) Charlie, a vegetarian, consumes apples and bananas. His utility function is u(x1 , x2 ) = x1 x2 . The price of apples is P1 , the price of bananas is P2 , and Charlie's income is M. (a) Write the equations for his budget constraint, and the tangency condition. [4 Points] (b) Find Charlie's demand functions for bananas and apples. [4 Points] (c) Explain these effects briefly in words, [6 Points] 1. Total Effect 2. Income Effect 3. Substitution Effect Now consider price of apple is P1 = 1$, the price of banana is P2 = 2$, and Charlie's income is M = 40$. The price of bananas suddenly falls to P2 = 1$. (d) Before the price change, what quantity of apples and bananas did Charlie consume? (Use demand functions you derived in part (b)) Draw Charlie's original budget line. Label his chosen consumption bundle on this budget line as "A". (Draw a big graph, since you will add more details to it in next parts) (e) Add the new budget line (after the price change) to your graph, label the new optimal bundle as point C. (f) If, after the price change, Charlie's income was adjusted so that with new prices he could exactly obtain the previous utility level, what would be his optimal bundle with this imaginary income level? Label this point on your graph as point B. Show the income effect, the substitution effect, and the total effect on the demand for bananas in your graph.