Let the inverse demand for a particular product be given by P = 250 − Q. The product is offered by two Cournot firms, each of which has a current marginal cost of $100. Both firms can invest a sum K to establish a research facility to develop a new process with lower marginal costs. The probability of success is ρ.

a. Assume that the new process is expected to have marginal costs of $70. Derive a relationship between K and ρ under which

i. neither firm establishes the research facility;

ii. only one firm establishes a research facility;

iii. both firms establish a research facility.

b. Can there be “too much” R&D? Illustrate your answers in a diagram with ρ on one axis and K on the other.

c. Now assume that the marginal costs of the new process are expected to be $40. How does this affect your answers to 1(a)?