Question
Modify the example of a two-commodity production economy given in Section 2.2.7 to allow the first consumer to have endowment $w_1=$ $(0,1)$.
Step 1
In the original example, the endowments of the two consumers were given as $w_1=(1,0)$ and $w_2=(0,1)$. We need to modify the endowment of the first consumer to be $w_1=(0,1)$. Show more…
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Consider an open economy with consumption matrix $$C=\left[\begin{array}{ll}\frac{1}{2} & 0 \\0 & 1\end{array}\right]$$ (a) Show that the economy can meet a demand of $d_{1}=2$ units from the first sector and $d_{2}=0$ units from the second sector, but it cannot meet a demand of $d_{1}=2$ units from the first sector and $d_{2}=1$ unit from the second sector. (b) Give both a mathematical and an economic explanation of the result in part (a).
Systems of Linear Equations and Matrices
Application: Leontief Input-Output Models
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