Three separate labs consider engaging in R&D for developing an anti-laziness pill. The value of this discovery is estimated to be V = $520. If more than one firm discovers the cure, the firms equally share the prize ( 520/2 or 520/3 ). Each firm has a probability 3 4 of discovering the cure, provided that it invests an amount of I = $100 in constructing a research lab. If a firm does not invest, the probability of discovery is zero.

1. Find the expected profit of firm 1 assuming that only this firm engages in R&D.

2. Find the expected profit of firm 1 assuming that only firm 1 and firm 2 engage in R&D.

3. Find the expected profit of firm 1 assuming that all three firms engage in R&D.

4. Find the level of social welfare assuming that only one firm engages in R&D.

5. Find the level of social welfare assuming that two firms engage in R&D.

6. Find the level of social welfare assuming that all three firms engage in R&D.