1. Use axiom of transitivity to prove that indifference curves cannot touch each other.
2. Use axiom of non-satiation to prove that indifference curves will always be downward sloping and utility functions will always be upward sloping.
3. Use the axiom of diminishing marginal rate of substitution to prove that utility function will always be concave.
4. In a two commodity space (good 1 and good 2) graphically derive the demand curve of good 1 when good 1 and good 2 are perfect complements.
5. In a two commodity space (good 1 and good 2) graphically derive the demand curve of good 1 when good 1 and good 2 are perfect substitutes. .
6. Prove that inferior goods (goods with a negative income effect) have a backward bending income consumption curve.
7. Prove that giffen goods have a positively sloped demand curve and a backward bending price consumption curve.
8. Comment about substitution effect and income effect when price of good one alone decreases if the goods are perfect substitutes.
9. Comment about substitution effect and income effect when price of good one alone decreases if the goods are perfect complements.
10. Prove that compensated demand curve is always negatively sloped.
11. Use weak Axiom of Revealed Preference to illustrate that substitution effect is always negative.