(Solved): Cali consumes coffee and tea. The local bulk store has s special pricing policy for coffee: if you ...

Cali consumes coffee and tea. The local bulk store has s special pricing policy for coffee: if you buy \( x \) servings of coffee, you need to pay a price of \( 2 \sqrt{x} \) dollars per serving. The price of tea is always \( \$ 1 \) regardless of the quantities purchased. Cali derives utility from the caffeine content of the two goods. In particular, caffeine in one serving of coffee is three times as large as that in one serving (a) Let \( x \) denote her consumption of coffee and \( y \) denote her consumption of tea. Write down one example of Cali's utility function \( u(x, y) \). (5 Marks) (b) Suppose Cali has a budget of \( \$ 16 \). What is her optimal bundle? Draw a diagram of your solution, which should include her budget constraint, indifference curve and the optimal point. Clearly label all the intercepts. (10 Marks) (c) Suppose the price of coffee is \( a \sqrt{x} \) dollars per serving, the price of tea is \( b \) dollars per serving, and Cali's budget is \( m \) dollars. Derive Cali's demand functions \( x(a, b, m) \) and \( y(a, b, m) \). (5 Marks)