Equilibrium of Affine Difference Equation

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When k grows very large (approaching infinity), we called it long run condition. Equilibrium value is the long term solution of the difference equation. Equation (3 ) shows the equilibrium value of the first order affine difference equation. In the long run condition  produces . When , the equilibrium value is a constant, which is . When , however,  has no solution (no equilibrium value) unless . If , there are infinite number of solution because any value of will do. Notice that the equilibrium value (unless ) does not dependent on the initial value, it only depends on the difference equation.

See: Numerical Example

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