Part I: Properties of Preferences 1. Prove that indifference curves cannot cross. 2. Explain the transitive property displayed by preferences using three consumption bundles: (X1, Y1). (X2, Y2), (X3, Y's) 3. On which indifference curve does the optimizing consumer consume? 4. Explain why indifference curves are convex. 5. What does the slope of the indifference curve represent? Part II: Indifference Curves 6. Goods X and Y are consumed as perfect complements (fixed proportions). 4 units of X are consumed with 3 units of Y. Sketch a few of the indifference curves for these two goods on the same set of axes. 7. Goods X and Y are consumed as perfect complements (fixed proportions). 1 unit of X are consumed with 2 units of Y. Sketch a few of the indifference curves for these two goods on the same set of axes. 8. X and Y are perfect substitutes. 2 X are worth 5 Y. Sketch a few of the indifference curves for these two goods on the same set of axes. 9. X and Y are perfect substitutes. 2 X are worth 1 Y. Sketch a few of the indifference curves for these two goods on the same set of axes. 10. Goods X and Y are consumed with diminishing marginal utility. Sketch a few of the indifference curves for these two goods on the same set of axes