Linus Piecewise Is an Expected Utility Maximizer

Essay

Linus Piecewise is an expected utility maximizer.There are two events, H and T, which each have probability 1/2.Linus's preferences over lotteries in which his wealth is h if event H happens and t if event T happens are representable by the utility function U(h, t)= u(h)/2 + u(t)/2.The function u takes the following form.For any x, u(x)= x if x < 100 and u(x)= 100 +x/2 if x is greater than or equal to 100.Draw a graph showing the indifference curves for Linus that pass through
a.the point (50, 0)
b.the point (50, 100)
c.the point (100, 100)
d.the point (150, 100)