Applications of Systems of Equations 415The results for initial arms expenditures which li e in region IV are similar
to the results for expenditures which lie in region II. A runaway arms race,
a stable arms race, or mutual disarmament may occur depending on where
(xo, Yo) lies within region IV.EXERCISES 10.1
- Perform an analysis for case 1 b. similar to the analysis performed in the
text for case la. What type of arms race results in this case? - Perform an analysis for case 2a. That is , perform an analysis for Richard-
son's arms race model when r < 0, s < 0 and the slope of line L 1 is
greater than the slope of L2 ( C /A > B / D). In what quadrant does the
equilibrium point (x*, y*) li e? How many distinct regions are there to
consider in the first quadrant? Draw an appropriate figure and construct
a table to aid you in performing your analysis. (Figure 10.3 includes an
appropriate figure and table for case 2b.) What kinds of arms races can
occur in this instance?- Perform an analysis for Richardson's arms race model for r > 0, s > 0
and
a. C /A > B / D (the slope of line L 1 is greater than the slope of line
L2.)b. C /A < B / D (the slope of line L1 is less than the slope of line L2.)
In each case, answer the following questions:
(i) Where is the equilibrium point?
(ii) What kinds of arms races can occur?4. Perform an analysis for Richardson's arms race model for r < 0, s > 0
anda. C/A > B/D and b. C/A < B/D.
Answer the following questions:
(i) Where is the equilibrium point?
(ii) What kinds of arms races can occur?- Using the results given in the text and the results of exercises 1-4
complete the following table by entering the type of arms race that
may occur in each case. (md =mutual disarmament, sar =stable arms
race, rar =runaway arms race)