QUESTION TWO

An economy is based on three sectors, Energy (E), Manufacturing (M), and Service (S). Production of a Shilling's worth of Energy requires an input of Ksh.0.20 from the Energy sector and Ksh.0.50 from the Manufacturing sector and Ksh.0.3 from the Services . Production of a Shilling's worth of Manufacturing requires an input of Ksh.0.30 from the Energy sector and Ksh.0.20 from the Manufacturing sector and Ksh.0.5 from the Services. Production of a Shilling's worth of Services requires an input of Ksh.0.20 from the Energy sector and Ksh.0.30 from the Manufacturing sector and Ksh.0.5 from the Services. It is known that the current final demand D₁ for Energy, D₂ for Manufacturing and D₃for Service sector's output is Ksh.30billion for Agriculture, Ksh.10 billion for Manufacturing, and Ksh.20 billion for Services sector

a) From above information, set up following Matrices

i)Transaction Matrix, A

ii) External Demand Matrix, D

iii)Total Output Matrix X presenting total output X₁ for Energy, x₂ for Manufacturing and X₃ for Service

iv)The Leontief Technical Coefficient Matrix (I-A)^-1

b)Suppose the external demand matrix for Agriculture rose by 10%, that of Manufacturing went down by 20% and that of Services remained constant and using the Leontief Input-Output Model X=(I-A)^-1D, determine the total output from each sector to satisfy the new demand levels and hence distribute the each sectors' output amongst the users