Consider the set of lotteries with three possible payoffs fixed at x1=1,x2=3, and x3=5. Suppose an individual has a Bernoulli utility function of u(x)=x2. (a) Derive the equation of the fair gamble (iso expected value line) passing through the origin of the isosceles triangle representation. Find and plot the gamble on this line that is on the hypotenuse of the triangle. Label it A. (b) Derive the equation of the indifference curve passing through the origin. Find and plot the gamble on this line that is on the hypotenuse of the triangle. Label it A. (c) Which gamble does our individual prefer, A or A ? (d) Plot the following gamble B={0.5,0.25,0.25}. Which gamble does our individual prefer, A or B? (e) How do your answers to (c) and (d) indicate whether this individual is risk averse, risk neutral, or risk inclined? Consider the set of lotteries with three possible payoffs fixed at x1=1,x2=3, and x3=5. Suppose an individual has a Bernoulli utility function of u(x)=x2. (a) Derive the equation of the fair gamble (iso expected value line) passing through the origin of the isosceles triangle representation. Find and plot the gamble on this line that is on the hypotenuse of the triangle. Label it A. (b) Derive the equation of the indifference curve passing through the origin. Find and plot the gamble on this line that is on the hypotenuse of the triangle. Label it A. (c) Which gamble does our individual prefer, A or A ? (d) Plot the following gamble B={0.5,0.25,0.25}. Which gamble does our individual prefer, A or B? (e) How do your answers to (c) and (d) indicate whether this individual is risk averse, risk neutral, or risk inclined