In our Model (12.36) for the arms race, assume that an– bm < 0, so the rest point lies in a quadrant other than the first one in the phase plane. Sketch the lines dx/dt = 0 and dy/dt = 0 in the phase plane, and label them and their intercepts on the coordinate axes. Perform a graphical stability analysis to respond to the following:

a. Do any potential equilibrium levels for defense spending exist? List any such points and classify them as periodic, asymptotically stable, or unstable.

b. Pick at least four starting points in the first quadrant, and sketch their trajectories in the phase plane.

c. What outcome for defense spending is predicted by your graphical analysis?

d. From the point of view of Country 1, interpret qualitatively the outcome predicted by your graphical analysis in terms of the relative values of the parameters in Model (12.36)

Model 12.36