J 1

Gary was bitten by a tick. The probability of Lyme disease is 0.2. If Gary takes antibiotic X within a week, he will guarantee himself to be disease free. Antibiotic AA costs 30 dollars, and Gary will experience no adverse reactions from taking the antibiotic even if he does not actually have Lyme disease. If Gary does nothing, and he has Lyme disease, Gary will become sick and will need to have special treatment BB to eliminate the disease. Treatment BB costs 100 dollars.

Jane tells Gary he has one additional option: he can take the over-the-counter test CC today, before deciding. Test CC is not perfect: the false positive probability for test CC is 0.3, and the false negative probability is 0.1. Gary is risk neutral and wishes to minimize expected cost.

How much is Gary willing to spend for test CC? Explain.