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Equilibrium Value of the First Order Affine Difference Equation

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 Difference Equation Tutorial: Equilibrium of Affine Difference Equation produces Difference Equation Tutorial: Equilibrium of Affine Difference Equation . When Difference Equation Tutorial: Equilibrium of Affine Difference Equation , the equilibrium value is a constant, which is Difference Equation Tutorial: Equilibrium of Affine Difference Equation . When Difference Equation Tutorial: Equilibrium of Affine Difference Equation , however, Difference Equation Tutorial: Equilibrium of Affine Difference Equation has no solution (no equilibrium value) unless Difference Equation Tutorial: Equilibrium of Affine Difference Equation . If Difference Equation Tutorial: Equilibrium of Affine Difference Equation , there are infinite number of solution because any value of Difference Equation Tutorial: Equilibrium of Affine Difference Equation will do. Notice that the equilibrium value (unless Difference Equation Tutorial: Equilibrium of Affine Difference Equation ) does not dependent on the initial value, it only depends on the difference equation.

See: Numerical Example

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Preferable reference for this tutorial is

Teknomo, Kardi (2015) Difference Equation Tutorial. http:\\people.revoledu.com\kardi\ tutorial\DifferenceEquation\