This question is designed to examine how we can utilize our basic theory without having an explicit indifference curve. Suppose Lia has an income of Y = $500 and only consumes two good: memory sticks (to store free economics papers she downloads from the library) and hardcover novels (which she refuses to check out from the library). Furthermore, let the price of memory sticks be PS = $25 and the price of hardcover novels be PN = $20.

1. (a)) Create a graph of Lias behaviour with the assumption that her utility is consistent with our normal assumptions (e.g. U/qi > 0 and 2U/qi2 < 0 for i = {S, N }) assuming Lias preferences would result in her purchasing 10 novels. What is the budget line? What is her real income in terms of memory sticks?

2. (b) Before Lia makes any purchases, the place she purchases books from offers the following deal: any additional books purchased after the first 10 will get a 25% discount. Use a revealed preferences argument to explain how we know Lia will be better off. Would this be true for all utility functions? Explain why or why not.

3. (c) Another seller of books makes the following offer: get a 25% discount on orders of the first 10 books. Create a graph of the new budget constraint. Explain how this would adjust Lias bundle with a reference to income and substitution effects (you do not have to give a specific bundle). Assume that both goods are normal.

4. (d) Could Lia be indifferent between the discount option in part (b) and (c)? Explain why or why not.