Lucetta 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 pA = 1 and B at the price pB = 2. Lucetta’s utility function is U(a, b) = ab, where a is the amount of A she consumes and b is the amount of B she consumes.
(a) Suppose that Lucetta’s admirers give her 100 units of A and 200 units of B. In the graph below, use red ink to draw her budget line. Label her initial endowment E.
(b) What are Lucetta’s gross demands for A? _______. And for
B? _______.
(c) What are Lucetta’s net demands?
(d) Suppose that before Lucetta has made any trades, the price of good
B falls to 1, and the price of good A stays at 1. Draw Lucetta’s budget line at these prices on your graph, using blue ink.
(e) Does Lucetta’s consumption of good B rise or fall? It rises. By how much? 25 units. What happens to Lucetta’s consumption of good A?
(f) Suppose that before the price of good B fell, Lucetta had exchanged all of her gifts for money, planning to use the money to buy her consumption bundle later. How much of good B will she choose to consume? _______. How much of good A? _______.
(g) Explain why her consumption is different depending on whether she was holding goods or money at the time of the price change.