Exercise 6: Numerical methods

Imagine that a rancher would have an income of $80,000 if his county remains free from a cattle parasite but only $50,000 if the county is exposed to the parasite. Further imagine that a county program to limit the impact of exposure to the parasite would reduce his income to $76,000 if the county remains free of the parasite but increase it to $70,000 if the county is exposed to the parasite. Assume that there is a 60 percent chance of exposure to the parasite and that the rancher's utility is the natural logarithm of his income. What is the rancher's option price for the county program? (Set up the appropriate equation and solve through iterative guessing.)