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Brian considers coffee, denoted (x1), and energy drinks, denoted (x2), as perfect substitutes. In particular, he is always indifferent between having two cups of coffee or one energy drink, regardless of his previous consumption of energy drinks or coffee.
a) Write down a utility function u(x1, x2) that models Brian's preferences for coffee and energy drinks. (1 mark) Is this function unique? If yes, explain why. If not, provide an example of another utility function v(x1, x2) that expresses the same preferences as u(x1, x2).
b) Is MU1 constant and independent of the values of x1 and x2? If yes, prove your answer. If no, provide a counterexample.
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