We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if it intersected some indifference curve twice?)

can u solve all questions below with step by step explanation?

The utility-maximizing bundle of x and x2may, in some instances, be found at a point of tangency between the budget line and an indifference curve. In other instances, the utility-maximizing bundle will be found at a corner point-that is, where the quantity consumed of one good is zero. For which types of indifference curves shown below will the utility-maximizing bundle definitely be found at a corner point? Choose one or more: A. B. "C. D.

Suppose that the only items you consume are bread and wine. If the price of bread were to increase tomorrow, and if simultaneously your income were to increase by just enough so that you were equally as happy tomorrow as today, what would happen to the level of your consumption of bread ? Illustrate your answer with indifference curves