With the search cost of $0.20 per draw from uniform distribution from $0 to $0.90 show that the risk neutral person is approximately indifferent between searching again and stopping if the current best draw is $0.30. To answer this question, it would help to address the following:
What is the probability that a draw is greater than $0.30?
What is the expected value of a draw that is greater than $0.30?
What is the probability that a draw is less than $0.30?
What is the expected value of a draw that is less than $0.30?
What is the expected gain from searching again?
What is the expected loss from searching again?