Economics linear algebra-demand and production

Question

Questions:

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

1. Consider an open Leontief system with three fixed-proportions production sectors. Assume that the vector of labour requirements is a^T₀ =(1,1,1), i.e. 1 unit of labour is needed to produce 1 unit of each output. The input-output matrix is

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?