If a consumer exhibits strictly convex preferences for two goods, any consumption bundle f… — JAMB UTME

If a consumer exhibits strictly convex preferences for two goods, any consumption bundle formed by taking a strict convex combination (weighted average) of two distinct bundles located on the same indifference curve will yield a strictly higher level of utility than either of the original bundles.

Answer: Answer

Answer

The statement is true because strict convexity of preferences dictates that a weighted average (convex combination) of two distinct bundles providing identical utility yields a strictly higher level of utility.

Strict convexity of preferences reflects the principle that consumers prefer balanced combinations of goods over extreme allocations. Geometrically, connecting two distinct bundles on a strictly convex indifference curve creates a line segment whose interior points lie entirely above the curve, placing the consumer on a higher indifference curve with greater utility.

Step-by-Step Solution

Define the economic property of strict convexity of preferences.

Strict convexity states that for any two distinct bundles

A = (x_1, y_1)

and

B = (x_2, y_2)

where

A \sim B

, the weighted average bundle

C = \alpha A + (1-\alpha)B

for any

0 < \alpha < 1

satisfies

C \succ A \sim B

This formalizes the core theoretical axiom that consumers prefer balanced consumption of both goods rather than extreme specialization.

Analyze the geometric relationship between the line segment and the indifference curve.

Drawing a straight line segment between bundle

A

and bundle

B

on indifference curve

IC_1

places all interior points of the line segment in the region strictly above

IC_1

Because indifference curves are strictly convex (bowed inward toward the origin), any straight line connecting two points on the curve lies strictly to the northeast of the curve.

Relate the geometric position to utility level and Marginal Rate of Substitution (

MRS_{xy}

Any point situated strictly above

IC_1

lies on a higher indifference curve

IC_2

, indicating a higher utility level (

U(C) > U(A) = U(B)

Strict convexity guarantees a diminishing Marginal Rate of Substitution (

MRS_{xy} = -\frac{dY}{dX} = \frac{MU_x}{MU_y}

), which ensures the curve curves inward away from the chord connecting

A

and

B

Evaluate the truth value of the given statement.

The statement correctly describes the mathematical and economic implications of strict convexity.

The proposition matches the foundational definition of strictly convex preferences.

Key Concept

Strict Convexity of Preferences and Indifference Curves

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic