3. Suppose there exist n = 1000 firms that seek to gain access to a small niche market that is regulated. Suppose that one firm will obtain access and that will get that firm an additional R = $50,000 in profits. Each firm already receives $1 million in profits from other ventures.

a. Suppose the probability of winning the rents is linear in investment, each firm has an equal chance of winning and they are all risk-neutral. How much will each firm invest in rent-seeking? Are the rents fully dissipated?

b. Suppose instead that the probability of winning changes with the amount invested in rent-seeking, so that each firm's odds of gaining access are (n,I) = I1/2 /n. Is the probability of winning increasing or decreasing in investment? Are there diminishing returns to rent-seeking?

c. How much will each firm invest in rent-seeking? Are the rents fully dissipated, less than fully dissipated, or more than fully dissipated?