Show that risk neutrality [u(w) = w for all w] can be regarded as a limiting case of negative exponential utility asα → 0 by showingthatthere are monotone affine transforms of negative exponential utility that converges to w as α → 0.

Hint: Take an exact first-order Taylor series expansion of negative exponential utility, expanding in α around α = 0. Writing the expansion as c0 + c1α, show that −e−αw −c0

α

→ w as α → 0.