Question

Consider a consumer's preferences over consuming two goods that are represented by the following utility function:

U（x₁，x₂）= x₁^a x₂^1-α

0 < α < 1

x₁，x₂ ≥ 0

(a) Do her preferences satisfy monotonicity? (4 mark)

(b) Do her preferences exhibit diminishing marginal utility?

(c) Are her preferences convex? In other words, do her preferences exhibit diminishing marginal rate of substitution? (Hint: Find MRS and its rate of changes with respect to the good on the horizontal axis.)

(d) Use a monotonic transformation of this function; write down the new utility function and show how your answers to part (1)(2)(3) change.

(e) Suppose now that a subsistence level of good x₂ is provided to all consumers. Use the utility function in part (1)(2)(3), denote this minimum level of consumption by x₂, and show how your answers to part (1)(2)(3) change.

Answer 1