10. What is the mathematical condition for utility maximization (at the optimum)? What is the interpretation of this condition? What is the adjustment process if this condition does not hold? 11. In case of a price increase, what happens to the utility level of a consumer if the person is compensated in cash to be able to buy the original combination? Support your answer graphically. 12. What happens to the utility of a food stamp recipient--coupons entitling certain type of food items--if he/she is compensated with cash instead? Support your answer graphically. 13. a. Derive graphically the demand curve from the utility analysis. b. Show how an income change affects the demand curve. 14. Show graphically income and substitution effects graphically for a normal good. How will the result change if the good in question is an inferior good. 15. How would a volume discount on one of the goods affect individual's optimum combination (volume discount: the price goes down for the additional quantities if more than a certain quantity is purchased)? 16. What is the price elasticity of demand for average size one-bedroom apartments if the quantity demanded increases from 900 units to 1,100 units, as the rent decreases from 7,200 units to 6,800 units? Interpret the result. 17. Explain the relationship between the price elasticity of demand and the slope of the demand curve. 18. What would you expect the price elasticity for the following commodities and commodity pairs why? Refrigerators in Siberia versus in Tropics Public transportation in the USA. versus in Mexico Gasoline in one week versus gasoline in three-years Each rubber bands Cross-Atlantic air travel versus air travel from Boston to New York Heating oil in Winter versus in Summer