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Economics Linear Algebra: Demand and Production, Zero-Profit, Output Prices

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Consider an open Leontief system with three fixed-proportions production sectors. Assume that the vector of labour requirements is a^T_0 =(1,1,1), i.e. 1 unit of labour is needed to produce 1 unit of each output. The input-output matrix is

A=[ 0.3, 0, 0.4
0.6, 0.1, 0
0, 0.2, 0.5]

Assume that the wage rate is w=1 and call p^T = (p1, p2,p3) the vector of output prices.
a) Explain what an element a_ij of the matrix A represents.
b) If the consumer demand for outputs is c^T= (290 million, 580 million, 145 million), how much of each good must the economy produce?
c) Write down the firms' zero-profit conditions in matrix format.
d) What are the output prices?

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The expert examines the demand and productions for zero-profit and output prices.

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Each element in the matrix is the amount of a commodity required to produce one ...

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