the firm $i$.

My question is the following : What should I take as constraint for my Lagrangian function ? I am having difficulties seeing how the authors came to the (4) conclusion :

enter image description here

I think the constraints is given by the relation

enter image description here

But I must admit I am not sure about my result with these constraints.

Could anyone give me a tip about the constraints and how to proove the $(4)$ relation ?

I have been reading the paper of Acemoglu et al., 2016 [Networks and the macroeconomy : an empirical exploration][1], and I have been struggling with a maximization programm in the early pages of the article. Even if I get the following parts, I am a bit frustrated I can't prove one of the first results.

The production function is :

enter image description here

With $x_{ij}$ the products of the firm $j$ treated as input for the output of the firm $i$.

My question is the following : What should I take as constraint for my Lagrangian function ? I am having difficulties seeing how the authors came to the (4) conclusion :

enter image description here

I think the constraints is given by the relation

enter image description here

But I must admit I am not sure about my result with these constraints.

Could anyone give me a tip about the constraints and how to proove the $(4)$ relation ?

I have been reading the paper of Acemoglu et al., 2016 Networks and the macroeconomy : an empirical exploration, and I have been struggling with a maximization programm in the early pages of the article. Even if I get the following parts, I am a bit frustrated I can't prove one of the first results.

The production function is :

enter image description here

With $x_{ij}$ the products of the firm $j$ treated as input for the output of the firm $i$.

My question is the following : What should I take as constraint for my Lagrangian function ? I am having difficulties seeing how the authors came to the (4) conclusion :

enter image description here

I think the constraints is given by the relation

enter image description here

But I must admit I am not sure about my result with these constraints.

Could anyone give me a tip about the constraints and how to proove the $(4)$ relation ?

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PGCD
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Finding the constraints for a profit maximization program in Acemoglu et al, 2016

I have been reading the paper of Acemoglu et al., 2016 [Networks and the macroeconomy : an empirical exploration][1], and I have been struggling with a maximization programm in the early pages of the article. Even if I get the following parts, I am a bit frustrated I can't prove one of the first results.

The production function is :

enter image description here

With $x_{ij}$ the products of the firm $j$ treated as input for the output of the firm $i$.

My question is the following : What should I take as constraint for my Lagrangian function ? I am having difficulties seeing how the authors came to the (4) conclusion :

enter image description here

I think the constraints is given by the relation

enter image description here

But I must admit I am not sure about my result with these constraints.

Could anyone give me a tip about the constraints and how to proove the $(4)$ relation ?