Topic: Uncertainty Diculty: 3% Correct Responses: 0 Discrimination Index: 012.3 Linus Piecewise is an expected utility maximizer. There are two events, H and T; whicheach have probability 1=2. Linus's preferences over lotteries in which his wealth is h if Event Hhappens 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 xis greater than or equal to 100. Draw a graph showing the indierence curves for Linus that passthrough a) the point (50; 0) b) the point (50; 100) c) the point (100; 100) d) the point (150; 100).Answer: Curve a is a line with slope ??1. Curve b has 3 linear segments: a line from(100; 50) to(50; 100); a line with slope ??2 to the left of (50; 100); and a line with slope ??1=2 to the right of(100; 50). Curve c has two segments: a line with slope ??2 going to the left and a line with slope??1=2 to the right of (100; 100). Curve d has 3 segments, a line from (150; 100) to (100; 150); and linesfrom (150; 100) to (200; 0) and from (0; 200) to (100; 150).