Assume that a firm has invested in a project that, as long as it runs, generates a fixed flow of output P(t). Assume that P(t) follows a geometric Brownian motion

dP(t) = P(t)dt + P(t)dBt

where and are constants, and Bt is a standard Brownian motion. The cost to keep the factory running over a period dt is cdt. Assume that the firm can temporarily suspend production at a constant cost E and can restart it at a constant cost I, such that I > E > 0. Assume a constant discount rate r.

a. What is the value of the project to the firm before it invests in the project? What is the value of the project to the firm after it has invested? Give an interpretation of each of the terms in the value function.

b. Comparative static results on the thresholds PH and PL indicate that PH I > 0. and PL I < 0. Explain the intuition behind these results.

c. Explain the notion of hysteresis in the context of the impact of uncertainty on the optimal entry and exit thresholds.

d. Show that PL < PLM, where PLM is the Marshallian exit threshold and is given by PLM = c rE.