Question

Problem 1. Do the following utility functions represent risk-averse, risk-neutral or risk-loving preferences? Motivate your answers. In each question, w is the wealth. (a) u(w)10w3 c) u(w)-e4 (d) u(w)-1- e

Answer 1

Given data, In the given data utility functions are their: we are calculating the values and note that the becoming answer 1. risk - averse (or) 2. risk - lover (or) 3. risk - preferences utility functions are: u(w) = 10w + 3 u(w) = w^3 + 3w u(w) = e^4w u(w) = 1 - e^-w Here: w = wealth u(w) = 10w + 3 Derivative on both side with respect to �w� partial differential u(w)/partial differential w = partial differential/partial differential (10w + 3) = 10(1) + 3(0) partial differential u(w)/partial differential w = 10 Second time derivative on both side partial differential^2 u(w)/partial differential w = partial differential/partial differential w (10) partial differential^2 u(w)/partial differential w = 0 therefore This utility function is risk - neutral. \r\n utility function: u(w) = w^3 + 3w Derivative on both side with respect to �w� partial differential u(w)/partial differential w = partial differential/partial differential w (w^3 + 3w) = 3w^2 + 3 Second derivative on both side partial differential^2 u(w)/partial differential w = partial differential/partial differential w (3w^2 + 3) 6w + 3(0) partial differential^2 u(w)/partial differential w