I cannot think of an answer to this question from the chapter on elasticity in Tyler Cowen and Alex Tabarrok's Modern Principles of Economics, Second Edition:
How might elasticities explain why people on vacation tend to spend more on food and necessities than the local population?
I am assuming Cowen and Tabarrok want me to say, "Vacationers' demand for food and necessities is more inelastic." I don't know why this should be true. For a given change in the price of food, the quantity demanded would barely budge for both vacationers and locals (there are, after all, no substitutes for it).
I first thought vacationers want food of just one kind, i.e., food commonly found in the place they came from, but this doesn't explain why the demand for necessities should be inelastic.