A blue jay must decide whether it is worthwhile to leave her nest in search of food. Every time the blue jay leaves her nest to forage, there is an 80% chance she will successfully return with an acorn. However, every time the jay leaves to forage, there is a 1 in 10,000 chance that she will be eaten by a hawk. This blue jay's nest can hold between 1 and 10 acorns, and she computes the utility of possessing a certain number of acorns using the following formula:

Utility of X acorns = log(X) * 100

Because the blue jay does not like the idea of being eaten by a hawk, she assigns a very low utility (-200,000) to this outcome.

According to expected utility theory, how many acorns will the blue jay stockpile in her nest before she decides it is no longer worthwhile to go foraging?

Hint: Figure out expressions for the utility of foraging and the utility of staying in the nest, given that the nest contains a certain number of acorns. Then compare the utilities of each action assuming different numbers of acorns in the nest, starting with one and working upward.

Does this seems like a reasonable way for a bird to decide whether or not to go out and forage on a particular day? Why or why not?