4. Lak consumes only two goods, A and B. Her only source of income is gifts of these commodities om 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 F4 " 1 and B at the price F3 "' 2 . Lak'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. 4.1 Suppose that Lak's admirers give her 100 units of A and 200 units of B. What are Lak's gross demands and net demands for A?.And for B? 4.2 Suppose that before Lak has made any trades, the price of good B falls to 1, and the price of good A stays at 1. Does Lak's consumption of good B rise or fall? By how much? What happens to Lak's consumption of good A? 4.3 Suppose that before the price of good B fell, Lak 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? 4.4 Explain why her consumption is different depending on whether she was holding goods or money at the time of the price change