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Ms Caffeine likes to enjoy coffee (C) and tea (T) according to this utility function: U (C
Ms Caffeine likes to enjoy coffee (C) and tea (T) according to this utility function:
U (C.T) = 3C+4T.
(1) If cups of coffee and tea sell for $3 each and she has $12 to spend, how many cups of each should she buy to maximize her utility?
(2) Would things change if the price of coffee fell to $2 per cup?
Expert Solution
(1) Ms. Caffeine has estimated that she gets 4 units of satisfaction, or utils, from each cup of tea she consumes. That's what the formula tells us. That means if she has $12 to spend, she will buy 4 cups of tea at $3 each, because tea makes her happier than coffee. She would get 4 units of happiness from each cup of tea, for a total of 16 utils for her $12. If she spent all her money on coffee, she could only buy 3 units of happiness for each $3 cup, or 12 utils in all. For that to change, either she would have to change her utility function because she's had enough tea, or the price of the goods would have to change.
(2) If the price of coffee went down to $2 per cup, then she could buy 3 utils of satisfaction or happiness for $2. If she spent all her money on coffee, she could buy 6 cups, which would give her 18 units of happiness or satisfaction. That would be more than the happiness she would get from the 4 cups of tea, so she would purchase that instead.
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