Consider the problem of a consumer who must choose between two types of goods, good 1 (x) and good 2 (y) 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(x, y) = 5 ln x + 3 ln y.

1. Write down the problem of the consumer.

2. Determine the optimal choice of good 1 and good 2, x* = x(p1, p2, m) and y* = y(p1, p2, m).

3. Find the optimal amounts of good 1 and good 2 the consumer will choose if p1 = 1, p2 = 3 and m = 10.