Eigen-Decomposition in Economic Input-Output Analysis
An economy is modeled with three sectors: Agriculture, Manufacturing, and Services. The flow of goods and services between these sectors is described by coefficients representing the fraction of each sector’s total output that is used as input by other sectors. The inter-sectoral coefficients are given as follows:\n\n* Agriculture (Sector 1) uses inputs from: 0.3 of […]
Population Model Stability via Eigenanalysis
A population is divided into two stages: juveniles and adults. The dynamics of the population are modeled by the following transition matrix: \(A = \begin{pmatrix} 0.7 & 0.3 \\ 0.4 & 0.6 \end{pmatrix}\). (a) Find the eigenvalues of \(A\) by solving the characteristic equation \(\det(A – \lambda I) = 0\). (b) Identify the dominant eigenvalue […]