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 hersister's experience that for the first four hours of piano lessons her satisfactionlevel will steadily decline as compared to taking no lessons at all. After thatevery extra second of piano lessons will make her happier.

1. Graph at least three of Belinda's indifference curves in a way that is consistentwith her preferences.Now assume that her love for chocolate is not as strong. After the sixth barshe 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 possiblethat it represents Belinda's preferences in (1), in (2) or none. Explain why.

u(x1, x2) = 40 + 3x21 - 24x1 + x22 + 12x2

v(x1, x2) = 10 + 3x21 + 24x1 - x22 + 12x2

w(x1, x2) = 20 + 3x21 - 24x1 - x22 + 12x2

4*. Consider the following bundles: x = (5, 2) and y = (3, 2). Find a newbundle z that is a weighted average of x and y and use this bundle to show thatpreferences represented by u(x1, x2) and w(x1, x2) are not convex.