Belinda loves chocolate and always thinks that more of it is better than less. She would love to take piano lessons as well. However, she knows from her sister's experience that for the rst four hours of piano lessons her satisfaction level will steadily decline as compared to taking no lessons at all. After that every extra second of piano lessons will make her happier. 1. Graph at least three of Belinda's indifference curves in a way that is consistent with her preferences. Now assume that her love for chocolate is not as strong. After the sixth bar she gets satiated and her happiness would decline were she to consume more. 2. Graph at least three of Belinda's indifference curves in a way that is consistent with this new feature. 3. For each of the following three utility functions, decide whether it is possible that it represents Belinda's preferences in (1), in (2) or none. Explain why. Mm, 322) = 40 + 3.7;? 24ml + mg + 12% 0(331, m2) = 10 + 3.93% + 243:1 33% + 12% w(ml,x2) = 20 + 3.7;? 243:1 mg + 12% 4*. Consider the following bundles: x = (5,2) and y = (3, 2). Find a new bundle 2 that is a weighted average of x and y and use this bundle to show that preferences represented by u(m1,m2) and w(ml, 932) are not convex