Given the Utility function, Budget constraint estimate maximum utility, Income and Substitution effect.

These customers n types of chocolate in quantities qit i = 1,..., n. His preferences are captured by the function where q, is the quantity consumed of chocolate of type z. Chocolate of type? Is of better quality and sold at a higher price than chocolate of type j if i > j. Are the following statements true or false? Briefly justify your answers.

(i) If Theo's total budget increases then he will spend a higher proportion of his budget on the highest quality of chocolate than he did before the increase.

Whatever Theo's budget, he will spend a higher share of his budget on the highest quality chocolate than on the lowest quality chocolate.