Question

Suppose prices are given by p₁ = 2 and p₂ = 4. Which of the following consumption patterns are consistent with the assumption that the consumer chooses the consumption bundle that he prefers the most among those affordable if his preferences are non-satiated (“more-is-better”) and strictly convex?

(a) If m = 10, he consumes (2, 1). If m = 14, he consumes (3, 2).

(b) If m = 12, he consumes (2, 2). If m = 18, he consumes (1, 4).

(c) If m = 12, he consumes (2, 2). If m = 18, he consumes (1, 1).

(d) If m = 10, he consumes (1, 2). If m = 16, he consumes (2, 3)

Answer 1

Budget line equation is p1 x1 + p2 x2 less than or equal to m . Assumption that the consumer chooses the consumption bundle that he prefers the most among those affordable if his preferences are non-satiated and strictly convex. It means that the consumer consume the whole of his income in the consumption of two goods and the indifference curve lies on the budget line.

(a) When x1 = 2 and x2 = 1. Then total expenditure = (2)(2) + (4)(1) = 4+4 =8 . So, it is not consistent with the assumption.

(b) When x1 = 2 and x2 = 2. then total expenditure = (2)(2) + (4)(2) = 4+ 8 = 12 . And when x1= 1 and x2= 4 , then total ependiture = (2)(1) +(4)(4) = 2 + 16 = 18 . It is consistent with the assumptions.

(c) similarly, this is not consistent.

(d) It is consistent.