Define and calculate the expected mitigation cost of a bioterrorism event to Country A.

Consider 2 different countries that face potential bioterrorism attacks, Country A and Country B. Let xa (xb) be the investment level by Country A (Country B) on preventative measures for bioterrorism (i.e. surveillance). Let C(xa) and C(xb) be the costs as functions of investment for Country A and Country B, respectively. In the case of a bioterrorism event suppose there are losses with the probability p(xa,xb) incurred by Country A (Country B) defined as potential mitigation costs Ra (Rb). Here the probability p(xa,xb) is a function of investment levels. State all assumptions.
a. Define and calculate the expected mitigation cost of a bioterrorism event to Country A.
b. Define the objective function of Country A to minimize bioterrorism costs (sum of investment costs and mitigation costs).
c. Derive the optimal level of investment for Country A?
d. Now consider both Country A and Country B’s joint investment decision to minimize bioterrorism costs. Specify the joint objective function.
e. Derive the optimal investment levels for Country A and Country B. Demonstrate the externality outcome of Country B potentially free riding on Country A (hint comparing this answer to part c). Explain.