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There are two goods, Good 1 and Good 2, with positive prices p1 and p2. A...

There are two goods, Good 1 and Good 2, with positive prices p1 and p2. A consumer has the utility function U(x1, x2) = min{2x1, 5x2}, where “min” is the minimum function, and x1 and x2 are the amounts she consumes of Good 1 and Good 2. Her income is M > 0.

(a) What condition must be true of x1 and x2, in any utility-maximising bundle the consumer chooses? Your answer should be an equation involving (at least) these two variables.

(b) Use the answer to (a), along with the budget constraint, to calculate the consumer’s demand functions for both goods.

(c) Is Good 2 a normal good? Explain your answer.

(d) Are the goods complements, substitutes, or neither? Explain your answer.

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