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Consider the problem of a consumer who must choose between two types of goods, good 1...

Consider the problem of a consumer who must choose between two types of goods, good 1 (x1) and good 2 (x2) costing respectively p1 and p2 per unit. He is endowed with an income m and has a quasi-concave utility function u defined by u(x1, x2) = 5 ln x1 + 3 ln x2. 1. Write down the problem of the consumer. 1 mark 2. Determine the optimal choice of good 1 and good 2, x ∗ 1 = x1(p1, p2, m) and x ∗ 2 = x2(p1, p2, m). 3 marks 3. Find the optimal amounts of good 1 and good 2 the consumer will choose if p1 = 1, p2 = 3 and m = 10.

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