According toAhmed et al. [3], an inflation-unemployment model is given by Un+1 = Un−b(m−In), In+1 = In−(1−c)f (Un)+f (Un−b(m−In)), where f (U) = β1 +β2e−U, Un and In are measures of unemployment and inflation at time n, respectively, and

b, c, β1, and β2 are constants. Show that the system has a unique fixed point of period one at ln

−β2

β1

,m

.

Given that m = 2, β1 = −2.5, β2 = 20, and c = 0.18, show that the eigenvalues of the Jacobian matrix are given by

λ1,2 = 1 −

5b 4 ±

√25b2 − 40bc 4

.