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Lucy consumes only two goods, A and B. Her only source of income is gifts of these commodities from her many admirers. She doesn't always get these goods in the proportions in which she wants to consume them, but she can always buy or sell A at the price, 33,; = l and B at the price, p3 = 2. Lucy's utility function is u(A, B) = db, where a is the amount of A she consumes and b is the amount of B she consumes. Answer the following questions. (a) Suppose Lucy's admirer gives her 100 units of A and 200 units of B. Draw her budget line. Label her initial endowment. (b) What are Lucy's gross demand for A? And for B? (c) What are Lucy's net demands for A and B? (d) Suppose that before Lucy has made any trades, the price of good B falls to $1, and the price of A stays the same. Draw her new budget line and label it. (e) Does Lucy's consumption of goods B rise or fall? By how much? What happens to Lucy's consumption of good A? (f) Suppose that before the price of good B fell, Lucy had exchanged all of her gifts for money, planning to money to buy her consumption bundle later. How much of good B will she choose to consume (after the price change)? How much of good A (after the price change)? (g) Explain why her consumption is different depending on whether she was holding goods or money at the time of the price change