Consider an individual whose preferences are defifined over bundles of non

negative amounts of each of two commodities. Suppose that this individ

ual's preferences can be represented by a utility function U : R2+ R of

the form U (x1, x2) = ln (x1 + 1) + 2x2, where x1 denotes the individual's

consumption of commodity one, and x2 denotes the individual's consump

tion of commodity two. This individual is a price taker in both commodity

markets. The price of commodity one is p1 > 0, and the price of commodity

two is p2 > 0. This individual is endowed with an income of y > 0.

1. Does this individual have quasi-linear preferences? Justify your an

swer.

2. Are this individual's preferences locally non-satiated? Justify your

answer.

3. What is this individual's budget-constrained utility maximisation

problem?