Ann views coffee and sugar as perfect complements. In particular, she always takes one cup of

coffee with 3/2 teaspoons of sugar. Let x1 denote the cups of coffee and x2 denote teaspoons

of sugar that Ann consumes.

a) Write down a utility function u(x1, x2) that models Ann's preferences for coffee and

sugar. (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). (1

mark)

b) Suppose that one unit of x1 (i.e. one cup of coffee) costs $1.5 and one unit of x2 (i.e. 1

tsp of sugar) costs $0.1. Ann spent $438.89 on coffee and sugar over a period of ten

months. During that period, how many cups of coffee and how many teaspoons of sugar

did she consume? (2 marks)

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c) Consider bundle A that contains one cup of coffee and no sugar, A = (xA1

, xA2

) = (1, 0).

Provide an economic explanation of the sign (i.e. positive, negative, zero) of MU1 at

bundle A as well as the sign of MU2 at bundle A. (2 marks)

d) Is MU1 constant and independent of the values of x1 and x2? If yes, prove your answer.

If no, provide a counterexample. (1 mark)