(Solved): The following problem refers to a closed Leontief model. Suppose the technology matrix for a closed ...

The following problem refers to a closed Leontief model. Suppose the technology matrix for a closed model of a simple economy is given by the following. \[ A=\left[\begin{array}{lll} \mathrm{P} & \mathrm{M} & \mathrm{H} \\ 0.5 & 0.1 & 0.8 \\ 0.1 & 0.3 & 0 \\ 0.4 & 0.6 & 0.2 \end{array}\right] \text { Products } \begin{array}{l} \text { Machinery } \\ \text { Households } \end{array} \] Find the gross productions for the industries. (Let \( H \) represent the number of household units produced, and give your answers in terms of \( \mathrm{H}_{\text {.) }} \) ) products X units machinery X units households units